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

$A$ circular coil of radius $8.0 \, cm$ and $20$ turns is rotated about its vertical diameter with an angular speed of $50 \, rad \, s^{-1}$ in a uniform horizontal magnetic field of $3.0 \times 10^{-2} \, T$. The maximum $emf$ induced in the coil will be $\ldots \ldots \ldots \times 10^{-2} \, V$ (rounded off to the nearest integer).

$A$ long solenoid is carrying a current $I = I_0 \sin(\omega t)$,having $N$ turns per unit length and radius $R$. $A$ square loop is placed inside the solenoid with its plane perpendicular to the solenoid axis,and its corners touching the solenoid. Find the emf induced in the square coil.

In an $AC$ generator,a rectangular coil of $100$ turns each having area $14 \times 10^{-2} \, m^2$ is rotated at $360 \, rev/min$ about an axis perpendicular to a uniform magnetic field of magnitude $3.0 \, T$. The maximum value of the emf produced will be $............ \, V$. (Take $\pi = \frac{22}{7}$)

When a magnet is pushed in and out of a circular coil $C$ connected to a very sensitive galvanometer $G$ as shown in the adjoining diagram with a frequency $\nu$,then

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