Question

A charge of uniform linear density 2.12 nC/m is distributed along a long, thin, nonconducting rod. The rod is coaxial with a long conducting cylindrical shell with an inner radius of 6.47 cm and an outer radius of 12.0 cm. If the net charge on the shell is zero,

a) what is the surface charge density on the inner surface of the shell?

b) What is the surface charge density on the outer surface of the shell?

Answer 1

The shell is a conductor, thus the electric field inside it must equal zero. This can only happen if the charge on the shell equals the enclosed charge, i.e., it must have an induced linear charge density of –l on the inner radius of the shell and +l on the outer radius of the shell.

For the inner radius we have

s = –l / 2pr

= (–2.12 nC/m) / (2)(3.14159)(0.0647 m)

= –5.21 nC/m2 (or -5.21 x 10^-9 C/m2)

The outer radius will have half of this,

or s = +2.61 nC/m2 (or +2.61 x 10^-9 C/m2)