Q. Two thin long parallel wires separated by a distance $b$ are carrying currents of $i$ amp each, the magnitude of the force per unit length exerted by one wire over the other is
A) $\frac{\mu_{0}i^{2}}{b^{2}}$
B) $\frac{\mu_{0}i^{2}}{2\pi b}$
C) $\frac{\mu_{0}i}{2\pi b}$
D) $\frac{\mu_{0}i}{2\pi b^{2}}$
Explanation
(b) When two infinitely long parallel conductors carrying currents $i_{1}\ and\ \ i_{2}$ are placed a distance $r$ apart, then force on the unit length of a conductor due to the other conductor is given by
$F = \frac{\mu_{0}}{4\pi}\frac{2i_{1}i_{2}}{r}$
Here, $i_{1} = i_{2} = i\ and\ r = b$
$\therefore F = \frac{\mu_{0}i^{2}}{2\pi b}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.