An electric dipole is placed at the centre of a sphere. Select the correct alternative(s).

Options

A. The flux of electric field through the sphere is zero
B. The electric field is zero at every point of the sphere
C. The electric field is not zero anywhere on the sphere
D. The electric field is zero on a circle on the sphere

Answer

To solve the problem regarding the electric dipole placed at the center of a sphere, we will analyze the statements provided and determine which ones are correct based on the principles of electrostatics.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have an electric dipole consisting of two charges: a positive charge (+q) and a negative charge (-q) separated by a distance 'd'. This dipole is placed at the center of a sphere.

2. **Electric Flux through the Sphere**:
- The electric flux (Φ) through a closed surface is given by Gauss's law, which states that Φ = Q_enc/ε₀, where Q_enc is the total charge enclosed by the surface and ε₀ is the permittivity of free space.
- In this case, the dipole does not enclose any net charge because the positive and negative charges cancel each other out (Q_enc = +q - q = 0).
- Therefore, the electric flux through the sphere is zero (Φ = 0).

3. **Electric Field Inside the Sphere**:
- While the electric flux through the sphere is zero, it does not imply that the electric field (E) is zero at every point inside the sphere. The electric field due to a dipole exists at various points in space, including inside the sphere.
- The electric field is not uniform and varies with position, but it is not zero anywhere inside the sphere.

4. **Analyzing the Statements**:
- **Statement 1**: The flux of electric field through the sphere is zero. **(Correct)**
- **Statement 2**: Electric field is zero at every point of the sphere. **(Incorrect)**
- **Statement 3**: Electric field is not zero at every point of the sphere. **(Correct)**
- **Statement 4**: Electric field is zero on a circle. **(Incorrect)**

5. **Conclusion**:
- The correct alternatives are **Statement 1** and **Statement 3**.