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

Answer

To solve the problem of finding the potential at the center of a hollow metal sphere given that the potential on its surface is 80 V, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Properties of a Hollow Metal Sphere**:
- A hollow metal sphere is a conductor. When charged, the charge resides on the surface of the sphere.
- Inside a conductor in electrostatic equilibrium, the electric field is zero.

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

3. **Given Data**:
- The radius of the sphere is 10 cm (this is not directly needed for the calculation of potential).
- The potential on the surface of the sphere is given as 80 V.

4. **Conclusion**:
- Since the potential inside the hollow metal sphere is the same as the potential on its surface, the potential at the center of the sphere is also 80 V.

Thus, the potential at the center of the sphere is **80 V**.

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

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