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 are is given by :

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$\frac{μ_{0}}{4 π} \frac{I}{a} [\frac{3 π}{2} + 1]$

$\frac{μ_{0}}{4 π} \frac{I}{a} [\frac{3 π}{2} + 2]$

$\frac{μ_{0}}{4 π} \frac{I}{a} [\frac{π}{2} + 1]$

$\frac{μ_{0}}{2 π} \frac{I}{a} [\frac{π}{2} + 2]$

answer is B.

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Detailed Solution

$\begin{array}{l} B_{1} = \frac{μ_{0} i}{4 πa} \otimes \\ B_{2} = \frac{μ_{0}}{4 π} \frac{i}{a} (\frac{3 π}{2}) \otimes \\ B_{3} = 0 \\ B = \frac{μ_{0}}{4 π} \frac{i}{a} (1 + \frac{3 π}{2}) \otimes \end{array}$

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