JEE MAIN - Physics (2025 - 28th January Evening Shift - No. 9)
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An infinite wire has a circular bend of radius a, and carrying a current I as shown in the figure. The magnitude of magnetic field at the origin O of the arc is given by:
$\frac{\mu_0}{2 \pi} \frac{\mathrm{I}}{\mathrm{a}}\left[\frac{\pi}{2}+2\right]$
$\frac{\mu_0}{4 \pi} \frac{\mathrm{I}}{\mathrm{a}}\left[\frac{3 \pi}{2}+1\right]$
$\frac{\mu_0}{4 \pi} \frac{\mathrm{I}}{\mathrm{a}}\left[\frac{\pi}{2}+1\right]$
$\frac{\mu_0}{4 \pi} \frac{\mathrm{I}}{\mathrm{a}}\left[\frac{3 \pi}{2}+2\right]$
Explanation
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$$\begin{aligned} & \mathrm{B}_1=\frac{\mu_0 \mathrm{i}}{4 \pi \mathrm{a}} \otimes \\ & \mathrm{~B}_2=\frac{\mu_0}{4 \pi} \frac{\mathrm{i}}{\mathrm{a}}\left(\frac{3 \pi}{2}\right) \otimes \\ & \mathrm{B}_3=0 \\ & \mathrm{~B}=\frac{\mu_0}{4 \pi} \frac{\mathrm{i}}{\mathrm{a}}\left(1 \frac{3 \pi}{2}\right) \otimes \end{aligned}$$
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