A metallic rod of $$10 \mathrm{~cm}$$ is rotated with a frequency 100 revolution per second about an axis perpendicular to its length and passing through its one end in uniform transverse magnetic field of strength $$1 \mathrm{~T}$$. The emf developed across its ends is:

The radius of the current carrying circular coil is doubled keeping the current passing through it the same. Then the ratio of the magnetic field produced at the centre of the coil before the doubling of the radius to the magnetic field after doubling of the radius.

A circular loop of area $$0.04 \mathrm{~m}^2$$ carrying a current of $$10 \mathrm{~A}$$ is held with its plane perpendicular to a magnetic field induction $$0.4 \mathrm{~T}$$ Then the torque acting on the circular loop is :

An electric current $I$ enters and leaves a uniform circular wire of radius $r$ through diametrically opposite points. A charged particle $$q$$ moves along the axis of circular wire passes through its centre with speed $$v$$. The magnetic force on the particle when it passes through the centre has a magnitude