Electrostatics Virtual Potential Lab

Use the HTML5 program Charges and Fields from PhET.

Turn the grid On and choose to Show numbers.   Using the menu found at lower right corner under Options choose “Projector mode” so that the background is light instead of dark.

To create a charge distribution, simply drag charges in or out of the boxes and place on the grid. Each charge has magnitude 1.0 nC. To make greater point charges you may place multiple charges on the same point of the grid – i.e. you can “stack them”.

You will be using the equipotential tool. Simply drag it to a desired position and it will give a readout of the potential at that point. If you click Plot the program will create an equipotential line.

Part A – Exploring The Connection Between Potential And Field:

1. Create a “random” distribution of 4 or 5 point charges on the screen.

2. Click and drag an E-field Sensor from the box. Find a location where the field is pointing precisely horizontally and has a magnitude between 3 and 15 V/m. Record the vector below. Leave the sensor in this position. Now take the equipotential tool and plot and record the potential at 0.10 m to the right and at 0.10 m to the left of the sensor. Record the values below. Calculate the difference in the potential divided by the difference in the two positions (a value sometimes called the gradient) -- include signs! Compare to the field measurement.


E = _______________________


∆V/∆x = ___________________

3. Repeat the above but this time search for a position where the sensor indicates a vertical field. Measure the potential 0.10 m above and below. Calculate the difference in potential divided by the difference in position. Compare.


E = _______________________


∆V/∆y = ___________________

4. Use the equipotential tool to create a map of contours all around your distribution of charges. Drag a field sensor all around your map and note how the magnitude and direction of the electric field compares to the equipotential lines.  Answer in the space given:

How does the direction of the field compare to the orientation of the equipotential lines?


How is the magnitude of the field relate to the spacing (or "density") of the equipotential lines?

Part B – Mapping and Analyzing Common Charge Distributions:

For each of the following exercises create the charge distribution and map the potential. Take a screenshot and copy into a word processing application. Crop and adjust the size to fit two maps to print on one piece of paper.

1. Place two positive charges of +1 nC each, separated horizontally by 1 m near the center of the grid. Plot lines at 10 to 34 V, steps of 4 V.

2. Place opposite charges of ±2 nC separated horizontally by 1 m near the center of the grid. Plot lines at -16 to 16 V, steps of 4 V.

3. Place charge q₁ = +3 nC and q₂ = -1 nC separated horizontally by 1 m, with q₁ only 0.5 m from the left edge of the grid. Plot lines at -1 to 11 V, steps of 1 V.

4. A horizontal line of sixteen +1nC charges, evenly spaced 0.1m apart, near the center of the grid. Plot lines at 60 to 300 V, steps of 20 V.

5. Two parallel horizontal rows of nine charges each separated by 1 m near the center of the grid. Make the charges in one row each +1 nC, evenly spaced 0.2 m apart; make the other the same but with charges of -1nC each. Plot lines at -50 to 50 V, steps of 10 V.

Analysis of the maps that you create (show work - directly on the printed map if possible):

1. For the first three maps only, draw and label a point somewhere along one of the equipotential lines. Calculate the potential at that point using techniques you learned in class.

2. For all five maps make a careful sketch of electric field lines surrounding the charge distributions, following the usual rules and conventions for such lines. The direction of the field lines should be drawn accurately based on the orientation of the equipotential lines!

3. For the last two maps only, draw and label a point between two equipotential lines. Calculate the field at that point using two methods: One method is to calculate ∆V/∆x. The other method is to determine the field produced by a line of charge, taking it to be a continuous charge per length (when it is actually, of course, a discrete set of point charges).

Conclusion:

Write a concise paragraph or two in which you evaluate the findings of this lab.