An electron and a proton move in circular orbits in a plane perpendicular to a u

Question

An electron and a proton move in circular orbits in a plane perpendicular to a uniform magnetic field B. part a) Find the ratio of the radii of their circular orbits when the electron and the proton have the same momentum. part b) Find the ratio of the radii of their circular orbits when the electron and the proton have the same kinetic energy.

Explanation / Answer

F = QvB = mv^2/r ==> QB = constant = mv/r B. With mv also given as constant, r is constant; i.e., the same for both particles. So re/rp = 1. A. With KE given as constant, v = sqrt(constant/m). mv/r = constant ==> sqrt(m)/r = constant. So re/rp = sqrt(me/mp).

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