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A wire of length “L” is bent in to arc of a circle subtending an angle of “ $θ$ ” radians at the center. If a current of “i” passes through it, the magnetic induction at the center of the circle is

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$\frac{μ_{0} i θ^{2}}{4 π L^{2}}$

$\frac{μ_{o} i θ}{4 π L}$

$\frac{μ_{o} i θ^{2}}{4 π L}$

$\frac{μ_{0} i θ}{4 π L^{2}}$

answer is C.

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Detailed Solution

$L = R θ, \begin{array}{l} B = \frac{μ_{0}}{4 π} \cdot \frac{i θ}{R} \\ B = \frac{μ_{0}}{4 π} \cdot \frac{i θ}{R} \\ B = \frac{μ_{0}}{4 π} \cdot \frac{i θ}{2 / θ} \\ B = \frac{μ_{0} i θ^{2}}{4 π L} \end{array}$

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