Two ions having masses in the ratio $1 : 1$ and charges $1 : 2$ are projected into uniform magnetic field perpendicular to the field with speeds in the ratio $2 : 3$. The ratio of the radii of circular paths along which the two particles move is

What is the radius of the path of an electron (mass $9 \times 10^{-31}\;kg$ and charge $1.6 \times 10^{-19} \;C )$ moving at a speed of $3 \times 10^{7} \;m / s$ in a magnetic field of $6 \times 10^{-4}\;T$ perpendicular to it? What is its frequency? Calculate its energy in $keV$. ( $\left.1 eV =1.6 \times 10^{-19} \;J \right)$

A proton of energy $8\, eV$ is moving in a circular path in a uniform magnetic field. The energy of an alpha particle moving in the same magnetic field and along the same path will be…..$eV$

A charged particle of specific charge $\alpha$ is released from origin at time $t = 0$ with velocity $\vec V = {V_o}\hat i + {V_o}\hat j$ in magnetic field $\vec B = {B_o}\hat i$ . The coordinates of the particle at time $t = \frac{\pi }{{{B_o}\alpha }}$ are (specific charge $\alpha = \,q/m$) 

A particle of charge $q$, mass $m$ enters in a region of magnetic field $B$ with velocity $V_0 \widehat i$. Find the value of $d$ if the particle emerges from the region of magnetic field at an angle $30^o$ to its ititial velocity:-