An infinitely long straight wire carrying a uniform linear charge density λ is placed along the axis of a hollow, cylindrical, conducting shell of inner radius a and outer radius b. The shell is initially uncharged and is kept isolated in air.
a. (i) Determine the magnitude of the electric field at a point located at a radial distance r from the common axis for the following ranges:
(A) r<a, (B) a<r<b, (C) r>b.
b. (ii) Calculate the surface charge densities induced on the inner and outer surfaces of the conducting shell.
c. (iii) Find the potential difference between the line charge (take its surface at an infinitesimal radius) and the outer surface of the shell.