An $\alpha$-particle and a proton travel with the same velocity in a magnetic field perpendicular to the direction of their velocities. Find the ratio of the radii of their circular paths.

An electron is moving along $+x$ direction with a velocity of $6 \times 10^{6} \, m/s$. It enters a region of uniform electric field of $300 \, V/cm$ pointing along $+y$ direction. The magnitude and direction of the magnetic field set up in this region such that the electron keeps moving along the $x$ direction will be:

Velocity and acceleration vectors of a charged particle moving perpendicular to the direction of a magnetic field at a given instant of time are $\overrightarrow{v}=2 \hat{i}+c \hat{j}$ and $\overrightarrow{a}=3 \hat{i}+4 \hat{j}$ respectively. Then the value of $c$ is

Under the influence of a uniform magnetic field,a charged particle is moving in a circle of radius $R$ with constant speed $v$. The time period of the motion

In a chamber,a uniform magnetic field of $6.5 \;G \left(1 \;G = 10^{-4} \;T \right)$ is maintained. An electron is shot into the field with a speed of $4.8 \times 10^{6} \;m s^{-1}$ normal to the field. Explain why the path of the electron is a circle. Determine the radius of the circular orbit. $\left(e = 1.6 \times 10^{-19} \;C, m_{e} = 9.1 \times 10^{-31} \;kg \right)$

Bohr model is applied to a particle of mass $m$ and charge $q$ moving in a plane under the influence of a transverse magnetic field $B$. The energy of the charged particle in the $n^{\text{th}}$ level will be $[h = \text{Planck's constant}]$