A long, straight wire has a uniform constant charge with linear charge density, - 3.60 nC/m. The wire is surrounded by a long nonconducting, thin-walled cylindrical shell that is charged on its outside surface, such that the electric field outside the shell is zero. The shell has a radius of 1.50 cm. Required:
What uniform area charge density rho is needed on the shell for the electric field to be zero outside the shell?

Uniform area charge density rho is needed is 3.82*10^-8 C.m^-2

Explanation:

See the attached files.

To find the rho, I used Gauss law for cylindrical shell which is equation 1 and Gauss law for the rod which is equation 4.

Note that in equation 4, Lamda is the charge per length while L is the length if the rod. Also R is the radius of the shell.

The final answer is 3.82*10^-8 C.m^-2 which is the uniform area charge density rho is needed.

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