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
For two parallel current-carrying wires:
$F = \frac{\mu_0 I^2}{2 \pi r}$
Wire 1 : upward, Wire 2 : downward, Wire 3 : upward, Wire 4 : downward
Forces on Wire 2:
$F_{21} = \frac{\mu_0 I^2}{2 \pi d}$ (repulsion from Wire 1 → right)
$F_{23} = \frac{\mu_0 I^2}{2 \pi d}$ (repulsion from Wire 3 → right)
$F_{24} = \frac{\mu_0 I^2}{2 \pi (2d)} = \frac{\mu_0 I^2}{4 \pi d}$ (attraction from Wire 4 → right)
Net force:
$F_{net} = \frac{\mu_0 I^2}{2 \pi d} + \frac{\mu_0 I^2}{2 \pi d} + \frac{\mu_0 I^2}{4 \pi d}$
$F_{net} = \frac{5 \mu_0 I^2}{4 \pi d}$ (towards right)
Final Answer: Net force on wire 2 is directed towards right.