The electric potential inside a conducting sphere

Options

A. increases from cente to surface
B. decreases from cente to surface
C. remians constant from centre to surface
D. is zero at every point inside

Explanation

### Step-by-Step Solution:

1. **Understanding the Conducting Sphere**:
- A conducting sphere is a conductor that has a uniform distribution of charge on its surface when charged. Inside the conductor, the electric field is zero.

2. **Electric Field Inside the Sphere**:
- According to electrostatic principles, the electric field (E) inside a conductor in electrostatic equilibrium is zero. This means that there is no change in electric potential inside the conducting sphere.

3. **Relation Between Electric Field and Electric Potential**:
- The electric field (E) is related to the electric potential (V) by the equation:
\[ E = -\frac{dV}{dr} \]
- Since the electric field inside the conducting sphere is zero (E = 0), we can conclude that:
\[ -\frac{dV}{dr} = 0 \]
- This implies that the derivative of the potential with respect to radius (r) is zero, indicating that the potential does not change with distance inside the sphere.

4. **Conclusion About Electric Potential**:
- Since the electric potential does not change, it must be constant throughout the interior of the conducting sphere. The value of this constant potential is equal to the potential at the surface of the sphere.

5. **Final Statement**:
- Therefore, the electric potential inside a conducting sphere is constant and equal to the potential at its surface.