Search any question & find its solution
Question:
Answered & Verified by Expert
A current $\mathrm{i}$ is flowing through the loop. The direction of the current and the shape of the loop are as shown in the figure. The magnetic field at the centre of the loop is $\frac{\mu_{0} \mathrm{i}}{\mathrm{R}}$ times
$\left(\mathrm{MA}=\mathrm{R}, \mathrm{MB}=2 \mathrm{R}, \angle \mathrm{DMA}=90^{\circ}\right)$
Options:
$\left(\mathrm{MA}=\mathrm{R}, \mathrm{MB}=2 \mathrm{R}, \angle \mathrm{DMA}=90^{\circ}\right)$
Solution:
1803 Upvotes
Verified Answer
The correct answer is:
$\frac{7}{16}$, but into the plane of the paper
(i) Magnetic field at the centre due to the curved portion $\mathrm{DA}=\frac{\mu_{0} \mathrm{i}}{4 \pi \mathrm{R}}\left(\frac{3 \pi}{2}\right)$
According to right hand screw rule, the magnetic field will be into the plane of paper.
(ii) Magnetic field at $M$ due to $\mathrm{AB}$ is zero.
(iii) Magnetic field at the centre due to the curved portion $B C$ is $\frac{\mu_{0} \mathrm{i}}{4 \pi 2 \mathrm{R}}\left(\frac{\pi}{2}\right)$.
According to right hand screw rule, the magnetic field will be into the plane of paper.
(iv) Magnetic field at M due to $D C$ is zero.
Hence, the resultant magnetic field at M
$$
=\frac{3 \mu_{0} \mathrm{i}}{8 \mathrm{R}}+0+\frac{\mu_{0} \mathrm{i}}{16 \mathrm{R}}+0=\frac{7 \mu_{0} \mathrm{i}}{16 \mathrm{R}}
$$
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.