Search any question & find its solution
Question:
Answered & Verified by Expert
In the loop shown, the magnetic induction at the point $\mathrm{O}$ is
Options:
Solution:
2002 Upvotes
Verified Answer
The correct answer is:
$\frac{\mu_{0} \mathrm{I}}{8}\left(\frac{\mathrm{R}_{1}+\mathrm{R}_{2}}{\mathrm{R}_{\mathrm{1}} \mathrm{R}_{2}}\right)$
Net magnetic field at $O$
$$
\begin{aligned}
B &=B_{1}+B_{2}=\frac{-\pi / 2}{2 \pi}-\frac{\mu_{0} I}{2 R_{1}}+\frac{\pi / 2}{2 \pi} \cdot \frac{\mu_{0} I}{2 R_{2}} \\
&=\frac{\mu_{0} I}{8}\left(\frac{R_{1}+R_{2}}{R_{1} R_{2}}\right)
\end{aligned}
$$
$$
\begin{aligned}
B &=B_{1}+B_{2}=\frac{-\pi / 2}{2 \pi}-\frac{\mu_{0} I}{2 R_{1}}+\frac{\pi / 2}{2 \pi} \cdot \frac{\mu_{0} I}{2 R_{2}} \\
&=\frac{\mu_{0} I}{8}\left(\frac{R_{1}+R_{2}}{R_{1} R_{2}}\right)
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.