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

Select the unit of the coefficient of mutual induction from the following.

Around the central part of an air cored solenoid of length $$20 \mathrm{~cm}$$ and area of cross section $$1.4 \times 10^{-3} \mathrm{~m}^2$$ and 3000 turns, another coil of 250 turns is closely wound. A current $$2 \mathrm{~A}$$ in the solenoid is reversed in $$0.2 \mathrm{~s}$$, then the induced emf produced is

A metallic rod of $$2 \mathrm{~m}$$ length is rotated with a frequency $$100 \mathrm{~Hz}$$ about an axis passing through the centre of the circular ring of radius $$2 \mathrm{~m}$$. A constant magnetic field $$2 \mathrm{~T}$$ is applied parallel to the axis and perpendicular to the length of the rod. The emf developed across the ends of the rod is :