In spherical coordinates, the surface of a solid conducting cone is described by = /4 and

In spherical coordinates, the surface of a solid conducting cone is described by θ = π/4 and a conducting plane by θ = π/2. Each carries a total current I. The current flows as a surface current radially inward on the plane to the vertex of the cone, and then flows radially outward throughout the cross section of the conical conductor.

(a) Express the surface current density as a function of r;

(b) Express the volume current density inside the cone as a function of r;

(c) Determine H as a function of r and θ in the region between the cone and the plane;

(d) Determine H as a function of r and θ inside the cone.