Answer to Question #209460 in Electricity and Magnetism for Anna

Question

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

field 𝐵⃗ . Find the ratio of the radii of their circular orbits when the electron and the proton have (a) 

the same momentum and (b) the same kinetic energy. (c) Sketch the path taken by the electron and 

proton when the magnetic field is directed into the board.

Answer 1

Part(a)

Kinetic energy

$K=\frac{1}{2}mv^2$

$V=\sqrt\frac{2K}{m}$

$r=\frac{mv}{qB}$

$r=\frac{\sqrt{2Km}}{qB}$

$\frac{r_e}{r_p}=\frac{q_p}{q_e}\times\sqrt{\frac{m_e}{m_p}}$

$\frac{r_e}{r_p}=\frac{e}{e}\times\frac{9.1\times10^{-31}}{1.67\times10^{-27}}$

$\frac{r_e}{r_p}=$

Part(b)

Momentum same

$r=\frac{P}{qB}$

$P=qBr$

$\frac{r_e}{r_p}=\frac{q_p}{q_e}=\frac{e}{e}=1$

Part(c)

Path of electron and proton show in daigram