A hollow metal sphere of radius 10cm is charged such that the potential on its surface is 80 V. The potential at the centre of the sphere is

Options

A. zero
B. `80 V`
C. `800 V`
D. `8V`

Answer

To solve the problem of finding the potential at the center of a hollow metal sphere, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Properties of Conductors**:
- In electrostatics, a hollow conductor (like a hollow metal sphere) has the property that the electric field inside the conductor is zero when it is in electrostatic equilibrium.

2. **Potential Inside the Hollow Sphere**:
- The potential inside a hollow conductor is constant throughout its volume. This means that the potential at any point inside the hollow sphere, including the center, is the same as the potential on its surface.

3. **Given Data**:
- The radius of the hollow metal sphere is 10 cm, and the potential on its surface is given as 80 V.

4. **Conclusion**:
- Since the potential is constant throughout the hollow sphere, the potential at the center of the sphere is also 80 V.

### Final Answer:
The potential at the center of the hollow metal sphere is **80 V**.

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