$A$ straight conductor of length $0.4\;m$ is moved with a speed of $7\;m/s$ perpendicular to a magnetic field of intensity $0.9\;Wb/m^2$. The induced $e.m.f.$ across the conductor will be......$V$.

$A$ 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 $30^{\circ}$).

$A$ conducting rod of length $L = 0.1 \, m$ is moving with a uniform speed $v = 0.2 \, m/s$ on conducting rails in a magnetic field $B = 0.5 \, T$ as shown. On one side,the end of the rails is connected to a capacitor of capacitance $C = 20 \, \mu F$. Then the charges on the capacitor plates $A$ and $B$ are:

$A$ conducting rod of length $\ell$ is moving with velocity $v$ in a uniform magnetic field $B$ directed into the plane of the paper,as shown in the diagram. Which end of the rod is at a lower potential?

$A$ conducting circular loop is placed in a uniform magnetic field of $0.4\,T$ with its plane perpendicular to the field. The radius of the loop starts expanding at a constant rate of $1\,mm/s$. The magnitude of the induced emf in the loop at an instant when the radius of the loop is $2\,cm$ will be $...........\,\mu V$.

$A$ conducting rod of length $\ell$ moves with a velocity $V$ in a uniform magnetic field $B$ perpendicular to the plane of the rails. $A$ capacitor of capacitance $C$ is connected across the rails as shown. Find the charge on the capacitor due to the induced emf in the rod.