Classical Mechanics (Kibble & Berkshire) · Problem 6.12

Orbits in a central field — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · magnetic-force-energy

Problem

A particle

P

carries a charge

e

and moves under the influence of the static magnetic field

\boldsymbol{B}(\boldsymbol{r})

which exerts the force

\boldsymbol{F} = e\boldsymbol{v}\times\boldsymbol{B}

P

, where

\boldsymbol{v}

is the velocity of

P

. Show that

P

travels with constant speed.