Question 28 of 276

An infinite wire has a circular bend of radius a, and carrying a current I as shown in figure. The magnitude of magnetic field at the origin $O$ of the arc is given by :

A$\frac{\mu_0}{4 \pi} \frac{I}{a}\left[\frac{\pi}{2}+1\right]$B$\frac{\mu_0}{4 \pi} \frac{\mathrm{I}}{\mathrm{a}}\left[\frac{3 \pi}{2}+2\right]$C$\frac{\mu_0}{2 \pi} \frac{\mathrm{I}}{\mathrm{a}}\left[\frac{\pi}{2}+2\right]$D$\frac{\mu_0}{4 \pi} \frac{\mathrm{I}}{\mathrm{a}}\left[\frac{3 \pi}{2}+1\right]$

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Answer: (D) $\frac{\mu_0}{4 \pi} \frac{\mathrm{I}}{\mathrm{a}}\left[\frac{3 \pi}{2}+1\right]$

$\begin{aligned} & \mathrm{B}_1=\frac{\mu_0 \mathrm{i}}{4 \pi \mathrm{a}} \otimes \\ & \mathrm{B}_2=\frac{\mu_0}{4 \pi} \frac{\mathrm{i}}{\mathrm{a}}\left(\frac{3 \pi}{2}\right) \otimes \\ & \mathrm{B}_3=0 \\ & \mathrm{~B}=\frac{\mu_0}{4 \pi} \frac{\mathrm{i}}{\mathrm{a}}\left(1 \frac{3 \pi}{2}\right) \otimes\end{aligned}$

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