A thin ring of radius '$$R$$' meter has charge '$$q$$' coulomb uniformly spread on it. The ring rotates about its axis with a constant frequency of $$f$$ revolution/s. The value of magnetic induction in $$\mathrm{Wb} \mathrm{m}^{-2}$$ at the center of the ring is ($$\mu_0=$$ Permeability of free space)

A charged spherical conductor has radius '$$r$$'. The potential difference between its surface and 3 point at a distance '$$3 r$$' from the centre is '$$v$$' The electric intensity at a distance '$$3 r$$' from the centre of the conductor is

In biprims experiment, the $$4^{\text {th }}$$ dark band is formed opposite to one of the slits. The wavelength of light used is $$(\mathrm{d}=$$ distance between the slits, $$\mathrm{D}=$$ distance between scource and the screen)

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