The force between two parallel current carrying wires is independent of

Options

A. their distance of separation
B. the length of the wires
C. the radii of the wires
D. the medium in which they are placed

Answer

To determine what the force between two parallel current-carrying wires is independent of, we can analyze the formula for the force per unit length between the wires.

### Step-by-Step Solution:

1. **Understand the Formula**: The force per unit length (F/L) between two parallel current-carrying wires is given by the formula:
\[ \frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi D} \]
where:
- \( F \) is the force between the wires,
- \( L \) is the length of the wires,
- \( \mu_0 \) is the permeability of free space,
- \( I_1 \) and \( I_2 \) are the currents in the wires,
- \( D \) is the distance between the wires.

2. **Identify Dependencies**: From the formula, we can identify the quantities that the force depends on:
- The force depends on the currents \( I_1 \) and \( I_2 \).
- The force is also dependent on the distance \( D \) between the wires.
- The force is influenced by the medium through the permeability \( \mu_0 \).

3. **Consider Length of Wires**: The force per unit length is independent of the actual length of the wires \( L \) since it is a per unit length quantity. However, the total force will depend on the length of the wires if we multiply by \( L \).

4. **Examine Wire Radius**: The formula does not include any term related to the radius of the wires. This indicates that the force between the wires does not depend on their radius.

5. **Conclusion**: Therefore, the force between two parallel current-carrying wires is independent of the radius of the wires.

### Final Answer:
The force between two parallel current-carrying wires is independent of the radius of the wires.