$A$ boy is playing with the empty rim of a cycle wheel of radius $40 \, cm$ by rolling it along a horizontal road towards north with an angular speed of $20 \, rad \, s^{-1}$. Considering the effect of the magnetic field of the Earth, the e.m.f. induced in the rim is (Horizontal component of Earth's magnetic field $= 0.26 \, G$)

$A$ metal wire of length $2500 \ m$ is kept in east-west direction,at a certain height from the ground. If it falls freely on the ground,then the current induced in the wire when its speed is $10 \ m/s$ is (Resistance of wire $= 25 \ \Omega$,$g = 10 \ m/s^2$ and Earth's horizontal component of magnetic field $B_{H} = 2 \times 10^{-5} \ T$). (in $A$)

$A$ 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 at $t = 0$. Find the magnitude of the $emf$ induced in the loop at $(a) \, t = 2 \, s$, $(b) \, t = 10 \, s$, and $(c) \, t = 22 \, s$.

$A$ wire of mass $m$ and length $l$ can slide freely on a pair of smooth,vertical rails (figure). $A$ magnetic field $B$ exists in the region in the direction perpendicular to the plane of the rails. The rails are connected at the top end by a capacitor of capacitance $C$. The acceleration of the wire,neglecting any electric resistance,is:

$A$ square-shaped wire loop of mass $m$,resistance $R$,and side $a$ moving with speed $v_{0}$,parallel to the $X$-axis,enters a region of uniform magnetic field $B$,which is perpendicular to the plane of the loop. The speed of the loop changes with distance $x$ $(x < a)$ in the field as: