$A$ circular coil of resistance $R$,area $A$,and number of turns $N$ is rotated about its vertical diameter with angular speed $\omega$ in a uniform magnetic field of magnitude $B$. The average power dissipated in a complete cycle is:

$A$ coil of $200$ turns and area $0.20 \ m^2$ is rotated at half a revolution per second and is placed in a uniform magnetic field of $0.01 \ T$ perpendicular to the axis of rotation of the coil. The maximum voltage generated in the coil is $\frac{2 \pi}{\beta} \ V$. The value of $\beta$ is . . . . . .

Write the equation for the maximum $emf$ in an $AC$ generator.

$A$ circular coil of area $0.01 \ m^2$ and $40$ turns is rotated about its vertical diameter with an angular speed of $50 \ rad \ s^{-1}$ in a uniform horizontal magnetic field of $0.05 \ T$. If the average power loss due to Joule heating is $25 \ mW$,then the closed loop resistance of the coil is: (in $\Omega$)

At the centre of a fixed large circular coil of radius $R$,a much smaller circular coil of radius $r$ is placed. The two coils are concentric and are in the same plane. The larger coil carries a current $I$. The smaller coil is set to rotate with a constant angular velocity $\omega$ about an axis along their common diameter. Calculate the $emf$ induced in the smaller coil after a time $t$ of its start of rotation.

The phase difference between the magnetic flux linked with a coil rotating in a uniform magnetic field and the induced $e.m.f.$ produced in it is