Figure shows a conducting circular loop of radius a placed in a uniform, perpendicular magnetic field B. A thick metal rod OA is pivoted at the centre O. The other end of the rod touches the loop at A. The centre O and a fixed point C on the loop are connected by a wire OC of resistance R. A force is applied at the middle point of the rod OA perpendicularly, so that the rod rotates clockwise at a uniform angular velocity $ω$ . Find the force

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$\frac{ω a^{3} B^{2}}{2 R}$ to the right of OA in the figure

$\frac{ω a^{3} B^{2}}{R}$ to the right of OA in the figure

$\frac{ω a^{3} B^{2}}{R}$ to the left of OA in the figure

None of these

answer is B.

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Detailed Solution

$e = B v l = \frac{B \times a \times ω \times a}{2}$

$i = \frac{B a^{2} ω}{2 R}$

$F = i l B = \frac{B a^{2} ω}{2 R} \times a \times B = \frac{B^{2} a^{3} ω}{2 R}$ towards right of OA

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