A charge of uniform linear density is distributed along a long, thin, nonconduct

Question

A charge of uniform linear density is distributed along a long, thin, nonconducting rod. The rod is coaxial with a long conducting cylindrical shell (inner radius r, outer radius R). The net charge on the shell is zero. (a) What is the magnitude of the electric field a distance d from the axis of the shell (where d > R)? What is the surface charge density on the (b) the inner and (c) outer surface of the shell? State your answers in terms of the given variables, using 0 when necessary.

(a)Ed =

(b)i =

Chapter 23, Problem 028 SN

A charge of uniform linear density is distributed along a long, thin, nonconducting rod. The rod is coaxial with a long conducting cylindrical shell (inner radius r, outer radius R). The net charge on the shell is zero. (a) What is the magnitude of the electric field a distance d from the axis of the shell (where d > R)? What is the surface charge density on the (b) the inner and (c) outer surface of the shell? State your answers in terms of the given variables, using 0 when necessary.

(a)Ed =

Explanation / Answer

a) From Gauss’s Law, and using cylindrical symmetry, we know that (electric field) X (area of cylinder) = (charge enclosed) / o. Since, d > R

So, electric field, E = (lambda)/( 2 x pi x r x 0)

b) Surface charge density on inner surface = (- lambda) / (2 x pi x r)

c) Surface charge density on outer surface =  (- lambda) / (4 x pi x r)

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