$A$ conducting square frame of side $a$ and a long straight wire carrying current $I$ are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity $V$. The $emf$ induced in the frame will be proportional to

$A$ circular coil of radius $10\; cm$,$500$ turns,and resistance $2\; \Omega$ is placed with its plane perpendicular to the horizontal component of the Earth's magnetic field. It is rotated about its vertical diameter through $180^{\circ}$ in $0.25\; s$. Estimate the magnitudes of the emf and current induced in the coil. The horizontal component of the Earth's magnetic field at the place is $3.0 \times 10^{-5}\; T$.

The figure shows a square loop of side $5 \ cm$ being moved towards the right at a constant speed of $1 \ cm/s$. The front edge enters the $20 \ cm$ wide magnetic field $(B = 0.6 \ T)$ at $t = 0$. Find the $emf$ induced in the loop at $(a) \ t = 2 \ s$,$(b) \ t = 10 \ s$,and $(c) \ t = 22 \ s$.

$A$ rectangular wire loop of sides $8 \;cm$ and $2 \;cm$ with a small cut is moving out of a region of uniform magnetic field of magnitude $0.3 \;T$ directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is $1 \;cm \,s^{-1}$ in a direction normal to the $(a)$ longer side,$(b)$ shorter side of the loop? For how long does the induced voltage last in each case?

$A$ jet plane is travelling towards west at a speed of $1800\; km/h$. What is the voltage difference developed between the ends of the wing having a span of $25\; m$,if the Earth's magnetic field at the location has a magnitude of $5 \times 10^{-4}\; T$ and the dip angle is $30^{\circ}$ (in $; V$)?

$A$ conducting rod $PQ$ of length $1 \ m$ is moving with a uniform speed $2 \ ms^{-1}$ in a uniform magnetic field of $4 \ T$ which is directed into the paper. $A$ capacitor of capacity $10 \ \mu F$ is connected as shown in the figure. Then,the charge on the plates of the capacitor are