A hollow ,thin-walled insulating cylinder of radius R and length L has charge Q uniformly distributed over its surface.a) caluclate the electric potential at all points along the axis of the tube.Take the orgin to be zero at infinity.b) shoe that L<

Dear student,

V(z) = sigma/(2*epsilon)*(sqrt(R^2 + z^2) - z), where z is the height above the disc and R is the radius of the disc. Now try to use this result to find the potential on the axis of a cylinder length L at a distance z from its center.

dV = K dQ / r, let dQ = sigma dA, use a geometric argument to get r. Your dA here is going to have fixed radius (call it R ), so dA = R dz dphi. You have angular symmetry, so the integration of d phi is 2 pi. This combines with K = 1 / (4 pi epsilon). Your integration of dz will run from -L/2 to L/2.