A sphere of radius 5 cm has electrostatic potential at the surface of 50 V. Potential at the centre is:

Options

A. 10V
B. Zero
C. 50 V
D. 250 V

Explanation

To solve the problem, we need to determine the electrostatic potential at the center of a sphere given that the potential at its surface is 50 V.

### Step-by-Step Solution:

1. **Understand the Properties of a Conducting Sphere**:
- A conducting sphere in electrostatic equilibrium has the property that the electric field inside the sphere is zero. This means that there is no change in potential inside the sphere.

2. **Given Data**:
- Radius of the sphere, \( r = 5 \, \text{cm} \)
- Electrostatic potential at the surface, \( V_{\text{surface}} = 50 \, \text{V} \)

3. **Electric Field Inside the Sphere**:
- Since the electric field inside a conducting sphere is zero, we can conclude that:
\[ E = 0 \quad \text{(inside the sphere)} \]

4. **Relation Between Electric Field and Potential**:
- The relationship between electric field \( E \) and potential \( V \) is given by:
\[ E = -\frac{dV}{dr} \]
- Since \( E = 0 \), it implies that:
\[ -\frac{dV}{dr} = 0 \implies dV = 0 \]
- This means that the potential does not change with respect to position inside the sphere.

5. **Conclusion about Potential Inside the Sphere**:
- Since there is no change in potential inside the sphere, the potential at any point inside the sphere, including the center, is equal to the potential at the surface.
- Therefore:
\[ V_{\text{center}} = V_{\text{surface}} = 50 \, \text{V} \]

### Final Answer:
The potential at the center of the sphere is **50 V**.

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