Asked by Jess

An electron and a proton move in circular orbits in a plane perpendicular to a uniform magnetic field B.

Find the ratio of the radii of their circular orbits when the electron and the proton have the same momentum.

Find the ratio of the radii of their circular orbits when the electron and the proton have the same kinetic energy.
Answered by bobpursley
centripetal force=mv^2/r

electron centripetal force=protoncentripetal force.

me*ve^2/re=mp*vp^2/rp

re/rp=me/mp * Ve/vp * Ve/Vp

but if they have the same momentum, then
meve/mpvp=1 so
re/rp=Ve/Vp

You do the energy.