Consider a long solenoid of length $I$ and radius $r$. If $n$ is the number of turns per unit length and $\mu_0$ is the permeability of free space, the inductance of the solenoid is :

Two identical inductors are connected in two different configurations $P$ and $Q$, where a time varying current $l(t)$ is flowing, as shown in the figure. The induced emf between points $a$ and $b$ for configuration $P$ is $E_P$ and that for configuration $Q$ is $E_Q$. The ratio $E_P / E_Q$ is:

[Neglect the effect of mutual inductance.]

A conducting loop of finite resistance lies on the $x-y$ plane. There is a constant magnetic field in the $z$ direction. The area of the loop varies with time $t$, as $A=A_0(1+\sin t)$ in appropriate units. The figure that correctly indicates the qualitative behaviour of the power $P$ dissipated in the loop as a function of time is:

A rectangular wire loop of sides 8 cm and 3 cm with a small cut, is moving out of a region of uniform magnetic field of magnitude 0.3 T directed normal to the plane of the loop. The emf developed across the cut, if the velocity of the loop is $2 \mathrm{~cm} \mathrm{~s}^{-1}$, in a direction normal to the shorter side of the loop, will be :