$A$ rectangular coil of $300$ turns has an average area of $25\;cm \times 10\;cm.$ The coil rotates with a speed of $50\;cps$ in a uniform magnetic field of strength $4 \times 10^{-2}\;T$ about an axis perpendicular to the field. The peak value of the induced $e.m.f.$ is (in volt): (in $\pi$)

In an $AC$ generator,a coil with $N$ turns,all of the same area $A$ and total resistance $R$,rotates with frequency $\omega$ in a magnetic field $B$. The maximum value of emf generated in the coil is

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

$A$ student pedals a stationary bicycle. The pedals of the bicycle are attached to a $100$ turn coil of area $0.10$ $m^2$. The coil rotates at half a revolution per second and it is placed in a uniform magnetic field of $0.01$ $T$ perpendicular to the axis of rotation of the coil. What is the maximum voltage generated in the coil (in $V$)?

An elliptical loop having resistance $R$,semi-major axis $a$,and semi-minor axis $b$ is placed in a magnetic field as shown in the figure. If the loop is rotated about the $x$-axis with angular frequency $\omega$,the average power loss in the loop due to Joule heating is:

Write down the formula for the induced $emf$ in an $AC$ generator and discuss how it varies with time.