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The magnetic field at O is

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$\frac{μ_{0} i}{4 a} (\frac{\sqrt{3}}{π} - \frac{1}{3})$

$\frac{μ_{0} i}{2 a} (\frac{\sqrt{3}}{π} - \frac{1}{3})$

$\frac{μ_{0} i}{2 a} (\frac{\sqrt{2}}{π} - \frac{1}{2})$

$\frac{μ_{0} i}{a} (\frac{\sqrt{3}}{π} - \frac{1}{3})$

answer is A.

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Detailed Solution

B_net = B_straight - B_curved

$B_{1} = \frac{μ_{0} i}{4 π a \cos 60 °} (\cos 30 ° + \cos 30 °)$

$= \frac{μ_{0} i}{2 π a} \cdot \sqrt{3}, \otimes$

$B_{2} = \frac{μ_{0} i}{2 a} \cdot \frac{120 °}{360 °} = \frac{μ_{0} i}{6 a}, ⊙$

$B_{O} = B_{1} - B_{2} = \frac{μ_{0} i}{2 a} (\frac{\sqrt{3}}{π} - \frac{1}{3}), \otimes$

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