Classical Electrodynamics · Problem 1.7

Boundary-Value Problems in Electrostatics: I — John David Jackson

Physics — E&M · parallel-cylinder-capacitance

Problem

Two long, cylindrical conductors of radii

a_1

and

a_2

are parallel and separated by a distance

d

, which is large compared with either radius. Show that the capacitance per unit length is given approximately by

C \approx \pi\epsilon_0\left(\ln\frac{d}{a}\right)^{-1}

where

a

is the geometrical mean of the two radii. Approximately what gauge wire (state diameter in millimeters) would be necessary to make a two-wire transmission line with a capacitance of

1.2 \times 10^{-11}

F/m if the separation of the wires was 0.5 cm? 1.5 cm? 5.0 cm?

Related theory

Capacitance Parallel Plate Capacitor

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