Question

A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is 10 V. The potential at the centre of the sphere is
A. Zero
B. 10 V
C. Same as at a point 5cm away from the surface
D. Same as at a point 25 cm away from the surface

Answer 1

Hint: There is no electric field inside a metal object, especially a hollow sphere. Electric potential can be defined as the amount of work done required to move a unit charge from a reference point to the measuring point against the electric field.

Complete Step-by-Step solution:
From the question itself we can find the answer. In this question we have to take care of two concepts. One is related to the electric field and the other one is about electric potential. The hollow sphere is made up of metal. That is, it can conduct electricity. So, there is no electric field inside the hollow sphere. Electric potential can be defined as the work done per coulomb against the electric field to move a charge from a reference point to a measuring point.
In this question, the electric potential is already given. Since the electric field is zero, the potential will be the same everywhere inside the object. That is, the potential at the centre is 10 V. So, the correct option is B.

Additional information:
It is better to remember this figure to understand potential and electric field due to the charged sphere of radius R. Where E is the electric field and V is the potential.

The electric field can be found out by using the formula,
\[E=\dfrac{1}{4\pi {{\varepsilon }_{0}}}\dfrac{Q}{{{r}^{2}}},r > R\], if \[r < R\] the electric field will be zero for a metallic charged sphere.
The potential can be found out by using the formula,
\[V=\dfrac{1}{4\pi {{\varepsilon }_{0}}}\dfrac{Q}{r},r > R\], if \[r < R\] the potential will be constant throughout the body of metallic charged sphere.

Note: Potential will be constant only if the electric field is zero. The electric field at the centre of the hollow sphere will be zero only if the body is a conducting material. At the outside of the material the electric field and potential will vary according to the distance between the measuring point and the body.