A solid conducting sphere of radius aa is surrounded by a thin conducting spherical shell of inner radius bb , with b>ab>a . The inner sphere carries total charge QQ , and the outer sphere carries charge −Q−Q .

a) Using Gauss's Law, find an expression for electric field EE at points a<r<ba<r<b . Show the Gaussian surface you use.

b) Using your expression for EE find the electric potential difference between the inner and the outer conductor, that is: ΔV=Va−Vb=∫baE.ds.ΔV=Va−Vb=∫abE.ds.

c) Using your results from b derive an expression for the capacitance of this capacitor, in terms of the quantities given.