Lab 1. Resistive Paper Electrostatics Analog

NAME                                

Introduction.

In RWVD, Sec. 1.13 (SES, p. 122), it is shown that Laplace's equation is satisfied for steady current flows in a resistive medium. Thus a resistive sheet can be used as an analog to plot the equipotentials and electric field lines, and to determine the capacitance, for a two-dimensional electrostatic field configuration. The analog is also related to graphical field mapping techniques as described in Sec. 1.19-1.20.

Procedure:

1. Using an ohmeter, measure the resistance of a square (approx. 4") of resistance paper coated with silver paint at its two opposite edges.          . Should the measured value of depend on the size of the square? Y/N.
2. Trace the coaxial line, template (#1) onto the center of a square ( ") of resistive paper. Carefully paint the silver around the inside of the inner circle and around the outside of the outer circle. Use heat lamp to dry the paint.
3. Use thumbtacks to attach copper strips to the inner and outer electrodes. Ground the outer electrode and apply 10 volts to the inner electrode.
4. Using a digital voltmeter with lead pencil probe, find and mark the 5 volt equipotential line. Sketch it in. Is it a circle? Y/N. Is it midway between the inner and outer electrodes? Y/N.
5. Disconnect the voltage source! Using an ohmeter, measure the resistance between the inner and outer electrodes:          .
6. From Eq. (2) in Sec. 1.21, the capacitance C per unit meter of the coax is given by . Calculate C from your measurements if farads/meter (free space dielectric): C=        F/m. Compare with the formula in RWVD, Table 5.11b, p. 250 (SES, Exercise 4.6, p. 120): C=        F/m from table.
7. Repeat steps 2-6 for the two-wire transmission line (Template #2, trace only the two circles). Plot a few equipotentials (including 2.5 volts) and compare with Fig. 1.8, pp. 21 of text. Determine C from your measurements, C=        F/m and compare with C=        F/m from Table 5.11b.
8. Method of images, RWVD Sec. 1.18 (SES p. 124). Trace the conducting plane of template #2 between your two previously painted circles and paint the right side of the plane with silver. Excite with 5 volts on the left circle and ground on the conducting plane, and replot the 2.5 volt equipotential. Does the method of images yield the same equipotential as found in the two-wire line? Y/N.
9. If you have time, plot a few equipotentials between the stepped conductor and the plane conductor, template #3, and compare with Fig. 1.19c, p. 52.

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