A metallic hollow spherical surface of radius 5 cm is charged such that the potential on its surface is 10 V. The potential at the centre is :

Options

A. zero
B. 10 V
C. same as at a point 5 cm away from the surface
D. same as at a point 25 cm away from the surface

Answer

To solve the problem of finding the potential at the center of a metallic hollow spherical surface with a radius of 5 cm and a potential of 10 V on its surface, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Properties of a Hollow Spherical Conductor:**
- A metallic hollow spherical conductor has the property that the electric field inside the hollow part is zero when it is charged. This means that the potential inside the hollow sphere is constant and equal to the potential on its surface.

2. **Identify Given Values:**
- Radius of the hollow sphere, \( R = 5 \, \text{cm} \)
- Potential on the surface, \( V_{\text{surface}} = 10 \, \text{V} \)

3. **Use the Property of Equipotential Surfaces:**
- Since the hollow sphere is a conductor, it is an equipotential surface. This means that the potential at any point inside the conductor (including the center) is the same as the potential on the surface.

4. **Conclude the Potential at the Center:**
- Therefore, the potential at the center of the hollow sphere is equal to the potential on its surface:
\[ V_{\text{center}} = V_{\text{surface}} = 10 \, \text{V} \]

5. **Final Answer:**
- The potential at the center of the hollow spherical surface is \( 10 \, \text{V} \).