Purpose: To gain a greater understanding of electrostatic potential by drawing lines of equal potential for a point charge. To investigate the dependence of the electrostatic potential on the distance from the point charge.

Discussion: In this experiment, the potential V near a point charge is expected to depend on the distance r as V = B + A ln r, where A and B are constants and "ln" is the natural logarithm (i. e. the logarithm to the base e). Do you know why the potential is not V = B + A/r, as in the textbook? (Hint: What is different about the experiment and the "real world"?)

The digital voltmeters used in this experiment are delicate and expensive, treat them with care.

Procedure:
1. Connect the positive and negative terminals of the battery to the electrodes on the black paper. Put the positive terminal on the point charge, the negative terminal on the outer circle. Measure the potential difference between the electrodes. Note that this potential does not depend on where you touch each electrode. This is due to the fact that the electrodes are "conductors".

2. By keeping one voltmeter lead on the negative electrode and placing the other lead at various points on the black paper, find curves of equal potential. The outer circle is set to a potential of zero. You should find points where the potential is 1.0, 2.0, 3.0 Volts, etc.... Transfer these points onto a drawing on a blank sheet of paper. (Note: The electric field points in the direction of decreasing potential.)

3. Take readings of the voltage every 0.5 cm as you move from the point charge towards the outer circle. Make more measurements if necessary.

4. Make a graph of V vs. r. Connect the points with a smooth curve. This curve represents the "potential hill" produced by the charge at the central point.

5. Make a graph of V vs. ln r. Draw the best line through your points. From the slope and intercept of your line, determine the constants A and B.