$A$ wire of length $1\,m$ is moving with a velocity of $8\,m/s$ at right angles to a magnetic field of $2\,T$. The magnitude of the induced emf between the ends of the wire will be $............\,V$.

$A$ rod of length $l$ is rotating in the plane of the paper with an angular speed $\omega$ about one of its ends,which is at a distance $a$ from an infinitely long conducting wire carrying current $i$ inwards the plane of the paper. Find the induced $emf$ in the rod at the instant as shown in the figure.

$A$ long solenoid with $2000$ turns per meter has a small loop of radius $3 \,cm$ placed inside the solenoid normal to its axis. If the current through the solenoid increases steadily from $1.5 \,A$ to $5.5 \,A$ in $\frac{\pi^2}{100} \,s$, the induced emf in the loop is (in $\,mV$)

Consider the situation shown in the figure. The wires $P_1Q_1$ and $P_2Q_2$ are made to slide on the rails with the same speed $5\, cm/s$. Find the electric current in the $9\,\Omega$ resistor if $(a)$ both the wires move towards the right and $(b)$ if $P_1Q_1$ moves towards the left but $P_2Q_2$ moves towards the right.

Explain the motional $emf$ by the Lorentz force acting on the free charge carriers of a conductor.

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 $\mu V$.