Two charges are at a distance `d` apart. If a copper plate (conducting medium) of thickness `d//2` is placed between them , the effictive force will be

Options

A. `(F)/(2)`
B. zero
C. 2F
D. `sqrt(2F)`

Answer

To solve the problem of finding the effective force between two charges when a copper plate (a conducting medium) is placed between them, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Initial Setup**:
- We have two charges, let's denote them as \( q_1 \) and \( q_2 \), separated by a distance \( d \).
- The force between these two charges in a vacuum (or air) can be calculated using Coulomb's law:
\[ F = k \frac{|q_1 q_2|}{d^2} \]
where \( k \) is Coulomb's constant.

2. **Introducing the Conducting Medium**:
- A copper plate of thickness \( \frac{d}{2} \) is placed between the two charges.
- Since copper is a conductor, it will affect the electric field between the two charges.

3. **Effect of the Conducting Plate**:
- When a conducting plate is placed between two charges, it will polarize and create an induced charge on its surfaces.
- This polarization effectively shields the electric field between the two charges.

4. **Dielectric Constant of a Conductor**:
- The dielectric constant \( K \) for a conductor is considered to be infinite. This is because a conductor can completely shield the electric field.
- Therefore, when calculating the effective force \( F' \) between the charges with the conducting plate in place, we use the formula:
\[ F' = \frac{F}{K} \]
- Since \( K \) is infinite for a conductor, we have:
\[ F' = \frac{F}{\infty} = 0 \]

5. **Conclusion**:
- The effective force between the two charges when a copper plate is placed between them is \( 0 \).

### Final Answer:
The effective force will be \( 0 \).