Q.
The magnetic field induction at the centre O, in the arrangement shown in figure is
A) $\frac{\mu_{0}}{4\pi}\frac{i}{r}(4 + \pi)$
B) $\frac{\mu_{0}}{4\pi}\frac{i}{r}(3 + \pi)$
C) $\frac{\mu_{0}}{4\pi}\frac{i}{r}(2 + \pi)$
D) $\frac{\mu_{0}}{4\pi}\frac{i}{r}(1 + \pi)$
Explanation
(c) $B_{0} = B_{PQ} + B_{QR} + B_{RO}$
$= \ \frac{\mu_{0}}{2\pi}\frac{i}{r} + \frac{\mu_{0}(1/2)i}{2\pi} + 0$
$= \ \frac{\mu_{0}}{4\pi}\frac{2i}{r} + \ \frac{\mu_{0}}{4\pi}\frac{\pi i}{r} = \frac{\mu_{0}}{4\pi}\frac{i}{r}\ (2 + \pi)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.