A spherical capacitor comprises two thin metal spheres of different radii but with
a common centre. The following series of operations is completed: The spheres are mutually connected by an internal wire. The outer sphere is raised to potential +V with respect to ground. The internal connection is broken. The outer sphere is returned to ground potential. Determine the final potential and the final charge on the inner sphere
The Attempt at a Solution
So initially when both spheres are raised to a potential V, no potential gradient exists across the two spheres, and hence no electric field can exist. So by Gauss' law the charge enclosed, ie. on the inner sphere, is zero. When the connection is broken and the outer sphere is returned to ground the charge will still be zero. But then this automatically implies that the potential must be zero? So no potential or charge resides on the inner sphere.
Does this sound reasonable? My only concern is that the inner sphere must maintain the same potential as the outer during the entire discharge process, or else an electric field would exist between them, which would not be consistent?
Many thanks :)