In a region where the Earth's magnetic field is $3 \times 10^{-4} \, T$ with a dip angle $\theta = \tan^{-1}(4/3)$,a metal rod of length $0.25 \, m$ is placed in the North-South direction. If it is moved towards the East with a velocity of $10 \, cm/s$,calculate the induced $emf$ in $\mu V$.

$A$ conducting circular loop is placed in the $X-Y$ plane in the presence of a magnetic field $\overrightarrow{B} = (3t^3 \hat{j} + 3t^2 \hat{k})$ in $SI$ units. If the radius of the loop is $1 \ m$,the induced emf in the loop at time $t = 2 \ s$ is $n\pi \ V$. The value of $n$ is:

$A$ wire of length $1\, m$ is perpendicular to the $x-y$ plane. It is moved with velocity $\vec{v} = (3\hat{i} + 3\hat{j} + 2\hat{k})\, m/s$ through a region of uniform magnetic field $\vec{B} = (\hat{i} + 2\hat{j})\, T$. The potential difference between the ends of the wire is (in $V$):

$A$ simple pendulum made of a mass of $10 \ g$ and a metallic wire of length $10 \ cm$ is suspended vertically in a uniform magnetic field of $2 \ T$. The magnetic field direction is perpendicular to the plane of oscillations of the pendulum. If the pendulum is released from an angle of $60^{\circ}$ with the vertical,then the maximum induced $EMF$ between the point of suspension and the point of oscillation is . . . . . . $mV$. (Take $g = 10 \ m/s^2$)

An $emf$ of $0.08\,V$ is induced in a metal rod of length $10\,cm$ held normal to a uniform magnetic field of $0.4\,T$,when it moves with a velocity of .......... $m/s$.

$A$ conducting loop of radius $R$ is present in a uniform magnetic field $B$ perpendicular to the plane of the ring. If radius $R$ varies as a function of time $t$,as $R = R_0 + t$,the e.m.f. induced in the loop is: