A charge $q$ is accelerated through a potential difference $V$. It is then passed normally through a uniform magnetic field, where it moves in a circle of radius $r$. The potential difference required to move it in a circle of radius $2 r$ is

A cyclotron's oscillator frequency is 10 MHz and the operating magnetic field is 0.66 T . If the radius of its dees is 60 cm , then the kinetic energy of the proton beam produced by the accelerator is

A proton, a deuteron and an $\alpha$-particle are projected perpendicular to the direction of a uniform magnetic field with same kinetic energy. The ratio of the radii of the circular paths described by them is

A magnetic dipole of magnetic moment $6 \times 10^{-2}$ A-m ${ }^2$ and moment of inertia $12 \times 10^{-6} \mathrm{~kg}-\mathrm{m}^2$ performs oscillations in a magnetic field of $2 \times 10^{-2} \mathrm{~T}$. The time taken by the dipole to complete 20 oscillations is ( $\pi \approx 3$ )