If the force exerted by an electric dipole on a charge q at distance of 1 m is F, the force at a point 2 m away in the same direction will be

Options

A. `F/2`
B. `F/4`
C. `F/6`
D. `F/8`

Answer

To solve the problem, we need to understand how the force exerted by an electric dipole on a charge varies with distance. The force \( F \) exerted by an electric dipole on a point charge \( q \) at a distance \( r \) is given by the formula:

\[ F \propto \frac{1}{r^3} \]

This means that the force is inversely proportional to the cube of the distance from the dipole.

### Step-by-Step Solution:

1. **Identify the initial conditions**:
- We know that the force \( F \) exerted by the electric dipole on the charge \( q \) at a distance \( r = 1 \, \text{m} \) is \( F \).

2. **Write the relationship for the force**:
- According to the relationship, we can express the force at a distance \( r \) as:
\[ F = k \cdot \frac{q}{r^3} \]
where \( k \) is a constant that depends on the dipole moment and other factors.

3. **Calculate the force at \( r = 2 \, \text{m} \)**:
- Now, we need to find the force \( F' \) at a distance \( r = 2 \, \text{m} \):
\[ F' = k \cdot \frac{q}{(2)^3} = k \cdot \frac{q}{8} \]

4. **Relate \( F' \) to \( F \)**:
- Since we know \( F = k \cdot \frac{q}{(1)^3} = k \cdot q \), we can relate \( F' \) to \( F \):
\[ F' = \frac{F}{8} \]

5. **Conclusion**:
- Therefore, the force at a distance of 2 meters in the same direction will be:
\[ F' = \frac{F}{8} \]

### Final Answer:
The force at a point 2 m away in the same direction will be \( \frac{F}{8} \).

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