Question

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

• A. $r_e<r_p<r_{\alpha }$
• B. $r_e<r_{\alpha }<r_p$
• C. $r_e>r_p=r_{\alpha }$
• D. $r_e<r_p=r_{\alpha }$

Answer 1

The correct option is D $r_e<r_p=r_{\alpha }$

For circular path in magnetic field,
$r=\frac{\sqrt{2mE}}{qB}whereE=kinetic$ energy
So
$\begin{array}{cccc}& e& p& \alpha \\ m& 1/1836& 1& 4\\ q& -e& +e& 2e\end{array}$

Therefore,
$r_e<r_p=r_{\alpha }$