A conducting circular loop is placed in a uniform magnetic field $$\mathrm{B}=0.125 \mathrm{~T}$$ with its plane perpendicular to the loop. If the radius of the loop is made to shrink at a constant rate of $$2 \mathrm{~mm} \mathrm{~s}^{-1}$$, then the induced emf when the radius is $$4 \mathrm{~cm}$$ is

A transformer of $$100 \%$$ efficiency has 200 turns in the primary and 40000 turns in the secondary. It is connected to a $$220 \mathrm{~V}$$ main supply and secondary feeds to a $$100 \mathrm{~K} \Omega$$ resistance. The potential difference per turn is

The current in a coil changes steadily from $$3 \mathrm{~A}$$ to $$5 \mathrm{~A}$$ in $$0.2 \mathrm{~s}$$ when an emf of $$2 \mu \mathrm{V}$$ is induced in it. The self-inductance of the coil is

The magnetic flux linked with a coil is given by the equation: $$\phi=8 t^2+t+10$$. The e.m.f. induced in the coil in the $$3^{\text {rd }}$$ second will be