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

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.

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

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 $\pi = \frac{22}{7}$)

Discuss the characteristics of the induced $emf$ in an $AC$ generator.

$A$ ring of resistance $10 \Omega$,radius $10 \text{ cm}$,and $100$ turns is rotated at a rate of $100$ revolutions per second about a fixed axis which is perpendicular to a uniform magnetic field of induction $10 \text{ mT}$. The amplitude of the current in the loop will be nearly $A$ (Take $\pi^2 = 10$).