Two charge spheres separated at a distance d exert a force F on each other. If they are immersed in a liquid of dielectric constant K=2, then the force (if all conditions are same) is

Options

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

Answer

To solve the problem, we will use Coulomb's law, which describes the force between two point charges. Let's break down the solution step by step.

### Step-by-Step Solution:

1. **Understanding Coulomb's Law**:
Coulomb's law states that the force \( F_0 \) between two point charges \( q_1 \) and \( q_2 \) separated by a distance \( r \) in a vacuum (or air) is given by:
\[ F_0 = \frac{K q_1 q_2}{r^2} \]
where \( K \) is Coulomb's constant, approximately \( 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \).

2. **Effect of Dielectric Medium**:
When the charges are placed in a medium with a dielectric constant \( K \), the force \( F \) between the charges is modified as follows:
\[ F = \frac{F_0}{K} \]
This means that the force in the medium is equal to the force in a vacuum divided by the dielectric constant.

3. **Given Values**:
- The initial force in air (or vacuum) is \( F_0 = F \).
- The dielectric constant of the liquid is \( K = 2 \).

4. **Calculating the New Force**:
Substitute the values into the modified formula:
\[ F = \frac{F_0}{K} = \frac{F}{2} \]

5. **Final Result**:
Therefore, the force between the two charged spheres when immersed in the liquid is:
\[ F = \frac{F}{2} \]

### Conclusion:
The force exerted by the two charged spheres when immersed in a liquid with a dielectric constant \( K = 2 \) is \( \frac{F}{2} \).

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