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)

A charged particle is moving along a magnetic field line. What is the magnetic force acting on the particle? $\left(\sin 0^{\circ}=0, \sin \frac{\pi}{2}=1\right)$

A current of 5 A flows through a toroid having a core of mean radius 20 cm . If 4000 turns of the conducting wire are wound on the core, then the magnetic field inside the core of the toroid is [permeability of free space $=4 \pi \times 10^{-7}$ SI units]

A particle having a charge 50 e is revolving in a circular path of radius 0.4 m with $1 \mathrm{r} . \mathrm{p} . \mathrm{s}$. The magnetic field produced at the centre of the circle is $\left(\mu_0=4 \pi \times 10^{-7}\right.$ SI units and $e=1.6 \times 10^{-19} \mathrm{c}$)