E x B drift and the cycloid

What you are seeing: a charged particle in crossed uniform fields, $\mathbf{B} = B \hat{z}$ (out of page) and $\mathbf{E} = E \hat{x}$ (right). Starting from rest, the particle traces a cycloid: it accelerates in the $+x$ direction under $\mathbf{E}$ until the resulting $\mathbf{v} \times \mathbf{B}$ curves it back, then repeats. The net motion is a uniform drift in the $\mathbf{E} \times \mathbf{B} / B^2$ direction (here $-y$).

The drift velocity $\mathbf{v}_d = \mathbf{E} \times \mathbf{B} / B^2$ is independent of the particle's charge and mass; positive and negative particles drift the same way. The cycloid amplitude is $E / B^2$ and its period equals the cyclotron period $T_c = 2 \pi m / (q B)$. Vary $E$ to make the drift faster; vary $B$ to tighten the cycloid loops.