An insulated charged conducting sphere of radius 5cm has a potential of 10V at the surface. What is the potential at centre?

Options

A. 10V
B. zero
C. same as that at 5 cms from the surface
D. same as that at 25 cms from the surface

Explanation

To solve the problem of finding the potential at the center of an insulated charged conducting sphere with a radius of 5 cm and a surface potential of 10 V, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Properties of a Conducting Sphere**:
- A conducting sphere has the property that any excess charge resides on its surface. Inside the conducting material, the electric field is zero. This means that the potential is constant throughout the conductor.

2. **Identifying Given Data**:
- Radius of the sphere (r) = 5 cm
- Potential at the surface (V_surface) = 10 V

3. **Applying the Concept of Electric Potential**:
- For a conducting sphere, the potential inside the sphere (including at the center) is the same as the potential at the surface. This is because the electric field inside a conductor in electrostatic equilibrium is zero.

4. **Conclusion**:
- Since the potential is constant throughout the conducting sphere, the potential at the center (V_center) is equal to the potential at the surface.
- Therefore, V_center = V_surface = 10 V.

### Final Answer:
The potential at the center of the sphere is **10 V**.

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