Question

Two thin long parallel wires separated by a distance \( r \) from each other in vacuum carry a current of 1 ampere in opposite directions. Then, they will

• A. Repel each other with a force per unit length of \( \frac{\mu_0 I^2}{2 \pi r} \)
• B. Attract each other with a force per unit length of \( \frac{\mu_0 I^2}{2 \pi r} \)
• C. Attract each other with a force per unit length of \( \frac{\mu_0 I^2}{\pi r} \)
• D. Repel each other with a force per unit length of \( \frac{\mu_0 I^2}{\pi r} \)

Hint:

For two parallel wires carrying currents in opposite directions, the force between them is repulsive and is proportional to the product of the currents and inversely proportional to the distance between them.

Answer 1

The Correct Option is A

The force per unit length between two parallel wires carrying currents in opposite directions is given by the formula: \[ F = \frac{\mu_0 I_1 I_2}{2 \pi r} \] where \( \mu_0 \) is the permeability of free space, \( I_1 \) and \( I_2 \) are the currents in the wires, and \( r \) is the distance between them. Since the currents are in opposite directions, the wires will repel each other. Thus, the correct answer is \( \frac{\mu_0 I^2}{2 \pi r} \), and the wires repel each other.