Question

An empty hollow metal sphere has a potential of $+400V$ with respect to ground (defined to be at $V=0$) and has a charge of $5.0\times {10}^{9}C$. Find the electric potential at the centre of the sphere.

• A. $+400V$
• B. $-400V$
• C. $0V$
• D. None of these

Answer 1

The correct option is A $+400V$

Since it is a hollow sphere, so electric field inside the sphere is zero. It follows that it takes no work to move a test charge from any surface point to center. Since the work done to move a charge from the surface to center $=$ the charge in potential energy of charge between these two points, it follows that there is no charge in the charge's potential energy. So, the potential at the center is $400$ V.