A hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the magnitude of a magnetic field at point p which lies on the centre of the semicircle.

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$\frac{μ_{0} I}{4 πr} (2 + π)$

$\frac{μ_{0} I}{2 πr} (2 + π)$

$\frac{μ_{0} I}{2 πr} (2 - π)$

$\frac{μ_{0} I}{4 πr} (2 - π)$

answer is A.

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Detailed Solution

$\begin{array}{l} B = \vec{B_{1}} + \vec{B_{2}} + \vec{B_{3}} \\ = \frac{μ_{0} I}{4 πr} + \frac{μoI}{4 πr} + \frac{μ_{0} I}{4 r} \\ = \frac{μ_{0} I}{4 πr} (2 + π) \end{array}$

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