A hollow sphere of charge does not produce an electric field at any-

Options

A. Interior point
B. Outer point
C. Surface point
D. None of the above

Answer

To solve the question regarding the electric field produced by a hollow sphere of charge, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**: We need to determine at which point (interior, surface, or exterior) a hollow sphere of charge does not produce an electric field.

2. **Applying Gauss's Law**: Gauss's law states that the electric flux through a closed surface is proportional to the charge enclosed by that surface. Mathematically, it is given by:
\[ \Phi_E = \oint \vec{E} \cdot d\vec{A} = \frac{Q_{\text{enc}}}{\epsilon_0} \]

3. **Analyzing the Interior Point**:
- Consider a point inside the hollow sphere (interior point).
- For a Gaussian surface inside the hollow sphere, the enclosed charge \( Q_{\text{enc}} = 0 \) (since all the charge resides on the surface).
- Therefore, by Gauss's law:
\[ \oint \vec{E} \cdot d\vec{A} = 0 \implies E = 0 \quad \text{(inside the hollow sphere)} \]

4. **Analyzing the Surface Point**:
- Now consider a point on the surface of the hollow sphere.
- For a Gaussian surface that coincides with the surface of the hollow sphere, the enclosed charge \( Q_{\text{enc}} = Q \) (the total charge on the surface).
- Applying Gauss's law:
\[ \oint \vec{E} \cdot d\vec{A} = \frac{Q}{\epsilon_0} \]
- This leads to a non-zero electric field at the surface, calculated as:
\[ E_{\text{surface}} = \frac{Q}{4\pi \epsilon_0 R^2} \quad \text{(where \( R \) is the radius of the sphere)} \]

5. **Analyzing the Exterior Point**:
- Now consider a point outside the hollow sphere.
- For a Gaussian surface outside the hollow sphere, the enclosed charge \( Q_{\text{enc}} = Q \).
- Again applying Gauss's law:
\[ \oint \vec{E} \cdot d\vec{A} = \frac{Q}{\epsilon_0} \]
- This results in a non-zero electric field outside the sphere:
\[ E_{\text{outside}} = \frac{Q}{4\pi \epsilon_0 r^2} \quad \text{(where \( r \) is the distance from the center)} \]

6. **Conclusion**: The electric field is zero only at interior points of the hollow sphere. At the surface and outside the sphere, the electric field is non-zero.

### Final Answer:
The correct option is **interior point**.