A hollow metallic sphere of radius 0.1 m is charged to a potential of 5 V. The potential at its centre is

Options

A. inifinite
B. 5 V
C. zero
D. cannot be determined

Answer

To solve the problem, we need to understand the properties of electric potential in a hollow metallic sphere.

### Step-by-Step Solution:

1. **Understand the Concept of Electric Potential**:
- The electric potential (V) at a point in space due to a charged object is defined as the work done in bringing a unit positive charge from infinity to that point without any acceleration.

2. **Properties of a Hollow Metallic Sphere**:
- For a hollow metallic sphere, the electric field inside the sphere is zero. This means that the potential inside the sphere is constant and equal to the potential at its surface.

3. **Given Data**:
- Radius of the hollow metallic sphere, \( R = 0.1 \, \text{m} \)
- Potential at the surface of the sphere, \( V = 5 \, \text{V} \)

4. **Potential at the Surface**:
- The potential at the surface of the sphere is given as 5 V.

5. **Potential at the Center**:
- Since the potential inside a hollow metallic sphere is constant and equal to the potential at the surface, the potential at the center of the sphere is also 5 V.

6. **Conclusion**:
- Therefore, the potential at the center of the hollow metallic sphere is **5 V**.

### Final Answer:
The potential at the center of the hollow metallic sphere is **5 V**.

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