A metal disc of radius $$R$$ rotates with an angular velocity $$\omega$$ about an axis perpendicular to its plane passing through its centre in a magnetic field of induction $$B$$ acting perpendicular to the plane of the disc. The magnitude of induced emf between the rim and axis of the disc is

A conductor $$10 \mathrm{~cm}$$ long is moves with a speed $$1 \mathrm{~m} / \mathrm{s}$$ perpendicular to a field of strength $$1000 \mathrm{~A} / \mathrm{m}$$. The emf induced in the conductor is (Given : $$\mu_0=4 \pi \times 10^{-7} \mathrm{~Wb} / \mathrm{Am}$$ )

Three coils of inductance $$\mathrm{L}_1=2 \mathrm{H}, \mathrm{L}_2=3 \mathrm{H}$$ and $$\mathrm{L}_3=6 \mathrm{H}$$ are connected such that they are separated from each other. To obtain the effective inductance of 1 henry, out of the following combinations as shown in figure, the correct one is

The magnet is moved towards the coil with speed '$$\mathrm{V}$$'. The induced e.m.f. in the coil is '$$\mathrm{e}$$'. The magnet and the coil move away from one another each moving with speed '$$\mathrm{V}$$'. The induced e.m.f. in the coil is