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A current $I$ flows through a closed loop shown in figure. The magnetic field at the centre $O$ is
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$\frac{μ_{0} I}{2 πR} (π - θ + \tan θ)$

$\frac{μ_{0} I}{2 πR} (π - θ + \sin θ)$

$\frac{μ_{0} I}{2 πR} (θ + \sin θ)$

none of these

answer is A.

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Detailed Solution

$B_{0} = B_{1} + B_{2}$

$= \frac{μ_{0} I}{2 R} [\frac{2 π - 2 θ}{2 π}] + \frac{μ_{0} I}{4 π R} [\sin θ + \sin θ] = \frac{μ_{0} I}{2 R} [\frac{π - θ}{π}] + \frac{μ_{0} I}{4 π (R \cos θ)} [2 \sin θ] = \frac{μ_{0} I}{2 π R} [π - θ + \tan θ]$

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