The force of repulsion between two point charges is F, when these are at distance 0.5m apart. Now the point charges are replaced by spheres of radii 5 cm each having the same charge as that of the respective point charge. The distance between their centres is again kept 0.5 m. Then the force of repulsion will

Options

A. increase
B. decrease
C. remain F
D. become `(10 F)/9`

Answer

To solve the problem, we need to analyze the change in the force of repulsion when point charges are replaced by spheres of the same charge.

### Step-by-Step Solution:

1. **Understanding the Initial Force**:
The initial force of repulsion \( F \) between two point charges \( q_1 \) and \( q_2 \) separated by a distance \( r = 0.5 \, m \) is given by Coulomb's law:
\[ F = \frac{k \cdot |q_1 \cdot q_2|}{r^2} \]
where \( k \) is Coulomb's constant, \( k = \frac{1}{4 \pi \epsilon_0} \).

2. **Replacing Point Charges with Spheres**:
Now, the point charges are replaced by spheres of radius \( r_s = 5 \, cm = 0.05 \, m \). The distance between the centers of the spheres remains \( 0.5 \, m \).

3. **Calculating the New Effective Distance**:
When considering the spheres, the effective distance \( r' \) between the charges is the distance between their centers, which is:
\[ r' = 0.5 \, m \]
However, since the spheres have a radius, we need to account for the radii of the spheres. The effective distance between the surfaces of the spheres is:
\[ r' = 0.5 \, m - 2 \times 0.05 \, m = 0.5 \, m - 0.1 \, m = 0.4 \, m \]
But since we are looking for the distance between the centers, we keep it as \( 0.5 \, m \).

4. **Calculating the New Force**:
The force of repulsion \( F' \) between the spheres is given by:
\[ F' = \frac{k \cdot |q_1 \cdot q_2|}{(r')^2} \]
Since \( r' = 0.5 \, m \), we can see that the distance remains the same for the centers of the spheres.

5. **Comparing the Forces**:
Since the distance between the centers remains the same, we can conclude that the force of repulsion does not change due to the replacement of point charges with spheres of the same charge. Therefore:
\[ F' = F \]

6. **Conclusion**:
The force of repulsion between the spheres remains the same as that between the point charges, which is \( F \).

### Final Answer:
The force of repulsion will remain \( F \).