CH19_ThorwarthS

=** Lab: Equipotential Surfaces **= toc
 * Purpose: ** To find the relationship between electric field lines and equipotentials.


 * Hypothesis: ** As we measure points that are farther away from the source charge the electric potential energy will get weaker. When there is a negative source charge the electric potential energy will decrease as we measure closer to this negative charge.


 * Procedure: **

1) 1. Select a sheet with silver conductive lines drawn on it. Use a conductive ink pen to draw one of the given shapes. 2) Place the sheet on the cork pad. Place one metal pin through each of the two painted silver points on the conducting paper. 3) Insert black probe in to COM socket of the voltmeter (VOM) and insert red probe into other Voltmeter socket. Then, set selector to 20V. 4) Set power supply to 20V. Test power supply with VOM to make sure that it is working. 5) Attach one lead wire from the power supply to one metal pin, then attach another wire from the other clip of the power supply to the second metal pin on the corkboard. 6) Attach the black COM wire from the voltmeter to one of the pins. 7) Create a numbered grid in Excel using the conducting sheet as a reference. 8) You will only do points 5 to 15 on the vertical axis, and 5 to 20 on the horizontal axis. 9) Touch the red wire from the voltmeter gently to point (5,5). Use the first number that appears on the voltmeter. Enter your data directly into Excel. Move to the next point (5,6). Repeat for all points until you reach (15, 20). 10)Repeat for the other designs.


 * Materials:**

|| Volt meter (VOM)
 * Alligator leads (2) || Metal push pins (2) ||
 * Cork board || Power supply || Silver marker ||


 * Data (provided by AP Physics period 8):**

**Charge of points in a dipolar system (Volts)** x-coordinates --> y-coordinates (going down)

10.34 || **__ 7 __** 10.78 || **__ 8 __** 11.03 || **__ 9 __** 10.79 || **__ 10 __** 10.61 || **__ 11 __** 9.68 || **__ 12 __** 9.79 || **__ 13 __** 9.64 || **__ 14 __** 9.16 || **__ 15 __** 8.46 || **__ 16 __** 7.83 || **__ 17 __** 7.68 || **__ 18 __** 7.31 || **__ 19 __** 6.39 || **__ 20 __** 6.28 || **__ 21 __** 6.65 || **__ 22 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">6.7 || **__ 23 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">6.84 ||
 * **__ 5 __**
 * __ 5 __** 9.69 || **__ 6 __**
 * **__ 6 __** 11.78 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">12.07 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">12.32 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">12.43 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">11.5 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">11.07 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">10.46 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">10.05 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">9.41 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">9.16 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">8.3 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">7.8 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">7.4 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">7.26 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">6.14 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">5.89 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">6.05 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">6.2 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">6.3 ||
 * **__ 7 __** 12.25 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">12.32 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">12.48 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">12.68 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">11.87 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">11.23 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">10.79 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">12.26 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">9.48 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">8.58 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">7.5 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">7.2 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">6.84 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">6.56 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">6.05 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">5.62 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">5.75 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">5.8 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">5.95 ||
 * **__ 8 __** 13.16 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">13.22 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">13.41 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">13.62 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">12.96 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">12.22 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">11.52 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">10.6 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">9.93 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">9.13 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">8.51 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">7.8 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">6.94 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">6.35 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">5.77 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">4.78 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">5.05 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">5.27 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">5.59 ||
 * **__ 9 __** 13.95 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">13.99 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">14.1 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">14.73 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">13.42 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">12.78 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">11.73 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">10.62 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">9.88 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">9.23 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">8.37 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">7.57 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">6.55 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">5.55 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">4.4 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">3.65 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">3.79 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">4.33 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">5.11 ||
 * **__ 10 __** 14 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">14.23 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">15.01 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">20 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">14.9 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">13.2 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">11.7 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">10.95 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">9.95 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">9.2 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">8.14 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">7.5 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">5.7 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">5.05 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">3.68 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">0 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">3.09 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">4.34 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">4.51 ||
 * **__ 11 __** 13.0 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">13.14 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">13.6 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">14.15 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">13.4 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">12.3 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">10.55 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">10.14 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">9.65 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">8.62 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">7.52 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">7.17 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">6.26 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">5.26 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">4.88 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">4.05 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">4.45 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">4.84 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">5.08 ||
 * **__ 12 __** 12.1 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">12.16 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">12.43 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">12.65 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">12.15 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">11.2 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">10.94 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">9.85 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">9.42 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">9.12 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">7.7 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">7.14 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">6.82 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">4.98 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">4.4 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">3.31 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">4.52 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">4.82 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">5.22 ||
 * **__ 13 __** 11.6 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">12.1 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">12.22 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">12.29 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">12.14 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">11.88 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">11.36 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">10.5 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">9.93 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">9.17 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">8.24 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">7.92 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">7.54 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">6.24 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">5.8 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">5.55 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">5.72 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">5.72 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">6.76 ||
 * **__ 14 __** 11.4 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">11.5 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">12.16 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">12.43 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">11.23 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">11.07 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">10.41 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">10.15 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">9.26 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">9.17 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">8.21 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">7.98 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">7.19 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">6.99 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">6.56 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">6.11 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">6.32 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">6.87 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">7 ||
 * **__ 15 __** 11.1 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">11.27 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">11.34 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">11.41 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">10.97 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">10.89 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">10.2 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">9.89 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">9.13 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">9.02 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">8.56 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">8 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">7.1 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">6.99 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">6.56 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">6.34 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">6.39 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">6.41 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">6.5 ||

**Charge of Points in System with two Positive Source Charges (Volts)** x-coordinates --> y-coordinates (going down)

**__ 16 __** 17.5 || **__ 6 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.77 || **__ 7 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.96 || **__ 8 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.98 || **__ 9 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.92 || **__ 10 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.04 || **__ 11 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.89 || **__ 12 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.67 || **__ 13 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.1 || **__ 14 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.08 || **__ 15 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.17 || **__ 16 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.23 || **__ 17 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.29 || **__ 18 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.05 || **__ 19 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.47 || **__ 20 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.25 || **__ 21 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.39 || **__ 22 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.06 ||
 * **__ 5 __**
 * **__ 15 __** 17.85 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.45 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.02 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.79 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.99 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.95 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.94 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.93 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.06 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.13 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.17 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.16 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.33 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.35 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.48 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.57 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.22 ||
 * **__ 14 __** 17.72 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.81 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.08 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.2 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.09 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.98 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.64 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.15 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.81 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.9 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.95 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.43 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.12 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.54 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.6 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.29 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.33 ||
 * **__ 13 __** 17.66 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.91 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.16 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.27 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.22 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.01 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.13 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.88 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.6 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.08 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.22 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.14 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.68 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.43 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.5 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.64 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.39 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.41 ||
 * **__ 12 __** 17.68 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.92 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.32 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.68 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.42 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.26 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.93 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.05 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.9 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.05 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.15 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.1 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.11 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.3 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.56 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.83 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.81 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.26 ||
 * **__ 11 __** 17.57 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.42 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.39 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">19.93 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.6 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.18 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.62 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.83 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.07 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.19 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.88 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.26 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.34 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.32 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.91 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">19.92 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.79 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.06 ||
 * **__ 10 __** 17.22 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.62 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.99 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.5 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.2 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.89 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.85 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.7 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.8 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.86 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.88 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.03 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.26 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.74 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.4 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.64 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.4 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.63 ||
 * **__ 9 __** 17.05 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.15 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.6 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.81 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.93 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.39 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.45 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.79 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.7 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.37 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.71 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.01 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.27 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.32 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.96 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.01 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.23 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.45 ||
 * **__ 8 __** 16.56 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">16.55 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.14 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.37 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.6 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.38 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.42 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.35 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.44 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.51 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.61 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.99 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.15 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.1 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.26 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.27 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.82 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.49 ||
 * **__ 7 __** 16.31 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">16.43 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">16.75 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">16.99 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.28 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">16.79 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.23 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">16.86 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.56 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.58 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.6 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.04 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.28 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.16 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.98 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.31 ||
 * **__ 6 __** 15.83 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">16.19 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">16.39 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">16.81 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">16.48 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">16.78 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">16.64 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.12 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.07 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.27 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.36 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.82 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.75 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.95 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.16 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.99 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">17.92 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 10.6667px; text-align: right;">18.1 ||

**Charge of Points in System with Two Parallel Plates (Volts)** x-coordinates --> y-coordinates (going down)

**__ 15 __** 2.7 || **__ 5 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">1.53 || **__ 6 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.9 || **__ 7 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.61 || **__ 8 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.43 || **__ 9 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.34 || **__ 10 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.29 || **__ 11 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.24 || **__ 12 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.23 || **__ 13 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.21 || **__ 14 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.19 || **__ 15 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.19 || **__ 16 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.21 || **__ 17 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.22 || **__ 18 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.27 || **__ 19 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.32 || **__ 20 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.38 || **__ 21 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.5 || **__ 22 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.81 || **__ 23 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">1.37 || **__ 24 __** <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">2.39 ||
 * **__ 4 __**
 * **__ 14 __** 3.25 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.02 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.02 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.03 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.02 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.02 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.02 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.02 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.01 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.01 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.00 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.00 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.01 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.01 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.01 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.01 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.02 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.02 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.02 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">0.03 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">2.98 ||
 * **__ 13 __** 4.88 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">3.69 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">3.05 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">2.79 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">2.67 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">2.71 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">2.67 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">2.86 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">2.81 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">2.71 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">2.70 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">2.82 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">2.67 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">2.67 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">2.85 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">2.74 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">2.41 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">2.47 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">2.69 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">3.52 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">4.29 ||
 * **__ 12 __** 6.4 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">5.93 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">5.71 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">5.33 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">5.32 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">5.31 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">5.36 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">5.14 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">5.19 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">5.22 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">4.95 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">5.28 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">5.23 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">5.23 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">5.21 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">5.10 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">5.22 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">5.05 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">5.41 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">5.75 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">6.22 ||
 * ** __11__ ** 8.39 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">7.98 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">7.95 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">7.75 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">7.74 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">7.77 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">7.70 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">7.61 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">7.81 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">7.64 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">7.77 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">7.63 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">7.59 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">7.71 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">7.73 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">7.17 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">7.50 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">7.56 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">7.59 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">7.88 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">8.06 ||
 * **__ 10 __** 10.43 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">10.19 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">10.20 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">10.08 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">10.44 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">10.02 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">10.10 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">10.02 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">10.21 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">10.14 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">10.19 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">10.22 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">10.26 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">10.09 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">10.14 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">10.08 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">10.15 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">10.01 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">9.95 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">10.11 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">10.10 ||
 * **__ 9 __** 12.27 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">12.55 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">12.76 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">12.77 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">12.80 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">12.73 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">12.57 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">12.63 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">12.82 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">12.63 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">12.55 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">12.71 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">12.89 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">12.76 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">12.60 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">12.99 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">12.82 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">12.32 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">12.39 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">12.14 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">12.20 ||
 * **__ 8 __** 14.15 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">14.85 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">15.16 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">15.38 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">15.01 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">15.21 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">15.04 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">15.22 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">15.18 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">15.19 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">15.08 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">15.12 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">15.41 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">15.34 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">15.22 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">15.49 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">15.14 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">15.10 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">15.01 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">14.42 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">14.02 ||
 * **__ 7 __** 15.76 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">17.06 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">17.48 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">17.57 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">17.71 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">17.57 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">17.57 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">17.72 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">17.43 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">17.57 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">17.69 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">17.60 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">17.67 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">17.74 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">17.64 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">17.64 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">17.64 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">17.61 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">17.50 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">16.86 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">15.94 ||
 * **__ 6 __** 19.93 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.98 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.98 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.98 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.98 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.97 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.97 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.97 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.98 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.99 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">20 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.99 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.98 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.97 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.95 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.95 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.95 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.95 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.94 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.93 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">17.21 ||
 * **__ 5 __** 17.31 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">18.38 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">18.98 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.27 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.39 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.49 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.53 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.55 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.61 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.57 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.63 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.54 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.53 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.49 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.56 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.44 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.44 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.29 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">18.97 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">18.47 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">17.55 ||
 * 44 **__4__** || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">17.74 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">18.30 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">18.66 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">18.78 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">18.89 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.05 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.04 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.06 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.12 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.22 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.17 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.22 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.15 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">19.04 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">18.05 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">18.60 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">18.63 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">18.26 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">18.09 || <span style="color: #000000; display: block; font-family: Calibri; font-size: 9.33333px; text-align: right;">17.60 ||

**Electric Potential in a Ring (Volts)** x-coordinates --> y-coordinates (going down) **__ 1 __** 1.8 || **__ 1 __**  1.6 || **__ 2 __**  1.5 || **__ 3 __**  1.5 || **__ 4 __**  1.5 || **__ 5 __**  1.6 || **__ 6 __**  1.2 || **__ 7 __**  1.1 || **__ 8 __**  1.1 || **__ 9 __**  1.4 || **__ 10 __**  1.3 || **__ 11 __**  1.3 || **__ 12 __**  1.2 || **__ 13 __**  1.2 || **__ 14 __**  1.2 || **__ 15 __**  1.1 || **__ 16 __**  1.1 || **__ 17 __**  1.1 || **__ 18 __**  1.1 || **__ 19 __**  1.2 || **__ 20 __**  1.2 || **__ 21 __**  1.3 || **__ 22 __**  1.4 || **__ 23 __**  1.5 || **__ 24 __**  1.5 || **__ 25 __**  1.5 ||
 * **__ 0 __**
 * **__ 2 __** 1.7 || 1.7 || 1.7 || 1.7 || 1.6 || 1.6 || 1.6 || 1.6 || 1.6 || 1.5 || 1.5 || 1.4 || 1.2 || 1.1 || 1 || 1 || 1.2 || 1.1 || 1.1 || 1.2 || 1.3 || 1.4 || 1.5 || 1.6 || 1.6 || 1.6 ||
 * **__ 3 __** 1.7 || 1.7 || 1.8 || 1.7 || 1.7 || 1.7 || 1.7 || 1.6 || 1.6 || 1.5 || 1.4 || 1.2 || 1.2 || 1.1 || 1 || 1 || 1 || 1 || 1.1 || 1.2 || 1.3 || 1.4 || 1.5 || 1.5 || 1.6 || 1.6 ||
 * **__ 4 __** 1.8 || 1.7 || 1.7 || 1.7 || 1.7 || 1.7 || 1.7 || 1.7 || 1.6 || 1.6 || 1.4 || 1.2 || 1.1 || 1 || 0.9 || 0.8 || 0.8 || 0.9 || 1 || 1.1 || 1.2 || 1.3 || 1.4 || 1.5 || 1.6 || 1.7 ||
 * **__ 5 __** 1.8 || 1.8 || 1.8 || 1.8 || 1.7 || 1.7 || 1.7 || 1.7 || 1.7 || 1.8 || 1.8 || 1.7 || 1.5 || 1.3 || 1 || 0.7 || 0.6 || 0.7 || 1 || 1.2 || 1.4 || 1.5 || 1.5 || 1.5 || 1.6 || 1.7 ||
 * **__ 6 __** 1.8 || 1.8 || 1.8 || 1.8 || 1.8 || 1.8 || 1.8 || 1.8 || 2.1 || 2.4 || 2.6 || 2.5 || 2.4 || 2.3 || 1.8 || 1.3 || 0.5 || 0.5 || 0.9 || 1.3 || 1.5 || 1.6 || 1.7 || 1.7 || 1.7 || 1.8 ||
 * **__ 7 __** 1.8 || 1.8 || 1.8 || 1.8 || 1.4 || 1.3 || 1.4 || 1.6 || 2.2 || 2.5 || 3 || 3.1 || 3.2 || 2.7 || 2.2 || 1.6 || 0.9 || 0.5 || 0.2 || 0.2 || 0.2 || 0.4 || 0.3 || 0.4 || 0.4 || 0.3 ||
 * **__ 8 __** 1.2 || 1.2 || 1.2 || 1.2 || 1.3 || 1.3 || 1.6 || 1.8 || 2.7 || 3.4 || 4 || 4.3 || 4.4 || 4 || 3.4 || 2.5 || 1.5 || 2.2 || 2.4 || 0.3 || 1.4 || 1.5 || 2 || 2 || 2 || 2 ||
 * **__ 9 __** 1.8 || 1.7 || 1.8 || 1.8 || 1.8 || 1.8 || 2.2 || 2.9 || 3.8 || 4.7 || 5.6 || 6.6 || 6.7 || 6.1 || 5 || 4.1 || 3.4 || 2.9 || 2.7 || 2.4 || 2.2 || 2.1 || 2 || 2 || 2 || 2 ||
 * **__ 10 __** 1.8 || 1.7 || 1.8 || 1.8 || 1.8 || 1.8 || 2 || 2.8 || 3.9 || 5.2 || 6.7 || 8.6 || 10.1 || 7.2 || 5.5 || 5.1 || 4 || 3.1 || 2.4 || 2 || 1.8 || 1.9 || 1.9 || 1.9 || 1.9 || 2 ||
 * **__ 11 __** 1.8 || 1.8 || 1.8 || 1.8 || 1.8 || 1.7 || 2.1 || 3.4 || 4.5 || 5.8 || 7.6 || 11.2 || 19.9 || 9.5 || 6.8 || 5.3 || 3.7 || 2.8 || 2 || 1.5 || 1.8 || 1.4 || 1.4 || 1.3 || 1.4 || 1.3 ||
 * **__ 12 __** 1.8 || 1.6 || 1.8 || 1.8 || 1.6 || 1.7 || 2.4 || 3.2 || 3.9 || 5.5 || 7 || 8.3 || 9.6 || 8.1 || 6.6 || 5 || 3 || 1.7 || 1.9 || 0.4 || 1.7 || 0.4 || 0.4 || 0.4 || 0.4 || 0.5 ||
 * **__ 13 __** 1.9 || 1.9 || 1.3 || 1.4 || 1.8 || 1.9 || 2.2 || 3.2 || 3.4 || 4.5 || 5.4 || 6 || 6.5 || 5.7 || 4.5 || 3.5 || 2.4 || 1.4 || 0.6 || 0.5 || 0.5 || 0.4 || 0.4 || 0.4 || 0.4 || 0.4 ||
 * **__ 14 __** 1.9 || 1.9 || 2 || 2 || 1.9 || 1.8 || 2.1 || 2.4 || 3.6 || 3.9 || 4.2 || 5.4 || 4.8 || 4.5 || 3.8 || 4 || 3.5 || 2.6 || 2.5 || 0.7 || 2.2 || 2.3 || 2.1 || 2.2 || 2.2 || 2.2 ||
 * **__ 15 __** 1.8 || 2.1 || 2.1 || 2.3 || 2.2 || 2.2 || 2 || 2.4 || 2.8 || 3.4 || 4.1 || 4.4 || 4.4 || 4.3 || 4 || 3.5 || 3 || 2.6 || 1.9 || 1.8 || 1.7 || 1.8 || 1.7 || 2.2 || 2.1 || 2.2 ||
 * **__ 16 __** 1.8 || 1.9 || 1.7 || 1.8 || 1.8 || 1.8 || 1.8 || 1.7 || 2.1 || 2.4 || 2.7 || 3 || 3 || 3 || 2.6 || 2.6 || 2.2 || 1.9 || 1.8 || 1.9 || 2 || 2 || 2.1 || 2.1 || 2.1 || 2 ||
 * **__ 17 __** 2 || 2.1 || 2 || 2 || 2.1 || 2.1 || 2 || 2.1 || 2.1 || 2.2 || 2.9 || 2.9 || 3 || 3 || 2.9 || 2.6 || 2 || 1.8 || 1.7 || 1.7 || 1.7 || 1.7 || 1.7 || 1.7 || 1.6 || 1.5 ||
 * **__ 18 __** 2 || 1.9 || 1.9 || 1.9 || 1.7 || 1.8 || 1.8 || 1.8 || 1.9 || 2.3 || 2.5 || 2.6 || 2.7 || 2.6 || 2.5 || 2.5 || 2.5 || 2.4 || 2.3 || 1.9 || 1.9 || 2 || 1.9 || 1.9 || 1.8 || 1.9 ||
 * **__ 19 __** 1.4 || 1.4 || 2 || 1.8 || 1.8 || 1.8 || 1.8 || 1.8 || 1.9 || 1.8 || 1.9 || 1.9 || 1.8 || 1.7 || 1.7 || 1.8 || 1.6 || 1.6 || 1.7 || 1.6 || 1.7 || 1.6 || 1.6 || 1.7 || 1.6 || 1.8 ||
 * **__ 20 __** 1.7 || 1.9 || 2.3 || 1.7 || 1.9 || 1.6 || 1.5 || 1.4 || 1.4 || 1.4 || 1.2 || 1.3 || 1 || 1.1 || 1.2 || 1 || 0.8 || 0.8 || 0.8 || 1 || 0.7 || 0.8 || 0.7 || 0.7 || 0.8 || 0.9 ||
 * **__ 21 __** 1.7 || 1.7 || 1.7 || 1.7 || 1.6 || 1.6 || 1.7 || 1.5 || 1.5 || 1.4 || 1.3 || 1.3 || 1.2 || 1.1 || 1 || 1 || 0.9 || 0.8 || 0.8 || 0.8 || 1.1 || 1 || 0.9 || 1.1 || 1 || 1 ||


 * Graphs:**

__Two positive Charges:__ The two peaks in this graph are the two positive charges involved in the data, and the concentric circles going around represent the equipotential lines.



__Dipolar(1+ and 1-):__ In this graph, the peak represents the positive source charge and the lowest point represents the negative source charge. The colored concentric circles around each charge represent the equipotential lines, with a noticeable decline in charge from the positive charge to the negative charge.

__Parallel “Plates”:__ side view

__Top View__ In this graph the multi-colored lines each represent equipotential lines between the plates, as well as on each side of them. As expected the charges decrease as the points get closer to the negatively charged plate and increase as they get closer to the positively charged plate.

__Circle Graphs:__ As expected, the charge is highest at the positive source charge (center peak) and decrease as the get closer to the negatively charged ring. The different colored circles around the positive source charge represent the different equipotential lines in this graph, which are all concentric to the charge in the center.
 * Analysis:**

__Top View of Two + Charges:__ For this graph, it can be seen that there are some irregular points that are lower than they should be in between the two source charges. It is also noticeable that the electric potential lines are less circular than what was expected, due to some irregular results. Other than that, however, the electric field lines follow a path very similar to what is expected, which demonstrates good results.

__Top View of Dipolar:__

In this graph the electric field lines take a slightly irregular path to the negative charge than is expected, but still flow in the direction expected. Also, the equipotential lines around each of the source charges should be more circular than they are. The irregularity is more easily seen around the negative charge.

__Top View of Parallel Plates:__ In this graph the electric field lines follow a path extremely similar to what is expected. The electric field lines go from the positively charged plate to the negatively charged plate, the electric field lines from points below the negative plate flow towards the negative plate, and the electric field lines above the positively charged plate flow farther upward, away from the positively charged plate.

__Top View of Circle:__ In this graph the electric field lines are extremely accurate, with the lines flowing away from the center positive charge to the outer negatively charged ring in every direction. The equipotential lines, however, are not as circular around the center charge as what is expected. There are several irregular results that cause the equipotential lines to take a different shape.


 * Conclusion:**

Based on the results of our data in the graphs, we can see that the greater amount of Electric Potential energy can be found closest to the positive source charge, regardless of whether it is a circular point, two positive points, or parallel planes, it requires more work to get a particle closer to the positive source charge. The results all came out pretty well, and this can be seen on the graphs because they all show a steady increase as the positions get closer to the positive source charge, besides for a few exceptions. As the positions approach the positive source charge(s) their voltage should increase, and as they approach a negative source charge they should decrease. Based on this information we can tell that the graphs are accurate. Looking back at my hypothesis, I agree with my previous statement, but I would add that as the position approaches the positive source charge its voltage increases. This can be seen extremely clearly on the parallel ‘planes’ graph from the side view. As the position gets closer to the positive plane, the voltage increases tremendously, regardless of the x-coordinate on the plane. The error that occurred in this lab was because the values of voltage at each point were very unstable. The volt meter would only get readings that were as steady as the person who was holding it. The harder a person pressed the volt meter against the point, for example, the higher the meter’s reading was, and this caused varying answers for each point. In some cases it caused values farther away from the source charge to be greater than values closer to the source charge. To fix this I would instruct the person holding the meter to press as hard as possible on each point, reducing any variation in strength in the readings.

Pre-Lab Questions
Pre-Lab Activity 1. The objective is stated in the title. What is your hypothesis? (Attempt to answer the question, to the best of your knowledge.) As we measure points father away from a source charge there will be a pattern of decreasing Voltage, and some points of similar distances will be equipotential (have the same Electric Potential).

2. What is the rationale for your hypothesis? (Provide detailed reasoning here. This may take the form of a list of what you already know about the topics, with a summary at the end.) - electric field lines show where the electric field of a certain charge is pointing (the direction). - equipotentials represent the same electric potential at different points on electric field lines. - electric Potential (∆v) is directly proportional to the distance from the source charge to the point measured. Due to this knowledge, I have concluded that the equipotentials will always be the same distance regardless of position around a charge, as well as that the charge of the points will have a direct relationship to the electric potential.

3. How do you think you might test this hypothesis? (What might you measure and how?) We can test this by measuring specific points around a source charge (or charges) and measure what the electric potential is at each point, displaying any patterns that may occur.

4. Predict the electric field lines (and the equipotential surfaces) of the following situations:

a. Two point sources (one negative and one positive)

b. A circle (negatively charged) and a positive point charge in the very center of it.

c. Two lines of charge (one negative and one positive) = =

**__Notes: 9/21__**:
Equation for electric potential energy (EPE)

W=Fd and Fe=Eq

W=(Eq)d and W=EPE


 * EPE = (Eq)d**

-W=EPE

Electric Potential Difference: V=voltage

V= change in potential energy/q = -W/q

voltage is in regards to electric potential difference, electric potential, and electric pressure.

=CH19 Lesson1:Current Electricity=

__Electric Field and the Movement of Charge:__ One of the fundamental principles that must be understood in order to grasp electric circuits pertains to the concept of how an electric field can influence charge within a circuit as it moves from one location to another. Action-at-a-distance forces are sometimes referred to as field forces. The space surrounding a charged object is affected by the presence of the charge; an electric field is established in that space. A charged object creates an electric field - an alteration of the space or field in the region that surrounds it. Other charges in that field would feel the unusual alteration of the space. Electric field is a vector quantity whose direction is defined as the direction that a positive test charge would be pushed when placed in the field. In a similar manner to gravity, to move a charge in an electric field against its natural direction of motion would require work. The exertion of work by an external force would in turn add potential energy to the object. The natural direction of motion of an object is from high energy to low energy; but work must be done to move the object //against// //nature//.

In Diagram C, the positive test charge is moving from location A to location B in the direction of the electric field. This movement would be natural - like a mass falling towards Earth. Work would not be required to cause such a motion and it would be accompanied by a loss of potential energy.

__Electric Potential:__

Moving a positive test charge against the direction of an electric field is like moving a mass upward within Earth's gravitational field. Both movements would be like //going against nature// and would require work by an external force. This work would in turn increase the potential energy of the object. In this section of Lesson 1, we will introduce the concept of ** electric potential **and relate this concept to the potential energy of a positive test charge at various locations within an electric field.

Consider the electric field created by a positively charged Van de Graaff generator. The direction of the electric field is in the direction that a positive test charge would be pushed; in this case, the direction is outward away from the Van de Graaff sphere. Work would be required to move a positive test charge towards the sphere against the electric field. The greater the charge on the test charge, the greater the repulsive force and the more work that would have to be done on it to move it the same distance. Just like gravitational potential energy, electric potential energy is dependent upon at least two types of quantities:

1) Electric charge - a property of the object experiencing the electrical field, and

2) Distance from source - the location within the electric field

While electric potential energy has a dependency upon the charge of the object experiencing the electric field, electric potential is purely location dependent. Electric potential is the potential energy per charge.



As we begin to discuss electric circuits, we will notice that a battery powered electric circuit has locations of high and low potential. Charge moving through the wires of the circuit will encounter changes in electric potential as it traverses the circuit. Within the electrochemical cells of the battery, there is an electric field established between the two terminals, directed from the positive terminal towards the negative terminal. The charge would lose potential energy as moves through the //external circuit// from the positive terminal to the negative terminal. The negative terminal is described as the low potential terminal.

__Electric Potential Difference:__

Electric potential is a location-dependent quantity that expresses the amount of potential energy per unit of charge at a specified location. As we begin to apply our concepts of potential energy and electric potential to circuits, we will begin to refer to the difference in electric potential between two points. Consider the task of moving a positive test charge within a uniform electric field from location A to location B as shown in the diagram at the right. In moving the charge against the electric field from location A to location B, work will have to be done on the charge by an external force. As a result of this change in potential energy, there is also a difference in electric potential between locations A and B. This difference in electric potential is represented by the symbol ** ∆V ** and is formally referred to as the ** electric potential difference **. By definition, the electric potential difference is the difference in electric potential (V) between the final and the initial location when work is done upon a charge to change its potential energy. In equation form, the electric potential difference is

Electric circuits are all about the movement of charge between varying locations and the corresponding loss and gain of energy that accompanies this movement. If a 12 volt battery is used in the circuit, then every coulomb of charge is gaining 12 joules of potential energy as it moves through the battery. And similarly, every coulomb of charge loses 12 joules of electric potential energy as it passes through the external circuit. The loss of this electric potential energy in the external circuit results in a gain in light energy, thermal energy and other forms of non-electrical energy. By providing energy to the charge, the cell is capable of maintaining an electric potential difference across the two ends of the external circuit. Once the charge has reached the high potential terminal, it will naturally flow through the wires to the low potential terminal. In a battery-powered electric circuit, the cells serve the role of the charge pump to supply energy to the charge to lift it from the low potential position through the cell to the high potential position. It is often convenient to speak of an electric circuit such as the simple circuit discussed here as having two parts - an internal circuit and an external circuit. The ** internal circuit ** is the part of the circuit where energy is being supplied to the charge. For the simple battery-powered circuit that we have been referring to, the portion of the circuit containing the electrochemical cells is the internal circuit. The ** external circuit ** is the part of the circuit where charge is moving outside the cells through the wires on its path from the high potential terminal to the low potential terminal. The movement of charge through the internal circuit requires energy since it is an //uphill// movement in a direction that is //against the electric field//. The movement of charge through the external circuit is natural since it is a movement in the direction of the electric field. When at the positive terminal of an electrochemical cell, a positive test charge is at a high ** electric pressure ** Being under high electric pressure, a positive test charge spontaneously and naturally moves through the external circuit to the low pressure, low potential location. As a positive test charge moves through the external circuit, it encounters a variety of types of circuit elements. Each circuit element serves as an energy-transforming device. Light bulbs, motors, and heating elements (such as in toasters and hair dryers) are examples of energy-transforming devices. In each of these devices, the electrical potential energy of the charge is transformed into other useful (and non-useful) forms. For instance, in a light bulb, the electric potential energy of the charge is transformed into light energy (a useful form) and thermal energy (a non-useful form). Upon leaving the circuit element, the charge is less energized. The location just prior to entering the light bulb (or any circuit element) is a high electric potential location; and the location just after leaving the light bulb (or any circuit element) is a low electric potential location. The loss in electric potential while passing through a circuit element is often referred to as a ** voltage drop **. By the time that the positive test charge has returned to the negative terminal, it is at 0 volts and is ready to be re-energized and //pumped back up to// the high voltage, positive terminal.

In Circuit A, there is a 1.5-volt D-cell and a single light bulb. In Circuit B, there is a 6-volt battery (four 1.5-volt D-cells) and two light bulbs. In each case, the negative terminal of the battery is the 0 volt location. The positive terminal of the battery has an electric potential that is equal to the voltage rating of the battery. The battery energizes the charge to //pump it// from the low voltage terminal to the high voltage terminal. By so doing the battery establishes an electric potential difference across the two ends of the external circuit. Being //under electric pressure//, the charge will now move through the external circuit. As its electric potential energy is transformed into light energy and heat energy at the light bulb locations, the charge decreases its electric potential. The total voltage drop across the external circuit equals the battery voltage as the charge moves from the positive terminal back to 0 volts at the negative terminal. In the case of Circuit B, there are two voltage drops in the external circuit, one for each light bulb.

=** Guiding Questions CH19 Electric Potential and Capacitance **=
 * 1) Review what you know about energy from last year’s notes! Also look in the Cutnell and Johnson text and on The Physics Classroom.
 * 2) What is energy? – The ability to do work.
 * 3) What is work? – A transfer of energy, work is equal to force times the distance it was exerted.
 * 4) When is energy conserved? – Energy is always conserved, just typically transformed into other forms of energy such as friction and heat energy.
 * 5) What is the difference between conservative and non-conservative types of forces and energies? – Conservative forces are forces that are able to be stored and preserve the ability to do work, while non-conservative forces are not able to be stored and remove the work on an object, such as friction.
 * 6) What is electrostatic force? Is it conservative or nonconservative? – Electrostatic force is the attraction or repulsion of charged particles. It is conservative and often becomes kinetic energy.

2. Combine the equations for work and for electric field strength to get a new expression for work.
 * W = Ft
 * E = Fe/q E x q = Fe
 * W = (E x q) x t

3. In a uniform electric field, a charge moves from one place to another. What are the only types of energy present in this situation?
 * Electrostatic energy and kinetic energy

4. Use this to find an expression for the change in potential energy.
 * EPEi = KEf

5. Check this out! Real footage of So Cal Edison opening a switch on a 500kV line while its under load to make repairs. Turn it up, the sound is cool. []

6. What is the definition of potential difference? What is the equation, symbol and unit of potential difference? Why is potential difference a relative value, not an absolute value?
 * Potential difference is the work required to move a charge from one point to the other in volts.
 * V(potential difference) = E/Q in volts
 * Potential difference is a relative value because it varies depending on how strong the source charge for the electric field is.