Four dipoles each of magnitudes of charges `+-e` are placed inside a sphere. The total flux of E coming out of the sphere is

Options

A. zero
B. `(4e)/epsilon_0`
C. `(8e)/epsilon_0`
D. none of these

Explanation

To solve the problem regarding the total electric flux coming out of a sphere containing four dipoles, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Dipole**:
- A dipole consists of two equal and opposite charges. In this case, each dipole has charges of +e and -e.

2. **Identifying the Total Charge**:
- Since there are four dipoles, we can calculate the total charge inside the sphere.
- Each dipole contributes a net charge of \( +e - e = 0 \).
- Therefore, for four dipoles, the total charge inside the sphere is:
\[ Q_{\text{net}} = 4 \times ( +e + (-e) ) = 0 \]

3. **Applying Gauss's Law**:
- Gauss's Law states that the electric flux \( \Phi_E \) through a closed surface is proportional to the charge enclosed by that surface:
\[ \Phi_E = \frac{Q_{\text{inside}}}{\epsilon_0} \]
- Here, \( Q_{\text{inside}} \) is the net charge inside the sphere, which we have found to be zero.

4. **Calculating the Total Flux**:
- Substituting the net charge into Gauss's Law:
\[ \Phi_E = \frac{0}{\epsilon_0} = 0 \]
- Thus, the total electric flux coming out of the sphere is zero.

5. **Conclusion**:
- The total flux of electric field \( E \) coming out of the sphere is \( 0 \).

### Final Answer:
The total flux of \( E \) coming out of the sphere is \( 0 \).

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