Q. In the figure shown there are two semicircles of radii $r_{1}$ and $r_{2}$ in which a current $i$ is flowing. The magnetic induction at the centre $O$ will be
A) $\frac{\mu_{0}i}{r}(r_{1} + r_{2})$
B) $\frac{\mu_{0}i}{4}(r_{1} - r_{2})$
C) $\frac{\mu_{0}i}{4}\left( \frac{r_{1} + r_{2}}{r_{1}r_{2}} \right)$
D) $\frac{\mu_{0}i}{4}\left( \frac{r_{2} - r_{1}}{r_{1}r_{2}} \right)$
Explanation
(c) The magnetic induction due to both semicircular parts will be in the same direction perpendicular to the paper inwards
$\therefore B = B_{1} + B_{2} = \frac{\mu_{0}i}{4r_{1}} + \frac{\mu_{0}i}{4r_{2}} = \frac{\mu_{0}i}{4}\left( \frac{r_{1} + r_{2}}{r_{1}r_{2}} \right)\bigotimes$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.