An electron,a proton,and an alpha particle having the same kinetic energy are moving in circular orbits of radii $r_e, r_p$,and $r_{\alpha}$ respectively in a uniform magnetic field $B$. The relation between $r_e, r_p$,and $r_{\alpha}$ is:

$A$ particle with charge $-Q$ and mass $m$ enters a magnetic field of magnitude $B$, which exists only to the of the boundary $YZ$. The direction of the motion of the particle is perpendicular to the direction of $B$. Let $T = 2\pi \frac{m}{QB}$. The time spent by the particle in the field will be:

An electron is orbiting in a circular orbit under the influence of a constant transverse magnetic field of strength $B$. Assuming that Bohr's postulate regarding the quantisation of angular momentum holds good for this electron,find the kinetic energy of the electron in the $n^{th}$ orbit. ($m_e =$ mass of electron,$e =$ magnitude of charge of electron)

In which of the following cases is no force exerted by a magnetic field on a charge?

$A$ particle of mass $0.6 \,g$ and having charge of $25 \,nC$ is moving horizontally with a uniform velocity $1.2 \times 10^4 \,ms^{-1}$ in a uniform magnetic field. The value of the magnetic induction is $\left(g=10 \,ms^{-2}\right)$.

$A$ proton is moving perpendicular to a uniform magnetic field of $2.5 \ T$ with $2 \ MeV$ kinetic energy. The force on the proton is . . . . . . $N$. (Mass of proton $= 1.6 \times 10^{-27} \ kg$,charge of proton $= 1.6 \times 10^{-19} \ C$)