A conducting loop of radius $\frac{10}{\sqrt{\pi }} \mathrm{cm}$ is placed perpendicular to a uniform magnetic field of $0.5 \mathrm{T}$. The magnetic field is decreased to zero in $0.5 \mathrm{s}$ at a steady rate. The induced emf in the circular loop at $0.25 \mathrm{s}$ is:

In the circuit shown in the figure, the ratio of the quality factor and the band width is _____ $\mathrm{s}$.

A metallic rod of length $L$ is rotated with an angular speed of $\omega$ normal to a uniform magnetic field $B$ about an axis passing through one end of rod as shown in figure. The induced emf will be :

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Three identical resistors with resistance $R=12 \mathrm{\Omega }$ and two identical inductors with sell inductance $L=5 \mathrm{mH}$ are connected to an ideal battery with emf of $12 \mathrm{V}$ as shown in figure. The current through the battery long after the switch has been closed will be________$\mathrm{A}$.

Find the mutual inductance in the arrangement, when a small circular loop of wire of radius $R$ is placed inside a large square loop of wire of side $L(L\gg R)$. The loops are coplanar and their centres coincide :