$A$ wheel with radial metal spokes $1 \ m$ in length is rotated in a magnetic field of $0.5 \times 10^{-4} \ T$ normal to the plane of the wheel. If the induced emf between the rim and axle is $\pi / 3000 \ V$,then the rotational speed of the wheel in revolutions per minute is

The magnetic field in a region is given by $\overrightarrow{ B }= B _{0}\left(\frac{ x }{ a }\right) \,\hat{ k }$. $A$ square loop of side $d$ is placed with its edges along the $x$ and $y$ axes. The loop is moved with a constant velocity $\overrightarrow{ v }= v _{0} \hat{ i }$. The emf induced in the loop is:

$A$ circular coil of radius $10 \, cm$ and resistance of $2 \, \Omega$ 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 $0.25 \, s$. If the magnitude of the induced emf is $3.8 \times 10^{-3} \, V$, then the number of turns of the coil is (Horizontal component of earth's magnetic field at the place is $3 \times 10^{-5} \, T$) (in $turns$)

$A$ solid metal cube of edge length $2\, cm$ is moving in a positive $y-$ direction at a constant speed of $6\, m/s$. There is a uniform magnetic field of $0.1\, T$ in the positive $z-$ direction. The potential difference between the two faces of the cube perpendicular to the $x-$ axis is.....$mV$.

In the given branch $AB$ of a circuit,a current $I = (10t + 5) \, A$ is flowing,where $t$ is time in seconds. At $t = 0$,the potential difference between points $A$ and $B$ $(V_A - V_B)$ is.....$V$.

$A$ wire of length $L$ having resistance $R$ falls from a height $\ell$ in the Earth's horizontal magnetic field $B$. The induced emf through the wire is ($g$ = acceleration due to gravity).