All Problems Motion of Charged Particles in Electric and Magnetic Fields
Problem 3.387
Uniform electric and magnetic fields with strength \(E\) and induction \(B\) respectively are directed along the \(y\) axis (Fig. 3.101). A particle with specific charge \(q / m\) leaves the origin \(O\) in the direction of the \(x\) axis with an initial non-relativistic velocity \(v_{0} .\) Find: (a) the coordinate \(y_{n}\) of the particle when it crosses the \(y\) axis for the \(n\) th time; (b) the angle \(\alpha\) between the particle's velocity vector and the \(y\) axis at that moment.
(a) \(y_{n}=\frac{2 \pi^{2} m E n^{2}}{q B^{2}}\) (b) \(\tan \alpha=\frac{v_{0} B}{2 \pi E n}\).