A $1 \mathrm{m}$ long thin metal bar of negligible resistance weighing $1 \mathrm{kg}$ rests on two metal supports as shown in the figure. The supports are connected in series to an ideal cell and a resistance. A uniform magnetic field $0.5 \mathrm{T}$ is applied in the region normal to the plane of the paper and into the paper. Maximum emf that the cell can have without breaking the circuit in volt is
(Acceleration due to gravity $=10 \mathrm{m} {\mathrm{s}}^{-2}$ )

A coil of area $10{ \mathrm{m}}^2$ is placed in a uniform magnetic field of $0.3 \mathrm{Wb} {\mathrm{m}}^{-2},$ with its plane perpendicular to the field. The coil rotates at a uniform rate to complete one revolution in $8 \mathrm{s}.$ Find the average $\mathrm{emf}$ in the coil during intervals when the coil rotates from

$\left(\mathrm{i}\right)0°$ to $90°$ 

(ii) $90°$ to $180°$ 

(iii) $180°$ to $270°$ 

(iv) $270°$ to $360°$

A flexible wire bent in the form of a circle is placed in a uniform magnetic field, such that the field is perpendicular to the plane of the coil. The radius of the coil changes as shown. The graph of magnitude of induced emf in the coil is represented by

The coupling coefficient of the perfectly coupled coil is:

Current in a coil with self-inductance $2 \mathrm{H}$ is increasing according to$I=\left(2{\mathrm{sint}}^2\right)$ ampere. Amount of energy spent during the period when current changes from $0$ to $2 \mathrm{A}$ is $\underline{ }$

Find the equivalent inductance between $A$ and $B$ in the given circuit.