Question

Two wires carrying currents \( I \) and \( 2I \) (in opposite directions) are parallel to each other. Third wire carrying current \( I \) is placed midway between the two wires and anti-parallel to a wire carrying current \( I \). Force due to magnetic field on third wire will be:

• A. towards a wire carrying current \( I \)
• B. perpendicular to plane of currents.
• C. zero
• D. towards a wire carrying current \( 2I \)

Hint:

The force between two parallel currents is attractive if the currents are in opposite directions and repulsive if they are in the same direction. The force is stronger for larger currents.

Answer 1

The Correct Option is D

Step 1: Understanding the Force on the Wire.
The force on a wire carrying current \( I \) due to the magnetic field from another wire is given by: \[ F = \frac{\mu_0 I_1 I_2}{2\pi d} \] where \( d \) is the distance between the wires. Since the third wire is placed midway between the two wires and anti-parallel to one of the wires, the force on it will be directed towards the wire carrying the larger current (i.e., towards the wire carrying current \( 2I \)).
Step 2: Final Answer.
Thus, the force on the third wire will be towards the wire carrying current \( 2I \).