Q. Two thin, long, parallel wires, separated by a distance $d$ carry a current of $i$ ampere in the same direction. They will
A) Attract each other with a force of $\frac{\mu_{0}i^{2}}{(2\pi d)}$
B) Repel each other with a force of $\frac{\mu_{0}i^{2}}{(2\pi d)}$
C) Attract each other with a force of $\frac{\mu_{0}i^{2}}{\left( 2\pi d^{2} \right)}$
D) Repel each other with a force of $\frac{\mu_{0}i^{2}}{(2\pi d^{2})}$
Explanation
(a) The force per unit length between the two wires is
$\frac{F}{l} = \frac{\mu_{0}}{4\pi}\ .\frac{2i^{2}}{d} = \frac{\mu_{0}i^{2}}{2\pi d}$
The force will be attractive as current directions in both are same.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.