Question 13 of 276

A current I flows in an infinitely long wire with cross section in the form of a semicircular ring of radius $\mathrm{R}$. The magnitude of the magnetic induction along its axis is

A$\frac{\mu_0 I}{2 \pi^2 R}$B$\frac{\mu_0 I}{2 \pi R}$C$\frac{\mu_0 I}{4 \pi^2 R}$D$\frac{\mu_0 l}{\pi^2 R}$

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Answer: (D) $\frac{\mu_0 l}{\pi^2 R}$

$\mathrm{d} \overrightarrow{\mathrm{B}}=\frac{\mu_0 \mathrm{di}}{2 \pi \mathrm{R}}[-\cos \theta \hat{\mathbf{i}}-\sin \theta \hat{\mathbf{j}}]$
$\mathrm{di}=\frac{\mathrm{T}}{\pi \mathrm{R}} \mathrm{Rd} \theta$
$=\frac{\mathrm{I}}{\pi} \mathrm{d} \theta$
$\mathrm{d} \overrightarrow{\mathrm{B}}=\frac{\mu_0 \mathrm{I}}{2 \pi^2 \mathrm{R}}(-\cos \theta \hat{\mathrm{i}}-\sin \theta \hat{\mathrm{j}})$


$\vec{B}=-\frac{\mu_0 I}{\pi^2 R} \hat{j}$

JEE Main Physics practice question on Magnetic Effects & Magnetism (Biot-Savart's Law and Ampere's Circuital Law), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.