A cylindrical capacitor consists of a cylindrical wire of radius , and a coaxial cylindrical shell of radius . Both the wire and cylindrical shell have length . The wire has a total charge of distributed on its surface. The cylindrical shell has a total charge of distributed on its surface.
Calculate the following:
Part 1: Electric field in the region
Part 2: Electric potential in the region
Part 3: Capacitance of the spherical capacitor.
Part 1: Electric field
The first thing to calculate is the electric field between the spherical shells. Use Gauss' law
The total charge enclosed in a Gaussian surface between the wire and the cylindrical shell is . For cylindrical geometry
The electric field from the inner spherical shell emanates radially outward, so
Part 2: Electric potential
Part 3: Capacitance