Fig. 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 `(omega)`. Find the force.

Options

A. `(omega a^(3)B^(2))/(R)` to the right of OA in the figure
B. `(omega a^(3)B^(2))/(2R)` to the right of OA in the figure
C. `(omega a^(3)B^(2))/(2R)` to the left of OA in the figure
D. None of these

Answer

B

Explanation

`e=Bvl = (B xx a xx omega xx a)/(2)`
`i=(Ba^(2) omega)/(2 R)`
`F=ilB = (Ba^(2) omega)/(2 R ) xx a xx B=(B^(2)a^(2)omega)/(2 R)`
towards right of OA.