# Electrostatics problem- two sphere

## Homework Statement

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

Gauss' law

## 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 :)

## Answers and Replies

Simon Bridge
Science Advisor
Homework Helper
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.
... you may want to expand on this reasoning. It is correct, but you have not explained it.

My only concern is that the inner sphere must maintain the same potential as the outer during the entire discharge process,..
That is not what the problem statement says.

(Note: a "two sphere" is a circle ... your problem involves "two spheres" - the "s" on the end indicates a plural so the reader realises there is more than one object.)

... you may want to expand on this reasoning. It is correct, but you have not explained it.

That is not what the problem statement says.

(Note: a "two sphere" is a circle ... your problem involves "two spheres" - the "s" on the end indicates a plural so the reader realises there is more than one object.)

But if there exists no electric field between the two spheres at any point then there can be no potential gradient between them at any point. But this would suggest that they always carry the same potential?

And sorry- my mistake (typo)

Simon Bridge
Science Advisor
Homework Helper
Try expressing in terms of the movement of charge.