Equipotential lines for a dipole

Physics Lab

Mapping the Electrostatic Potential and Electric Field

The objective of this experiment is to study the potentials, equipotential curves and electric fields produced by various two-dimensional electrostatic charge distributions. In practice, direct measurement of the electric field turns out to be quite difficult. Instead, we exploit the fact that the electric force is a conservative force, and thus can be considered to be associated with a potential – the electric potential , where the components of the electric field vector are given by the change of the electric potential in that direction,

(1)

One consequence of Equation 1 is that if one can identify a line (or surface) along which the potential has a constant value then the electric field is necessarily perpendicular to that line at all points, see Figure 1. Therefore, in order to map the electric field for a charge configuration, it is sufficient to map out the equipotential lines.

There is a technical difficulty, however, with setting up and controlling static charge distributions: it is not easy to fix charges at precise locations. For this reason we will simulate static charge distributions using a small direct current flowing through electrodes, drawn to look like our static charge distributions, and conducting paper. The electric field shapes, potential and equipotential lines will be identical to those for the simulated static charge configurations.

Figure 1. Equipotentials and electric field lines for a positive point charge (circle at center).

NOTE: You may want to reference your text or other sources to confirm your results and aid in mapping the fields accurately and expeditiously.

Learning Goals for this Laboratory:

· Practice visualizing electric fields and electric potentials around conductors of many shapes.

· Practice graphing and analyzing nonlinear relations.

· Practice connecting simple circuits.

Apparatus
Pasco field mapping board, digital voltage meter with point probes, D.C. power supply, several sheets of conducting paper with different electrode configurations, push pins

Figure 2. Setup for Part IV of this lab showing the cork board with the parallel plate electrode configuration on conducting paper, voltmeter and D.C. power supply.

Part I. Point Source and Guard Ring
Figure 3. Point source and ring guard configuration. Voltmeter probes not shown.

1. The electrodes in this experiment are made with conducting silver paint on conductive paper. Locate the conductive paper with the point source and guard ring electrode configuration (Figure 3) and pin the corners of the paper to the cork board.

2. Take a cable with a banana plug on one end and a ring terminal on the other and plug the banana end into the positive of the power supply, then pin the ring terminal end of the cable into the central point electrode using a metal pushpin as in Figure 3. Make sure there is good contact between the ring terminal and the painted electrode. Try to avoid making new holes in the electrode with the pushpin, it is sufficient to have physical contact between the terminal of the wire lead and the silver of the electrode.

3. Similarly, connect the negative of the power supply with the circle-shaped guard ring electrode.

4. Turn on the power supply and set it to 5 V by first increasing the current limit knob, then increasing the voltage to 5 V. This voltage provides a continuous source of charge to the electrodes, creating the electric field and potential we will measure.

5. Before measuring the field and potential, let’s check the electrodes for proper conductivity (a damaged electrode could skew your results).

If the electrode is a good conductor, all points on the electrode should have nearly the same potential. For our purposes, the maximum potential between any two points on a single electrode should not be more than a few mV. Use the voltmeter to probe the potential between different points along an electrode. Please do not push the voltmeter probes through the paper; simply placing the probes on the paper should give you a good reading. If you see a potential larger than a few mV between different points on an electrode, first check that the power supply wires are firmly connected to the electrode via the pushpin. If you still see a potential where there shouldn’t be one the electrodes could be damaged, so ask your lab instructor to double-check your setup and get a replacement electrode if necessary.

6. Once you’ve checked for good conductivity, you’re ready to measure the potential of the point source. Place the black (common) voltmeter probe on the guard ring so that it is the reference, and use the red probe to measure the voltage starting at the point 2 mm from the edge of the point source and ending 20 mm from the point source at intervals of 2 mm. In this way, you will have 10 data points: 2, 4, 6, 8, and 10 mm from the point source. If it helps, you can use a pencil to mark the 2 mm points. The voltage at 2 mm should be somewhere in the 3 - 5 V range.

7. Make a graph of the potential as a function of distance from the point source (the edge of the point source is at = 0.0 cm, and = 5 V).

8. Make a second graph of potential vs. (do this by having Excel calculate in new column).

Question 1. According to theory, how does the potential of a point charge vary with distance as you move away from the point charge? Is this what your graph shows? For an ideal point source, the graph of potential vs. should be a line, is yours a line? Our point source is not ideal because the negative electrode is not infinitely far away. However, very near the point source the negative electrode is sufficiently far away as to have no influence, thus the first few points at higher voltage in the graph should follow a linear trend.

9. Mapping equipotential lines. Use the voltmeter to find equipotentials by keeping the black probe on the negative electrode and placing the red probe at a point somewhere inside the circle. Watch the voltmeter voltage reading while you slide the red probe along the paper while also trying to keep the voltage constant. This line of constant potential is an equipotential. Try doing this for one or two other values of potential nearer and farther from the point source.

Question 2. What are the shapes of the equipotentials in the region around a point source? Do your results agree with the equipotentials show in Figure 1?

10. Briefly survey the potential in the region outside the guard ring.

Question 3. Does the potential vary much from one point to another outside of the guard ring? What does this imply about the electric field outside the guard ring? Refer to equation 1 for help with your answer.

Part II. Electric Dipole
1. Replace the point source electrode with the electric dipole configuration and connect the leads to the 5 V source as in Fig. 4, making sure the pushpins provide good contact between the ring terminal and the silver paint.

Figure 4. Dipole configuration. Voltmeter probes not shown.

2. Place the black reference voltage probe halfway between the two electrodes, we’ll keep it fixed at this location. Place the red probe somewhere on the paper. Then slide the red probe along the paper while watching the voltage reading. Use this method to map out several equipotential curves nearer and farther from the point charges. Record your results on the white grid paper provided. To see what the shape should be in theory, refer to online or text sources for the potential of a dipole.

3. After drawing several equipotentials on your grid paper, use a different color to draw in the corresponding electric field lines. To do this, start at the positive charge and draw a line moving outward such that it crosses any equipotential lines at right angles. The electric field lines should terminate at the negative charge. Be sure to indicate the direction of your e-field with arrows along the lines. To see what the shape of these field lines should be, refer to online or text sources for the electric field of a dipole. Once you have several field lines drawn, take a picture of the resulting map of electric field and potential for your lab report.

Question 4. Note all but one of the equipotential lines for a dipole are curved. Where is the uniquely straight equipotential line for a dipole?

Part III. Like Charges in a Box
1. Set up the configuration shown in Fig. 5 and apply 5 V. Note that the two point charges are positive, you can use a wire to daisy-chain them together so they are both charged. Also note that the box electrode surrounding the point charges is negative. As in Part II, place your reference voltage probe halfway between the two electrodes.

Question 5. Relative to this halfway point, where on the conducting paper is the potential highest? Where is it lowest?

Figure 5. Like Charges in a Box. Voltmeter probes not shown.

2. As you did with the dipole, map out a few equipotential lines near the point charges and also near the walls of the box. Make a rough map of these equipotentials and their corresponding E-field and include it with your lab report.

Part IV. Parallel Plates
Figure 6. Parallel plate electrodes (blue lines) connected to power supply. Voltmeter probes not shown.

The potential and field in between charged parallel plates differs significantly from that of a point source (Part I).

1. Connect the parallel plate electrodes to a power supply as shown. Measure the potential every 0.5 cm along a line from the midpoint of the negative electrode to the midpoint of the positive electrode (i.e. along the dotted line in the figure at right). Use the negative electrode as the fixed reference for your measurement.

2. Make a graph of the potential as a function of distance from one plate (the reference probe is at = 0.0 cm).

Question 6. Referring to your graph, describe in how the potential changes with distance from the electrode. How does this contrast to the potential vs distance for a point source you found in Part I?

For Your Lab Report:
Refer to the lab syllabus and grading rubric for what to include in the report. It may be helpful to use the answers to the questions to aid in writing the discussion.