Find the magnetic field at the point P in figure. The curved portion is a semicircle connected to two long straight wires.

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$\frac{μ_{0} i}{2 r} (1 + \frac{1}{π})$

$\frac{μ_{0} i}{2 r} (1 + \frac{2}{π})$

$\frac{μ_{0} i}{2 r} (\frac{1}{2} + \frac{1}{π})$

$\frac{μ_{0} i}{2 r} (\frac{1}{2} + \frac{1}{2 π})$

answer is D.

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Detailed Solution

$\begin{array}{l} \vec{B} = (\frac{μ_{0}}{4 π}) \frac{i}{r} + (\frac{μ_{0}}{4 π}) \frac{πi}{r} \\ = \frac{μ_{0} i}{4 πr} + \frac{μ_{0} i}{4 r} \\ = \frac{μ_{0} i}{2 r} (\frac{1}{2 π} + \frac{1}{2}) \end{array}$

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