Answer to Question #89674 in Electricity and Magnetism for Sukritha p

Question

A charged particle moves in a plane perpendicular to a magnetic field B. If it starts with some additional speed v parallel to B, the trajectory of the charged particle will be

Answer 1

The trajectory is a spiral, its axis is parallel to the magnetic field. The step of the spiral is

$$h = v \frac{2\pi}{\omega} = v \frac{2\pi m}{eB}$$

in nonrelativistic mechanics and

$$h = v \frac{2\pi E}{eBc^2}$$

in relativistic mechanics.