Equal currents are flowing in four infinitely long wires. The distance between each other is the same and directions of currents are as shown in the figure. The net force on wire 2 is
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → directed towards right
Two long parallel wires exert a force per unit length \( \mu_0 I_1 I_2/2\pi r \) on each other: parallel currents attract and antiparallel currents repel. Let \( F_0 = \mu_0 I^{2}/2\pi d \) be the force per unit length for neighbouring wires at distance \( d \); a wire at distance \( 2d \) gives \( F_0/2 \). Take right as positive. The currents in wires 1, 2, 3, 4 are up, down, up, down.
\( \displaystyle F_{21} = +F_0 \quad \text{(wire 1 is antiparallel to 2 and repels it, to the right)} \)
\( \displaystyle F_{23} = -F_0 \quad \text{(wire 3 is antiparallel to 2 and repels it, to the left)} \)
\( \displaystyle F_{24} = +\frac{F_0}{2} \quad \text{(wire 4 is parallel to 2 at distance } 2d \text{ and attracts it, to the right)} \)
\( \displaystyle F_{2} = F_0 - F_0 + \frac{F_0}{2} = +\frac{F_0}{2} \)
So the net force on wire 2 is directed towards the right.