The self inductance of solenoid of length $$31.4 \mathrm{~cm}$$, area of cross section $$10^{-3} \mathrm{~m}^2$$ having total number of turns 500 will be nearly [$$\mu_0=4 \pi \times 10^{-7}$$ SI unit]

A circuit has self-inductance 'L' H and carries a current 'I' A. To prevent sparking when the circuit is switched off, a capacitor which can withstand 'V' volt is used. The least capacitance of the capacitor connected across the switch must be equal to

Eddy currents are produced when

The magnitude of flux linked with coil varies with time as $$\phi=3 t^2+4 t+7$$. The magnitude of induced e.m.f. at $$t=2 \mathrm{~s}$$ is