ELECTRIC POTENTIAL FROM MULTIPLE POINT CHARGES– 1302Lab2Prob3

You are a member of a team building the world’s highest intensity particle accelerator. In this machine, charged atomic nuclei are brought from a very slow speed to almost the speed of light by passing them through a charged electrode structure. You need to determine the effect of these electrodes on the speed of various nuclei. The first step is to calculate the electric potential that affects the nuclei. Because the charged electrode configuration is so complicated, your team has decided to use a computer simulation. Your task is to determine if the simulation results agree with the physics that you know. You decide to calculate the electric potential at a point caused by a set of charged objects that is complex enough to test the simulation but simple enough to make your calculation possible. The first configuration that you try is a square with two equal negatively charged point objects in opposite corners and a positively charged point object of 1/3 the magnitude of the negative charges in a third corner. You will calculate the electric potential at the remaining corner of the square and compare your result to that of the computer simulation of the same configuration.

Instructions: Before lab, read the required reading from the textbook and the laboratory in its entirety. In your lab notebook, respond to the warm up questions and derive a specific prediction for the outcome of the lab. During lab, compare your warm up responses and prediction in your group. Then, work through the exploration, measurement, analysis, and conclusion sections in sequence, keeping a record of your findings in your lab notebook. It is often useful to use Excel to perform data analysis, rather than doing it by hand. At the end of lab, disseminate any electronic copies of your results to each member of your group.

Read: Tipler & Mosca Sections 23.1 and 23.2 and Example 23-4.

Equipment

The computer program Electrostatics 3D, a protractorand a ruler.

If equipment is missing or broken, submit a problem report by sending an email to . Include the room number and brief description of the problem.

Warm up

1. Draw a schematic of the charge configuration. Label the objects and their charges. Show and label all relevant distances and angles using geometry. Choose an appropriate coordinate system.

2. Write down equations for the (scalar) electric potentials at the point of interest caused by each of the three charged objects using the value of each charge and the size of the square.

3. Determine the total electric potential at the point of interest by adding the electric potentials from each point charge. Remember that the charges are of different sign.

Prediction

Restate the problem. What are you trying to calculate in your prediction? How do you calculate a total electric potential from a collection of point charges?

Exploration

In the folder Physics on the desktop, open Electrostatics 3D and click on the Point Charge button found on the far left side of the toolbar. You can now place a point charge within the workspace. Once placed, a dialog box opens allowing you to enter the magnitude of the point charge, and whether it is positive or negative.

Click the Closed Equipotential Surfaces button and move the cursor within the workspace to where you would like to evaluatethe electric potential. Position and values for potential and field will be displayed on the bottom of the workspace as you move the cursor around the work area. Clicking the mouse will cause an equipotential surface to be displayed, and moving the cursor will display new position and potential values for the new location.

You can reveal simulated electric potentialvalues anywhere in the workspace by moving the cursor where you would like to evaluate the electric field.

To place objects at precise points on the screen you will need to keep track of the position data displayed at the bottom of the workspace. You might find it helpful to map out the (x) and (y) positions required in the workspace to simulate the assigned configurations.

Try different magnitudes of charge. What range of charge values allows you to accurately measure the electric potential at a large number of locations on the screen?Try using negative charges. How does this change the electric potential?Look at the cases of (a) equal and opposite charges and (b) two identical charges. Does the potential behave as you predict in each case? Does it go to zero where you predict it?

Check to see if you get the correct behavior of the electric potential from a point charge:

  • Predict the shape of a graph of potential vs. distance (r). Graph the electric potential vs. the distance from the center of the charged point object. Is it the shape you expected?
  • Predict the shape of a graph of potential vs. inverse distance (1/r). Graph the electric potential vs. (1/r). Is it the shape you expected?

Qualitatively check to see if the program combines the electric potentials from two charged point objects correctly. Look at the cases of (a) equal and opposite charges and (b) two identical charges. Does the potential behave as you predict in each case? Does it go to zero where you predict it?

Now, explore the distribution of three charges. Drag two equal negative charges and one positive charge of 1/3 the value of one negative charge onto the screen in the configuration specified in the problem statement above. Make sure the charges are accurately placed using the position data. Note the value of the electric potential in the fourth corner of the square. What parameter can you easily vary to change the value of the potentialin that cornerwhile preserving the other conditions of the problem? In your notebook, note whether or not such manipulations change the direction of the electric field at that corner, and record the direction. Determine a measurement plan.

Measurement

Measure the electric potential at the point of interest for several different values of the varying parameter according to your measurement plan. Record the data in your notebook.

Analysis

For the situation in the problem, compare your calculated electric potential to that from the computer simulation.

Conclusion

How did your expected result compare to your measured result? Explain any differences. From your results, which general properties of the electric potential does the simulation faithfully reproduce? What is the specific evidence?