A current I flows through a closed loop shown in figure. The magnetic field at the centre O is

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$\frac{μ_{0} I}{2 πR} (π - θ + tanθ)$

$\frac{μ_{0} I}{2 πR} (θ + sinθ)$

$\frac{μ_{0} I}{2 πR} (π - θ + sinθ)$

None of these

answer is A.

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Detailed Solution

$B_{0} = B_{1} + B_{2}$
$\begin{array}{l} = \frac{μ_{0} I}{2 R} [\frac{2 π - 2 θ}{2 π}] + \frac{μ_{0} I}{4 πr} [\sin θ + \sin θ] \\ = \frac{μ_{0} I}{2 R} [\frac{π - θ}{π}] + \frac{μ_{0} I}{4 π (Rcos θ)} (2 \sin θ) \\ = \frac{μ_{0} I}{2 πR} [π - θ + \tan θ] \end{array}$

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