An alpha particle and a proton are moving with the same momentum in a transverse uniform magnetic fi

Question

An alpha particle and a proton are moving with the same momentum in a transverse uniform magnetic field. What is the ratio of the radii of their circular paths ($r_\alpha : r_p$)?

Professor PC Thomas Classes · Answer

Radius $r = \frac{p}{qB}$. Since they have the same momentum $p$, $r \propto \frac{1}{q}$. Because $q_\alpha = 2q_p$, $r_\alpha = \frac{r_p}{2}$. The ratio is 1:2.