Electric Fields and Electric Potentials II

Abstract

By Gauss’s law, it is possible to determine electric field caused by highly symmetric charge distribution. Electric field of a long, straight wire: where, is the permittivity of free space, is the charge per unit length of the wire, r is the distance from the center of the wire to the field point and is the electric field direction.

The difference in potential between two points, say and b, where = the path taken from to b. For coaxial rings, the equation takes the form. With the probes immersed in water in the experiment, use absolute permittivity of water and not permittivity of free space. The value of permittivity of water is 710×10-12 C2/ Nm2 at a temperature of 20oC.

Objectives

• To experimentally determine the electric potential at various positions in a dipole
• To determine the charge per unit length in coaxial rings

Procedure

Part 1: I created a set of dipole conductors by using pennies and clamping them to the bottom of the tank with the long conducting braces provided with the equipment. I ensured the connection between brace and penny was tight and put the centers of the pennies 12 cm apart, with the tank center halfway between the pennies. Then, I adjusted the frequency of sine wave from the signal generator to 200 Hz and maximized its amplitude. I traced six equipotential lines in one-half of the tank and measured the electric field at the specified locations on the board. Finally, I drew the electric field vectors.

Part 2: I removed the pennies and the braces and used the largest ring and the smallest ring to set up a pair of oppositely charged coaxial rings. The connection between the signal generator leads and the rings were through alligator clips. From the previous experiment, I predicted whether the cylinders were themselves equipotential. I measured the potential and discussed the results (in discussion)

I selected the inner ring as the zero potential location and measured the rms voltages at five different distances measured from the common axis between the two rings. For each distance r, I measured rms voltage at the angles of 0o, 90o, 180o and 270o from positive X-axis. I computed the average value of the rms voltages for each distance. I entered the measurements in Graphical analysis, creating columns to plot Vrms vs ln(r). From the graph, I determined the charge per unit length on the inner ring and its error.

I switched to the to the fixed spacing probe assembly to make measurements of the electric field between the two circles. I did the measurements along two different radii at every 1.0 cm and recorded the corresponding values of E and r. I recorded the values in Graphical analysis and made a plot of E vs. 1/r with the assistance of the calculated column option. I determined the slope and used it to determine the charge per unit length and its error.

I measured the E-field outside the outermost cylinder and checked if it is in consistency with the Gauss’s Law. The assumption that I made was that the cylinders were infinitely long.

Experimental data

X(m) Y(m) V(X) volts V(Y) volts V(180o) volts ln(r) 1/r 0.03 0.03 4 4 4 1.380 0.250 0.05 0.05 5.277 5.277 5.277 1.663 0.190 0.07 0.07 6.05 6.05 6.05 1.800 0.106

r(m) Vrms(r) in volts Vrms(r) average ln(r) 0o 90o 180o 270o

r in metres E in volts per metre 1/r in per metre

Results

Discussion

Conclusion