Q. Two similar coils of radius $R$ are lying concentrically with their planes at right angles to each other. The currents flowing in them are $I$ and $2I$, respectively. The resultant magnetic field induction at the centre will be
A) $\frac{\sqrt{5}\mu_{0}I}{2R}$
B) $\frac{3\mu_{0}I}{2R}$
C) $\frac{\mu_{0}I}{2R}$
D) $\frac{\mu_{0}I}{R}$
Explanation
(a) $B_{1} = \frac{\mu_{0}I}{2R}$
$B_{2} = \frac{\mu_{0}(2I)}{2R}$
$B_{net} = \sqrt{B_{1}^{2} + B_{2}^{2}}$
$= \frac{\mu_{0}(I)}{2R}\sqrt{1 + 4} = \frac{\sqrt{5}\mu_{0}I}{2R}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.