$A$ coil of $n$ turns and area $A$ is placed with its axis parallel to a magnetic field. If the coil is rotated by $180^o$,the charge $Q$ induced in the circuit is given. If the resistance of the circuit is $R$,what is the magnitude of the magnetic field $B$?

$A$ 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 $R$.

$A$ 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:

$A$ straight conductor of length $4 \,m$ moves at a speed of $10 \,m/s$. When the conductor makes an angle of $30^{\circ}$ with the direction of a magnetic field of induction $0.1 \,Wb/m^2$, the induced emf is: (in $\,V$)

$A$ cycle wheel contains $24$ spokes of $0.5 \, m$ length. It is rotated in a horizontal plane with $120 \, \text{revolution/min}$ in the presence of the Earth's magnetic field. If the total magnetic field of the Earth is $10^{-4} \, T$ (given $10^4 \, G = 1 \, T$), then find the dynamic $emf$ induced across the centre and the rim of the wheel (angle of dip is $30^{\circ}$).

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