$A$ conducting loop in the form of a circle is placed in a uniform magnetic field with its plane perpendicular to the direction of the field. An emf will be induced in the loop, if

In an $L-R$ circuit connected to a battery of constant $e.m.f.$ $E$,switch $S$ is closed at time $t = 0$. If $e$ denotes the magnitude of induced $e.m.f.$ across the inductor and $i$ the current in the circuit at any time $t$,then which of the following graphs shows the variation of $e$ with $i$?

$A$ conducting wire frame is placed in a magnetic field which is directed into the paper. The magnetic field is increasing at a constant rate. The directions of induced currents in wires $AB$ and $CD$ are

Two different coils have inductances $L_1 = 4 \ mH$ and $L_2 = 2 \ mH$. At a certain instant,the current in the two coils is increasing at the same constant rate,and the power supplied to the first coil is four times that of the second coil. If $e$,$I$,and $U$ indicate the potential difference,current,and energy stored in the inductance respectively,then which of the following is correct?

$A$ small circular loop of area $A$ and resistance $R$ is fixed on a horizontal $xy$-plane with the center of the loop always on the axis $\hat{n}$ of a long solenoid. The solenoid has $m$ turns per unit length and carries current $I$ counterclockwise as shown in the figure. The magnetic field due to the solenoid is in $\hat{n}$ direction. $List-I$ gives time dependences of $\hat{n}$ in terms of a constant angular frequency $\omega$. $List-II$ gives the torques experienced by the circular loop at time $t=\frac{\pi}{6\omega}$. Let $\alpha=\frac{A^2 \mu_0^2 m^2 I^2 \omega}{2R}$.

$List-I$	$List-II$
$(I)$ $\frac{1}{\sqrt{2}}(\sin \omega t \hat{j}+\cos \omega t \hat{k})$	$(P)$ $0$
$(II)$ $\frac{1}{\sqrt{2}}(\sin \omega t \hat{i}+\cos \omega t \hat{j})$	$(Q)$ $-\frac{\alpha}{4} \hat{i}$
$(III)$ $\frac{1}{\sqrt{2}}(\sin \omega t \hat{i}+\cos \omega t \hat{k})$	$(R)$ $\frac{3\alpha}{4} \hat{i}$
$(IV)$ $\frac{1}{\sqrt{2}}(\cos \omega t \hat{j}+\sin \omega t \hat{k})$	$(S)$ $\frac{\alpha}{4} \hat{j}$

Which one of the following options is correct?

Two circular coils $P$ and $Q$ are fixed coaxially and carry currents $I_1$ and $I_2$ respectively.