Question

A particle P carries a charge e and moves under the influence of static magnetic field B(r) which exerts the force F × ev × B

on P, where v is the velocity of P . Show that P travels with constant speed.

Answer 1

$F_1=evB,$

$F_2=ma=\frac{mv^2}{r},$

$F_1=F_2,$

$\frac{mv^2}{r}=evB,$

$v=\frac{eBr}{m}=const.$