$A$ 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 $V$)?

$A$ 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 $\pi$)

$A$ circular coil of radius $10\, cm$ is placed in a uniform magnetic field of $3.0 \times 10^{-5}\, T$ with its plane perpendicular to the field initially. It is rotated at a constant angular speed about an axis along the diameter of the coil and perpendicular to the magnetic field so that it undergoes half a rotation in $0.2\, s$. The maximum value of $EMF$ induced (in $\mu V$) in the coil will be close to the integer $....\mu V$.

Discuss the principle and construction of an $A.C.$ generator (dynamo). Derive the formula for the induced $emf$ in an $A.C.$ generator.

$A$ generator with a circular coil of $100$ turns of area $2 \times 10^{-2} \,m^2$ is immersed in a $0.01 \,T$ magnetic field and rotated at a frequency of $50 \,Hz$. The maximum emf which is produced during a cycle is (in $\,V$)

$A$ 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 . . . . . .