PHYSICS 220/230
Lab 3: Electric Fields and Potentials

Object:

To experimentally investigate the concept of the electric field and to map (represent graphically) some field lines for particular charge configurations.

Background:

The electric field intensity is defined as the electrical force per unit of charge, or E = F/q. Theoretically, the electric field is determined by using a positive test charge q and determining the force acting on it at every point in space. The direction of the field is found by the laws of vectors and the rule that tells you whether the force is attractive or repulsive. Since a free charge moves in an electric field by the action of the electric force, then work (W = F * d) is done by the field in moving charges from one point to another (e.g., point a to point b ). To move a positive charge from "b" to "a" against the electric field would require work supplied by an external force. The ratio of the work done, W, to the charge, q, in moving the charge between two points in an electric field is called the potential difference, V_ab, between the points: V_ab = W/q. If a charge is moved along a path at right angles (i.e., perpendicular) to the field lines, there is no work done (W = 0) since there is no force component along the path. No work means no potential difference from point to point. Hence, the potential is constant along paths perpendicular to field lines. Such paths are called equipotentials. Thus, an electric field set up by charges may be "mapped" by determining the equipotential lines (equipotential surfaces in three dimensions) that exist in the region around the charges. Potential difference is easily read by a voltmeter, whereas the measurement of forces would present numerous experimental problems.

Part 1: Measuring Equipotentials

The apparatus consists of a flat board on which is placed a sheet of carbonized conducting paper imprinted with a grid. The sheet has electrode configurations of conducting silver paint which provide an electric field when connected to a battery. The standard electrode configurations provided are two circular dots representing point charges of an electric dipole and two parallel linear electrodes representing a two-dimensional cross section of parallel plates. Place one conducting sheet on the board and connect the conductor wires from the battery terminals to the two electrodes. Make connections to the electrodes with thumbtacks to hold spade lugs in contact with the electrodes. The voltmeter measurements will be made using the Pasco Science Workshop data acquisition program. Instructions for the use of the program will be given in the laboratory.

Procedure:

• For each field investigation, sketch the electrode configuration on the paper provided using the same coordinates as those of the painted electrodes on the grid of the carbonized paper. You will plot your data directly on this paper.
• The wire from the computer interface that has a free end is to be used as a probe to investigate how the potential changes in the region between the two electrodes. Since you will be graphing equipotential lines, first choose which equipotential line you will locate, for example, one might choose 0.3 volts. Double-click on the Voltage window and change the display to 2 digits to the right of the decimal.
• Place the tip of the probe against the conducting paper at various positions between the electrodes until you find a position such that the meter reads 0.3 volts. Each time it does, you have found another point on that equipotential. Plot the points' coordinates on the paper provided. About 6 to 8 points throughout the region will be sufficient for each equipotential value.
• Repeat the process for at least three other potential choices that are spread throughout the approximate 1.5 volt range, e.g., 0.6 volts, 0.9 volts, and 1.2 volts. The choices of the potential values may need to be different to suit your apparatus.
• Once you have finished plotting all your points on your paper, draw a smooth curve through each set of points that have the same potential and label each with its potential. You now have mapped the equipotentials around the electrodes.
• Since the electric field lines must be perpendicular to the equipotential lines, sketch smooth dashed lines to represent the electric field.

Part 2: Computer-Aided Field Mapping

We are now going to use two software programs that calculate the potential and electric fields for various two- and three-dimensional distributions of charge. The programs can then plot the potentials and the electric fields and help you visualize them and their properties.

A: EMField

Run the mapping program EMField by using the following operations: open PY Software, then EMField.win, then Ctwinx.exe, and then open EMField.ctb.

• Under Sources, choose 3D Point Charges. Then drag two equal and opposite point charges into the region so that their configuration resembles the point charges from the electric dipole of Exercise 1. Then under Field and Potential choose Field vectors. At any point in the region you can click and the magnitude and direction of the electric field at that point will be displayed. Click enough points so that you have a good feel for the structure of the electric field in this region.
• Now choose Display and Clean up screen.
• Under Field and Potential choose Field Lines. Map a dozen or more field lines to show you the field in the region. Then choose Equipotentials and map a dozen or more equipotential lines.
• Print the screen by using the PrintKey software.  Open MS Word and paste the picture into it. Now you are ready to annotate and/or print the picture.
• Give an explanation for the nature of the equipotential lines and electric field vectors near the charges. Is the angle between the field and equipotential lines 90 degrees?
• While still in the Equipotentials mode, click on the mouse to see the value of the potential. Where is the potential highest and lowest? Where is it zero?

B: Poisson

Run the mapping program Poisson by double-clicking on the following folders or files in order: "Py Software", "cups", "Cupsem", "Poisson", "Poisson.exe". If the program asks you for a place to store temporary files, just type c:\temp\ and hit enter.

• Sketch a parallel plate capacitor (there is an icon with two lines on the toolbar) near the center of the screen. The top plate will have the potential selected by the slider, and the lower plate will have the same magnitude but opposite sign. Construct it to look like the one you mapped in Exercise 1. Note that the "Modify" box selection will allow you to change, move, or delete parts of the drawing until it is suitable. Click on Plot How, then Contour map of potential. Then Run the program to calculate the equipotential lines.
• Print the screen as follows:

• Describe the equipotential lines near the middle of the plates.
• Click on the Plot How menu item and select Plot Electric Field Vectors. Print the screen. What is the direction of the E field near the plate (on the inside and the outside)?
• Give an explanation for the nature of the equipotential lines and E vectors near the plates.
• Choose Field Line Through a Point from the Extras menu. Click on about a dozen points on the equipotential plot and notice the relationship between the field lines and the equipotential lines. Print the screen. Is the angle between the field and equipotential lines 90 degrees?
• Choose Crossection of E & V from the Extras menu. Move the mouse around to see the value of the potential at various points. Where is it highest and lowest? Where is it zero?

• Experiment with some other electrode configurations. For example, at +100 volts, draw a line on the screen by clicking on the line tool and then click-dragging near the center of the screen. Change the voltage slider to -100 volts and draw a circle on the screen. Click on the RUN option. Does this mapping also match the conclusions you drew from the standard configurations?