An electric dipole is placed at the centre of a sphere. Mark the correct options:

Options

A. Electric field is zero at every point of the sphere
B. Electic field is zero anywhere on the sphere
C. The flux of electric field is not zero through the sphere
D. All of these

Explanation

To analyze the situation of an electric dipole placed at the center of a sphere, we will go through the relevant concepts step by step.

### Step 1: Understanding the Electric Dipole
An electric dipole consists of two equal and opposite charges separated by a small distance. The net charge of the dipole is zero, which is crucial for our analysis.

**Hint:** Remember that the electric dipole has a total charge of zero.

### Step 2: Applying Gauss's Law
According to Gauss's Law, the electric flux through a closed surface is proportional to the net charge enclosed within that surface. Since the dipole has a net charge of zero, the electric flux through the sphere surrounding the dipole is also zero.

**Hint:** Recall that Gauss's Law states that the electric flux (Φ) is given by Φ = Q_enclosed/ε₀, where Q_enclosed is the charge inside the surface.

### Step 3: Evaluating Electric Field Inside the Sphere
Even though the electric flux through the sphere is zero, this does not mean that the electric field is zero at every point inside the sphere. The electric field due to a dipole varies with position, and there will be points within the sphere where the electric field is non-zero.

**Hint:** Consider that the electric field can be non-zero even if the total flux is zero.

### Step 4: Analyzing Electric Potential
The electric potential is related to the electric field. While the electric field may not be zero at every point, the potential can be constant or zero at certain points. However, the potential is not necessarily zero everywhere in the sphere.

**Hint:** Remember that electric potential can be constant even if the electric field is not zero.

### Conclusion
Based on the analysis:
- The electric flux through the sphere is zero.
- The electric field is not zero at every point on the sphere.
- The electric potential is not zero everywhere in the sphere.

Thus, the correct option is that the electric field is not zero at every point on the sphere, and the flux through the sphere is zero.

### Final Answer
- The electric field is not zero at every point on the sphere.
- The electric flux through the sphere is zero.