An electron $$(e)$$ is revolving in a circular orbit of radius $$r$$ in hydrogen atom. The angular momentum of the electron is ($$M=$$ magnetic dipole moment associated with it and $$m=$$ mass of electron)

A charged particle is moving in a uniform magnetic field in a circular path of radius $$R$$. When the energy of the particle becomes three times the original, the new radius will be

A charge $$q$$ moves with velocity $$v$$ through electric field $$\mathrm{E}$$ as well as magnetic field (B). Then, the force acting on it is

Maximum kinetic energy gained by the charged particle in the cyclotron is independent of