Classical Mechanics (Kibble & Berkshire) · Problem 2.4

Newton's laws of motion and the law of gravitation — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · general-particle-motion

Problem

The trajectory of a charged particle moving in a magnetic field is given by

\boldsymbol{r} = b\cos\Omega t\,\boldsymbol{i} + b\sin\Omega t\,\boldsymbol{j} + ct\,\boldsymbol{k},

where

b

\Omega

and

c

are positive constants. Show that the particle moves with constant speed and find the magnitude of its acceleration.