$A$ conducting rod $AB$ of length $l$ is projected on a frictionless frame $PSRQ$ with velocity $v_0$ in a uniform magnetic field $\vec{B}$ directed into the plane. The velocity of the rod after time $t$ is

$A$ wheel with ten metallic spokes,each $0.50\,m$ long,is rotated with a speed of $120\,rev/min$ in a plane normal to the Earth's magnetic field at the place. If the magnitude of the field is $0.40\,G$,the induced $emf$ between the axle and the rim of the wheel is equal to:

At a place,the value of the horizontal component of the Earth's magnetic field $H$ is $3 \times 10^{-5} \, Wb/m^2$. $A$ metallic rod $AB$ of length $2 \, m$,placed in the east-west direction with end $A$ towards the east,falls vertically downward with a constant velocity of $50 \, m/s$. Which end of the rod becomes positively charged,and what is the value of the induced potential difference between the two ends?

$A$ circular coil of radius $8.0\; cm$ and $20$ turns is rotated about its vertical diameter with an angular speed of $50\; rad \;s^{-1}$ in a uniform horizontal magnetic field of magnitude $3.0 \times 10^{-2}\; T$. Obtain the maximum and average $emf$ induced in the coil. If the coil forms a closed loop of resistance $10\; \Omega,$ calculate the maximum value of current in the coil. Calculate the average power loss due to Joule heating. Where does this power come from?

Find the current in the wire for the configuration shown in the figure. Wire $PQ$ has negligible resistance. $\vec{B}$ is the magnetic field coming out of the paper. $\theta$ is a fixed angle made by $PQ$ as it travels smoothly over two conducting parallel wires separated by a distance $d$.

$A$ horizontal straight wire $10 \; m$ long extending from east to west is falling with a speed of $5.0 \; m \, s^{-1}$,at right angles to the horizontal component of the earth's magnetic field,$0.30 \times 10^{-4} \; Wb \, m^{-2}$.
$(a)$ What is the instantaneous value of the $emf$ induced in the wire?
$(b)$ What is the direction of the $emf$?
$(c)$ Which end of the wire is at the higher electrical potential?