Q. Two straight long conductors $AOB\ and\ COD$ are perpendicular to each other and carry currents $i_{1}\ and\ i_{2}$. The magnitude of the magnetic induction at a point $P$ at a distance $a\ from\ the\ point\ O\ in\ \ a\ direction\ perpendicular\ to\ the\ plane\ ABCD$ is
A) $\frac{\mu_{0}}{2\pi a}\left( i_{1} + i_{2} \right)$
B) $\frac{\mu_{0}}{2\pi a}\left( i_{1} - i_{2} \right)$
C) $\frac{\mu_{0}}{2\pi a}\left( i_{1}^{2} + i_{2}^{2} \right)^{1/2}$
D) $\frac{\mu_{0}}{2\pi a}\ \frac{i_{1}i_{2}}{(i_{1} + i_{2})}$
Explanation
(c) The point $P$ is lying symmetrically w.r.t. the two long straight current carrying conductors. The magnetic field at $P$ due to these current carrying conductors are mutually perpendicular.
$B_{1} = \frac{\mu_{0}}{2\pi}.\frac{i_{1}}{a}$
$B_{2} = \frac{\mu_{0}}{2\pi}.\frac{i_{2}}{a}$
$B\ \ = \ \sqrt{B_{1}^{2} + B_{2}^{2}} = \frac{\mu_{0}}{2\pi a}\ \left( i_{1}^{2} + i_{2}^{2} \right)^{1/2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.