A hollow spherical conductor of radius 1m has a charge of `250mu C` then electric intensity at a point distance of 0.5m from the centre of the spherical conductor is

Options

A. zero
B. `2.25 xx 10^(6)N//C`
C. `4.5 xx 10^(4) N//C`
D. `9 xx 10^(4) N//C`

Answer

To solve the problem of finding the electric intensity at a point 0.5 m from the center of a hollow spherical conductor with a charge of 250 µC, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Geometry and Charge Distribution**:
- We have a hollow spherical conductor with a radius of 1 m and a total charge of 250 µC.
- The point of interest is located at a distance of 0.5 m from the center of the sphere.

2. **Apply Gauss's Law**:
- Gauss's Law states that the electric field (E) times the area (A) of a closed surface is equal to the charge (Q) enclosed by that surface divided by the permittivity of free space (ε₀):
\[ \Phi_E = E \cdot A = \frac{Q_{\text{enc}}}{\epsilon_0} \]

3. **Determine the Enclosed Charge**:
- Since the point at 0.5 m is inside the hollow conductor (the radius of the conductor is 1 m), the charge enclosed (Q_enc) is zero. This is because the charge resides on the surface of the conductor, and there is no charge within the hollow part.

4. **Calculate the Electric Field**:
- Since the enclosed charge (Q_enc) is zero, we can substitute this into Gauss's Law:
\[ E \cdot A = \frac{0}{\epsilon_0} \]
- This implies that:
\[ E \cdot A = 0 \implies E = 0 \]
- Therefore, the electric field intensity at a point 0.5 m from the center of the hollow spherical conductor is 0.

5. **Conclusion**:
- The electric intensity at a distance of 0.5 m from the center of the hollow spherical conductor is **0 N/C**.

### Final Answer:
The electric intensity at a point 0.5 m from the center of the hollow spherical conductor is **0 N/C**.