$A$ small coil is introduced between the poles of an electromagnet so that its axis coincides with the magnetic field direction. The number of turns is $n$ and the cross-sectional area of the coil is $A$. When the coil turns through $180^o$ about its diameter,the charge flowing through the coil is $Q$. The total resistance of the circuit is $R$. What is the magnitude of the magnetic induction?

$A$ conducting wire $XY$ of mass $m$ and negligible resistance slides smoothly on two parallel conducting wires as shown in the figure. The closed circuit has a resistance $R$ due to $AC$. $AB$ and $CD$ are perfect conductors. There is a magnetic field $\vec{B} = B(t) \hat{k}$.
$(i)$ Write down the equation for the acceleration of the wire $XY$.
$(ii)$ If $\vec{B}$ is independent of time,obtain $v(t)$,assuming $v(0) = u_0$.
$(iii)$ For $(ii)$,show that the decrease in kinetic energy of $XY$ equals the heat lost in $R$.

$A$ long metal bar of $30\,cm$ length is aligned along a north-south line and moves eastward at a speed of $10\,ms^{-1}$. $A$ uniform magnetic field of $4.0\,T$ points vertically downwards. If the south end of the bar has a potential of $0\,V$,the induced potential at the north end of the bar is.....$V$.

$A$ metal rod of length $l$ rotates about one of its ends in a plane perpendicular to a magnetic field of induction $B$. If the e.m.f. induced between the ends of the rod is $e$,then the number of revolutions made by the rod per second is:

Consider the situation given in the figure. The wire $AB$ is slid on the fixed rails with a constant velocity $v$. If the wire $AB$ is replaced by a semicircular wire of the same length,the magnitude of the induced current will:

$A$ square loop of area $25 \, cm^2$ has a resistance of $10 \, \Omega$. The loop is placed in a uniform magnetic field of magnitude $40 \, T$. The plane of the loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in $1 \, s$ will be: