Question

Two long straight parallel wires separated by a distance, carrying equal currents exert a force F per unit length on each other. If the distance of separation is doubled, and the current in each is halved, the force per unit length, between them will be :

• A. F
• B. F/2
• C. F/4
• D. F/8

Answer 1

The correct option is D F/8

$F=\frac{{\mu }_o{i}_1{i}_2}{2\pi d}$

by halfing each current, we get and distance is doubled, then

$F=\frac{{\mu }_o\frac{i_1}{2}\frac{i_2}{2}}{2\pi \left(2d\right)}=\frac{1}{8}(\frac{{\mu }_o{i}_1{i}_2}{2\pi d})=\frac{F}{8}$