Question

A spherical capacitor is made from a solid conducting sphere surrounded by a spherical, silver-coated balloon. The potential difference between the inner and outer spheres is held constant, Vo. The region between the sphere and balloon is filled with air (dielectric constant = 1). Under these conditions, the capacitance of the arrangement is given by C(t) where ‘a’ is the radius of the inner sphere and ‘b’ is the radius of the balloon.

a) Find the displacement current, I, if the balloon is expanding so that b(t)=Rot, where Ro is a constant. b) Would your answer change if a dielectric filled the space between the conducting sphere and balloon (for all time) and all else remains the same? If so, how? If not, why not?

Answer 1