Fine electric dipoles of charge 'q' each are placed into the shell .What will be the amount of electric flux associated with shell ?

Options

A. `Sqe_(0)`
B. `(10q)/(epsilon_(0))`
C. Zero
D. `(5q)/(epsilon_(0))`

Explanation

To solve the problem of finding the electric flux associated with a shell containing 5 electric dipoles of charge 'q' each, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Electric Dipoles**:
An electric dipole consists of two equal and opposite charges. For each dipole, we have a positive charge (+q) and a negative charge (-q).

2. **Total Charges in the Shell**:
Since there are 5 dipoles, we can calculate the total number of positive and negative charges:
- Total positive charge = 5 * (+q) = +5q
- Total negative charge = 5 * (-q) = -5q

3. **Calculating Net Charge**:
The net charge (Q_net) inside the shell can be calculated by adding the total positive and negative charges:
\[ Q_{net} = +5q + (-5q) = 0 \]

4. **Applying Gauss's Law**:
According to Gauss's Law, the electric flux (Φ) through a closed surface is given by:
\[ \Phi = \frac{Q_{net}}{\epsilon_0} \]
where \( \epsilon_0 \) is the permittivity of free space.

5. **Substituting the Net Charge**:
Since we found that the net charge \( Q_{net} = 0 \), we substitute this into Gauss's Law:
\[ \Phi = \frac{0}{\epsilon_0} = 0 \]

6. **Conclusion**:
Therefore, the total electric flux associated with the shell is zero.

### Final Answer:
The amount of electric flux associated with the shell is **zero**.

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