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The magnetic field at centre O is

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$\frac{μ_{0} I}{2 R} [\frac{1}{π \sqrt{3}} - \frac{5}{6}], \otimes$

$\frac{μ_{0} I}{2 R} [\frac{1}{π \sqrt{3}} + \frac{5}{6}], \otimes$

$\frac{μ_{0} I}{4 R} [\frac{1}{π \sqrt{3}} + \frac{5}{3}], \otimes$

$\frac{μ_{0} I}{R} [\frac{1}{π \sqrt{3}} + \frac{5}{2}], \otimes$

answer is B.

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Detailed Solution

$B_{1} = \frac{μ_{0} I}{4 π \cdot R \cos 30^{0}} (\cos 60^{0} + \cos 60^{0}) = \frac{μ_{0} I}{2 \sqrt{3} π R}, \otimes$

$B_{2} = \frac{μ_{0} I}{2 r} \cdot \frac{300^{0}}{360^{0}} = \frac{5 μ_{0} I}{12 R}, \otimes$

$B_{0} = B_{1} + B_{2} = \frac{μ_{0} I}{2 R} [\frac{1}{π \sqrt{3}} + \frac{5}{6}], \otimes$

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