A sphere encloses an electric dipole withon it. The total flux across the sphere is

Options

A. zero
B. half that due to a single charge
C. double that due to a single charge
D. dependent on the position of dipole.

Explanation

To solve the problem of finding the total electric flux across a sphere that encloses an electric dipole, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Electric Flux**:
Electric flux (Φ) through a closed surface is defined as the integral of the electric field (E) over the surface area (A) of the closed surface. Mathematically, it is expressed as:
\[ \Phi = \oint E \cdot dA \]

2. **Apply Gauss's Law**:
According to Gauss's Law, the total electric flux through a closed surface is equal to the charge enclosed (Q_enclosed) divided by the permittivity of free space (ε₀):
\[ \Phi = \frac{Q_{\text{enclosed}}}{\epsilon_0} \]

3. **Identify the Charges in the Dipole**:
An electric dipole consists of two equal and opposite charges, +q and -q, separated by a small distance. Therefore, when we consider the dipole placed inside the sphere, the total charge enclosed by the sphere is:
\[ Q_{\text{enclosed}} = +q + (-q) = 0 \]

4. **Calculate the Total Flux**:
Since the total charge enclosed by the sphere is zero, we can substitute this value into Gauss's Law:
\[ \Phi = \frac{0}{\epsilon_0} = 0 \]

5. **Conclusion**:
The total electric flux across the sphere that encloses the electric dipole is zero.

### Final Answer:
The total flux across the sphere is **0**.

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