An infinitely long cylindrical shell of uniform volume densi

An infinitely long cylindrical shell of uniform volume density has an inner radius a and an outer radius b. What infinite line of charge must be places at the center of the cylinder (r=0) to make the external (r>b) electric field zero?

Solution

By Gauss Law, the flux through a surface is directly dependent on the total charge inside the surface

So, for the electric field to be 0, total charge of the shell and line must be 0

Let Charge on the cylindrical shell:be Q1

So, charge on the line must be -Q1