$A$ conducting circular loop is rotated about its diameter at a constant angular speed of $100 \ rad/s$ in a magnetic field of $0.5 \ T$ perpendicular to the axis of rotation. When the loop is rotated by $30^{\circ}$ from the horizontal position, the induced $EMF$ is $15.4 \ mV$. The radius of the loop is . . . . . . $mm$. (Take $\pi = 22/7$)

$A$ straight line conductor of length $0.4 \ m$ is moved with a speed of $7.0 \ ms^{-1}$ perpendicular to a magnetic field of intensity $0.8 \ Wb \ m^{-2}$. The induced e.m.f. across the conductor is (in $V$)

$A$ conducting rod of length $L$ lies in the $XY$-plane and makes an angle $30^{\circ}$ with the $X$-axis. One end of the rod is initially at the origin. $A$ magnetic field exists in the region pointing along the positive $Z$-direction. The magnitude of the magnetic field varies with $y$ as $B = B_0 \left(\frac{y}{L}\right)^3$,where $B_0$ is a constant. At some instant,the rod starts moving with a velocity $v_0$ along the $X$-axis. The emf induced in the rod is

If current $I$ is flowing in a closed circuit with total resistance $R$,the rate of production of heat energy in the loop as we pull it with a constant speed $V$ is ($L=$ length of conductor,$B=$ magnetic field).

$A$ long rectangular conducting loop of width ' $\ell$ ',mass ' $m$ ' and resistance ' $R$ ' is placed partly in a perpendicular magnetic field ' $B$ '. It is pushed downwards with velocity ' $V$ ' so that it may continue to fall freely. The velocity ' $V$ ' is

$A$ wire of length $1 \, m$ is moving at a speed of $2 \, ms^{-1}$ perpendicular to its length and a homogeneous magnetic field of $0.5 \, T$. The ends of the wire are joined to a circuit of resistance $6 \, \Omega$. The rate at which work is being done to keep the wire moving at constant speed is: