Q. The magnetic induction at the centre $O$ in the figure shown is
A) $\frac{\mu_{0}i}{4}\left( \frac{1}{R_{1}} - \frac{1}{R_{2}} \right)$
B) $\frac{\mu_{0}i}{4}\left( \frac{1}{R_{1}} + \frac{1}{R_{2}} \right)$
C) $\frac{\mu_{0}i}{4}\left( R_{1} - R_{2} \right)$
D) $\frac{\mu_{0}i}{4}\left( R_{1} + R_{2} \right)$
Explanation
(a) In the following figure, magnetic fields at $O$ due to section 1, 2, 3 and 4 are considered as $B_{1},\ B_{2},\ B_{3}$ and $B_{4}$ respectively
$B_{1} = B_{3} = 0$
$B_{2} = \frac{\mu_{0}}{4\pi} \bullet \frac{\pi i}{R_{1}}\bigotimes$
$B_{4} = \frac{\mu_{0}}{4\pi} \bullet \frac{\pi i}{R_{2}}\bigodot\ \ As\ \left| B_{2} \right| > \left| B_{4} \right|$
So $B_{net} = B_{2} - B_{4} \Rightarrow B_{net} = \frac{\mu_{0}i}{4}\left( \frac{1}{R_{1}} - \frac{1}{R_{2}} \right)\bigotimes$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.