A charged particle of charge ' $q$ ' is accelerated by a potential difference ' $V$ ' enters a region of uniform magnetic field ' $B$ ' at right angles to the direction of field. The charged particle completes semicircle of radius ' $r$ ' inside magnetic field. The mass of the charged particle is

A charged particle is moving in a uniform magnetic field in a circular path with radius ' $R$ '. When the energy of the particle is doubled, then the new radius will be

A massless square loop of wire of resistance ' $R$ ' supporting a mass ' M ' hangs vertically with one of its sides in a uniform magnetic field ' B ' directed outwards in the shaded region. A d.c. voltage ' V ' is applied to the loop. For what value of ' $V$ ' the magnetic force will exactly balance the weight of the supporting mass ' M '? (side of loop = L, $\mathrm{g}=$ acceleration due to gravity)

A thin ring of radius ' $R$ ' carries a uniformly distributed charge. The ring rotates at constant speed ' $N$ ' r.p.s. about its axis perpendicular to the plane. If ' $B$ ' is the magnetic field at the centre, the charge on the ring is ( $\mu_0=$ permeability of free space)