A hollow metal sphere of radius `5 cm` is charged so that the potential on its surface is `10 V`. The potential at the centre of the sphere is

Options

A. `0 V`
B. `10 V`
C. same as at point `5 cm` away from the surface
D. same as at point `25 cm` away from the surface

Explanation

To find the potential at the center of a hollow metal sphere with a given surface potential, we can follow these steps:

### Step 1: Understand the properties of a hollow metal sphere
A hollow metal sphere has the property that the electric field inside the sphere is zero. This means that the potential inside the sphere is constant and equal to the potential on its surface.

**Hint:** Remember that in electrostatics, the electric field inside a conductor in electrostatic equilibrium is zero.

### Step 2: Identify the given values
We are given:
- Radius of the sphere = 5 cm (not directly needed for the calculation of potential)
- Surface potential (V_surface) = 10 V

**Hint:** Focus on the potential values rather than the physical dimensions when determining the potential inside the sphere.

### Step 3: Apply the concept of electric potential
Since the electric field inside the hollow sphere is zero, the potential inside the sphere (including at the center) must be the same as the potential on the surface. Therefore, the potential at the center (V_center) is equal to the potential on the surface.

**Hint:** Recall that the potential difference (ΔV) is related to the electric field (E) by the equation ΔV = -∫E·dr. If E = 0, then ΔV = 0.

### Step 4: Conclude the potential at the center
Since the potential at the surface is 10 V, the potential at the center of the sphere is also 10 V.

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