Lab 1, Electric Fields and Equipotentials

Cuong Nguyen, ctnguyendinh@wpi.eduPH 1121, Section D01

March 28, 2015

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1 Objectives

For this lab, we inspect the the equipotential lines between two parallel plateconductors and concentric cylindrical electrodes. From these equipotential lines,we can infer the direction and estimated magnitude of the electric fields.

2 Procedure

2.1 Parallel plate electrodes

This configuration consists of two straight plates as electrodes placed in parallelon a conducting paper. The two electrodes are then connected to a power supplyof 8 volts. After that, we measure the potentials at a set of points and markedthem with white pen.

Figure 1: Parallel plates configuration.

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2.2 Concentric cylindrical electrodes

This configuration consists of a ring and a disc as electrodes. They are placedconcentrically on a conducting paper. The two electrodes are then connectedto a power supply of 8 volts. After that, we measure the potentials at a set ofpoints and marked them with white pen.

Figure 2: Concentric cylindrical configuration.

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3 Data

After measuring the electric potential at various points, we mark them withwhite pen and connect the points on the same equipotential lines. The directionof the electric field in both configurations can be determined from these lines.

3.1 Parallel plate electrodes

Figure 3: Equipotential lines and electric field vectors for the parallel platesconfiguration.

Figure 4: Electric potential and estimated electric field acquired from parallelplates configuration. The uncertainty of s and x is obtained by halving thesmallest division of the ruler. The uncertainty of E is obtained by finding therange of E from the range of ∆s.

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3.2 Concentric cylindrical electrodes

Figure 5: Equipotential lines and electric field vectors for the concentric elec-trodes configuration.

Figure 6: Electric potential and estimated electric field acquired from concentricelectrodes configuration. The uncertainty of r and x is obtained by halving thesmallest division of the ruler. The uncertainty of E is obtained by finding therange of E from the range of ∆r.

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4 Result

4.1 Parallel plate electrodes

In order to assess the accuracy of the measured electric potential and electricfield values shown in figure 4, we compare them to the results of the followingequations:

V (s) = 8− 8

d× s (1)

|E(x)| =∣∣∣∣∂V (x)

∂x

∣∣∣∣ =8

d(2)

In which, d = 0.214 m, s is substituted with values in the first column, and x issubstituted with values in the last column in figure 4.

Figure 7: Result calculated using equations (1) and (2).

In the following graphs, the measured values in figure 4 are plotted as pointsand the predicted results in figure 7 are plotted as a smooth curve.

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Figure 8: V versus s graph for parallel plate configuration.

Figure 9: E versus x graph for parallel plate configuration.

4.2 Concentric cylindrical electrodes

In order to assess the accuracy of the measured electric potential and electricfield values shown in figure 6, we compare them to the results of the followingequations:

V (r) = 8− 8

ln RB

RA

× lnr

RA(3)

|E(x)| =∣∣∣∣∂V (x)

∂x

∣∣∣∣ =8

ln RB

RA

× 1

x(4)

In which RA = 0.02 m, RB = 0.06 m, s is substituted with values in the firstcolumn, and x is substituted with values in the last column in figure 6.

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Figure 10: Result calculated using equations (3) and (4).

In the following graphs, the measured values in figure 6 are plotted as pointsand the predicted results in figure 10 are plotted as a smooth curve.

Figure 11: V versus r graph for concentric electrodes configuration.

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Figure 12: E versus x graph for concentric electrodes configuration.

5 Discussion

Next, we will discuss about the agreement between the experimental data andthe predicted results in both configurations.

The graph V versus s of the first configuration (figure 8) shows that theexperimental values follow the linearity of the predicted line. However, the graphE versus x (figure 9) does not show a smooth match between the experimentaldata with the constant line of electric field. This might be due to the fact thatthe those electric field values are estimated roughly from the rate of changebetween two discrete equipotential line with respect to their distance, insteadof taking derivative on a continuous set of equipotential lines. Nevertheless, theavarage of these estimated points are actually pretty close to the constant line(37.5 V/m).

In the second configuration, both of the graph V versus r (figure 11) and Eversus x (figure 12) shows a high degree of agreement between the experimentaldata and the predicted curves. However, taking a closer look to the latter graphshows that there are some large inaccuracies in the first few points. The bestexplanation for this is that when using our estimating method at the pointscloser to the disc, a small change in the distance may cause a big differencein the electric field. To illustrate, for r = 0.003 m, the estimated electric fieldwill be 333.3 V/m. For r = 0.002 m, the estimated electric field will be 500V/m. Given that the instrument for measuring distance is not very precise andthere are always small human errors in reading the values, this inaccuracy isinevitable.

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