Topic : motion in a magnetic field

A proton and a deuteron enter in a uniform magnetic field with equal kinetic energy in the direction perpendicular to the field. The ratio of radius of circular path is

When a charged particle is projected perpendicular to a uniform magnetic field, its path is circular. If a charged particle is thrown with double the speed in same magnetic field, then

An electron (mass $9 \times 10^{-31}$ kg and charge $1.6 \times 10^{-19}$ C) moving with speed c/100 (c = speed of light) is injected into a magnetic field $\vec{B}$ of magnitude $9 \times 10^{-4}$ T perpendicular to its direction of motion. We wish to apply an uniform electric $\vec{E}$ together with the magnetic field so that the electron does not deflect from its path. Then (speed of light c = $3 \times 10^8$ ms$^{-1}$)

A proton of energy 12 eV is moving in a circular path in uniform magnetic field. The energy of an alpha particle moving in the same magnetic field and along the same path will be

A proton carrying 4 MeV kinetic energy is moving in a circular path of radius R in uniform magnetic field. Energy of $\alpha$-particle to describe a circle of same radius in same field should be