$A$ metallic rod of length $20 \,cm$ is placed in the North-South direction and is moved at a constant speed of $20 \,m/s$ towards the East. The horizontal component of the Earth's magnetic field at that place is $4 \times 10^{-3} \,T$ and the angle of dip is $45^{\circ}$. The emf induced in the rod is ............. $mV$.

$A$ rectangular loop of wire is placed in the $XY$-plane with its side of length $3 \,cm$ parallel to the $X$-axis and the side of length $4 \,cm$ parallel to the $Y$-axis. It is moving in the positive $X$-direction with the speed $10 \,cm/s$. $A$ magnetic field exists in the space with its direction parallel to the $Z$-axis. The field decreases by $2 \times 10^{-3} \,T/cm$ along the positive $X$-axis and increases in time by $2 \times 10^{-2} \,T/s$. The induced emf in the wire is

In the given branch $AB$ of a circuit,a current $I = (10t + 5) \, A$ is flowing,where $t$ is time in seconds. At $t = 0$,the potential difference between points $A$ and $B$ $(V_A - V_B)$ is.....$V$.

$A$ metal wire $PQ$ slides on parallel metallic rails having separation $0.25 \ m$,each having negligible resistance. There is a $2 \ \Omega$ resistor and $10 \ V$ battery as shown in the figure. There is a uniform magnetic field directed into the plane of the paper of magnitude $0.5 \ T$. $A$ force of $0.5 \ N$ to the left is required to keep the wire $PQ$ moving with constant speed to the right. With what speed is the wire $PQ$ moving? ..... $m/s$ (Neglect self-inductance of the loop)

The radius of a circular loop placed in a perpendicular uniform magnetic field is increasing at a constant rate of $r_0 \ m s^{-1}$. If at any instant the radius of the loop is $r$,then the emf induced in the loop at that instant will be:

$A$ conducting rod moves towards the right with a constant velocity $v$ in a uniform transverse magnetic field. Determine the nature of the graphs between the force applied by the external agent versus velocity and the power supplied by the external agent versus velocity.