A current 'I' produces a magnetic flux '$$\phi$$' per turn in a coil of '$$n$$' turns. Self inductance of the coil is '$$L$$'. The relation between them is

A current $$I=10 \sin (100 \pi t)$$ ampere, is passed in a coil which induces a maximum emf $$5 \pi$$ volt in neighbouring coil. The mutual inductance of two coils is

A rectangular loop $$\mathrm{PQMN}$$ with movable arm $$\mathrm{PQ}$$ of length $$12 \mathrm{~cm}$$ and resistance $$2 \Omega$$ is placed in a uniform magnetic field of $$0.1 \mathrm{~T}$$ acting perpendicular to the plane of the loop as shown in figure. The resistances of the arms MN, NP and MQ are negligible. The current induced in the loop when arm PQ is moved with velocity $$20 \mathrm{~ms}^{-1}$$ is

A coil has an area $$0.06 \mathrm{~m}^2$$ and it has 600 turns. After placing the coil in a magnetic field of strength $$5 \times 10^{-5} \mathrm{Wbm}^{-2}$$, it is rotated through $$90^{\circ}$$ in 0.2 second. The magnitude of average e.m.f induced in the coil is

$$\left[\cos 0^{\circ}=\sin 90^{\circ}=1 \text { and } \sin 0^{\circ}=\cos 90^{\circ}=0\right]$$