Chapter 6.4, Problem 6P

The force acting on a moving charged particle in a magnetic field $B$ is $F=q(v\times B)$ where $q$ is the electric charge of the particle, and $v$ is its velocity. Suppose that a particle moves in the $(x,y)$ plane with a uniform $B$ in the $z$ direction. Assuming Newton’s second law, $mdv/dt=F,$ show that the force and velocity are perpendicular and that both have constant magnitude. Hint: Find $(d/dt)(v\cdot v)$.