A hollow metal sphere of radius `5 cm` is charged such that the potential on its surface is `10 V`. The potential at a distance of `2 cm` from the centre of the sphere

Options

A. Zero
B. `10 V`
C. `4 V`
D. `10//3 V`

Explanation

To find the potential at a distance of 2 cm from the center of a hollow metal sphere with a radius of 5 cm and a surface potential of 10 V, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Properties of Conductors:**
- A hollow metal sphere is a conductor. Inside a conductor, the electric field is zero. This means that the potential is constant throughout the conductor.

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

3. **Determine the Location of Interest:**
- We need to find the potential at a distance of \( r = 2 \, \text{cm} \) from the center of the sphere.

4. **Analyze the Location Relative to the Sphere:**
- The distance \( r = 2 \, \text{cm} \) is less than the radius of the sphere \( R = 5 \, \text{cm} \). Therefore, this point lies inside the hollow sphere.

5. **Apply the Concept of Equipotential Surfaces:**
- Since the electric field inside the hollow conductor is zero, the potential inside the sphere is constant and equal to the potential on the surface.

6. **Conclude the Potential Inside the Sphere:**
- Therefore, the potential at a distance of 2 cm from the center of the sphere is the same as the potential on the surface, which is \( 10 \, \text{V} \).

### Final Answer:
The potential at a distance of 2 cm from the center of the sphere is \( 10 \, \text{V} \).

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