Evaluate the induced emf (in $\mu V$) in the loop if the long wire carries a current of $50 \mathrm{A}$ and the loop has an instantaneous velocity $v=10 \mathrm{m} {\sec }^{-1}$ at the location $x=0.2 \mathrm{m}$ as shown in figure. (Take $a=0.1 \mathrm{m}$)

Calculate current (in $A$) in $L_1$ at steady state for given circuit.

(Given $L_1=2 \mathrm{mH}, L_2=4 \mathrm{mH}, E=9 \mathrm{V}, R=2 \mathrm{\Omega }$)

Calculate current (in $A$), which given by battery for the following circuit, just after closing of the key.

A wire forming one cycle of sine curve is moved in $x-y$ plane with velocity $\overrightarrow{v}=4\hat{\mathrm{i}}+3\hat{\mathrm{j}}$. The exists a magnetic field $\overrightarrow{B}=-5\hat{\mathrm{k}}$ Tesla. Find the motional emf (in $V$) develop across the ends $PQ$ of wire. $\left(\lambda =40 \mathrm{cm}\right)$

A rectangular loop with sliding connector of length $\ell =1.0 \mathrm{m}$ is situated in a uniform magnetic field $B=2 \mathrm{T}$ perpendicular to the plane of loop. Resistance of connector is $r=2 \mathrm{\Omega }$. Two resistance of $6 \mathrm{\Omega }$ and $3 \mathrm{\Omega }$ are connected as shown in figure. Find the external force (in $N$) required to keep the connector moving with a constant velocity $v=2 \mathrm{m} {\mathrm{s}}^{-1}$.

A horizontal wire is free to slide on the vertical rails of a conducting frame as shown in figure. The wire has a mass $=900 \mathrm{gm}$ and length $\ell =3 \mathrm{m}$ and resistance of the circuit is $R=20 \mathrm{\Omega }$. If a uniform magnetic field $B=2 \mathrm{T}$ is directed perpendicular to the frame. Find the terminal speed of the wire as it falls under the force of gravity.

In the given circuit, find the ratio of $i_1$ to $i_2$ is the initial (at $t=0$) current and $i_2$ is steady state (at $t=\infty$) current through the battery.

In a $L-R$ decay circuit, the initial current at $t=0$ is $I$. Find the total charge (in $C$) that has flown through the resistor till the energy in the inductor has reduced to one-fourth its initial value.

(Given $L=16 \mathrm{H}, I=2 \mathrm{A}, R=4 \mathrm{\Omega }$)