The magnetic field B shown in is directed into the plane of the paper. ACDA is a semicircular conducting loop of radius r with the centre at O. The loop is now made ot rotate clockwise with a constant angular velocity `omega` about on axis passing through O and perpendicular to the plane of the paper. The resistance of the loop is R. Obtain an expression for the magnitude of the induced current in the loop. Plot a graph between the induced current i and `omegat`, for two periods of rotation.

Explanation

Area of loop inside field
`A=(1)/(2)a^(2)theta=(1)/(2)a^(2)omegat`( :. `theta=omegat)`
Flux through the loop
`phi=BA=(Ba^(2)omega)/(2)`
`e=(dphi)/(dt)=(Ba^(2)omega)/(2)`
Induecd current
Induced current
`I=(e)/(R)=(Ba^(2)omega)/(2R)`
`t=0` to `t=T,phi` increasing, `I` is anticlockwise `(+ve)`
`t=(T)/(2)` to `t=T,phi` is decreasing, `I` is clockwise `(-ve)`