A force of `4N` is acting between two charges in air.If the space between them is completelly filled with glass `(epsilon_(r)=8)` then the new force will be

Options

A. `2N`
B. `5N`
C. `0.2N`
D. `0.5N`

Explanation

To solve the problem of finding the new force between two charges when the space between them is filled with glass (dielectric constant \( \epsilon_r = 8 \)), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Initial Force**:
The initial force \( F \) between the two charges in air is given as \( 4 \, \text{N} \).

2. **Coulomb's Law**:
According to Coulomb's law, the force between two point charges \( q_1 \) and \( q_2 \) separated by a distance \( r \) in a vacuum (or air) is given by:
\[ F = \frac{1}{4\pi \epsilon_0} \cdot \frac{q_1 q_2}{r^2} \]
where \( \epsilon_0 \) is the permittivity of free space.

3. **Effect of Dielectric Medium**:
When a dielectric medium is introduced, the force between the charges changes. The new force \( F' \) in a medium with dielectric constant \( \epsilon_r \) is given by:
\[ F' = \frac{F}{\epsilon_r} \]

4. **Substituting Values**:
Here, the dielectric constant \( \epsilon_r \) for glass is given as \( 8 \). Therefore, we can substitute the values:
\[ F' = \frac{4 \, \text{N}}{8} \]

5. **Calculating the New Force**:
Performing the calculation:
\[ F' = \frac{4}{8} = 0.5 \, \text{N} \]

6. **Final Answer**:
The new force between the charges when the space is filled with glass is \( 0.5 \, \text{N} \).

### Summary:
The new force acting between the two charges when the space is filled with glass is \( 0.5 \, \text{N} \).

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