Question

A.) We'll start with a very long coaxial cable that has two parts. There's a conducting cylindrical inner wire of radius a, and a conducting cylindrical sheath around that with radius b. The space in between (a<r<b) is empty. Let the inner conductor have some linear charge density lambda along its length. Derive an expression for the magnitude of the electric field between the inner and outer conductors as a function of r.

B.) Consider the same geometry as the first part. However, for this part assume that the space in between the inner wire and outer sheath is filled with some inhomogeneous dielectric such that the electric field between the two conductors can be written as E(r)=C*lambda*r, where C is a positive known constant. Derive an expression for the potential difference between the two conductors.

Answer 1