A given charge is situated at a certain distance from an electric dipole in the end-on position experiences a force `F` If the distance of the charge is doubled, the force acting on the charge will be

Options

A. 2F
B. `(F )/(2)`
C. `(F)/(4)`
D. `(F )/(8)`

Answer

To solve the problem, we need to analyze how the force acting on a charge due to an electric dipole changes when the distance from the dipole is altered. Here are the steps to derive the solution:

### Step-by-Step Solution:

1. **Understand the Initial Setup**:
- We have an electric dipole and a charge placed at a distance \( R \) from the dipole in the end-on position. The force experienced by the charge at this distance is \( F \).

2. **Express the Force in Terms of Distance**:
- The force \( F \) acting on the charge due to the dipole is inversely proportional to the cube of the distance from the dipole. This can be expressed as:
\[ F \propto \frac{1}{R^3} \]
- We can write this relationship as:
\[ F = k \cdot \frac{1}{R^3} \]
where \( k \) is a proportionality constant.

3. **Change the Distance**:
- Now, we double the distance from the dipole, so the new distance becomes \( R' = 2R \).

4. **Calculate the New Force**:
- The new force \( F' \) acting on the charge at this new distance can be expressed similarly:
\[ F' \propto \frac{1}{(2R)^3} \]
- This simplifies to:
\[ F' \propto \frac{1}{8R^3} \]
- We can write this as:
\[ F' = k \cdot \frac{1}{(2R)^3} = k \cdot \frac{1}{8R^3} \]

5. **Relate the Two Forces**:
- Now we can relate \( F' \) to \( F \):
\[ F' = \frac{1}{8} \cdot k \cdot \frac{1}{R^3} = \frac{F}{8} \]

6. **Conclusion**:
- Therefore, when the distance of the charge is doubled, the new force \( F' \) acting on the charge will be:
\[ F' = \frac{F}{8} \]

### Final Answer:
When the distance of the charge is doubled, the force acting on the charge will be \( \frac{F}{8} \).