D4d - crossed electric and magnetic fields

\vec{E} = (\begin{matrix} 0 & E_{y} & 0 \end{matrix}) \vec{B} = (\begin{matrix} 0 & 0 & B_{z} \end{matrix}) F^{α}_{β} = (\begin{matrix} 0 & 0 & E_{y} / c & 0 \\ 0 & 0 & B_{z} & 0 \\ E_{y} / c & - B_{z} & 0 & 0 \\ 0 & 0 & - B_{x} & 0 \end{matrix})

\frac{d u^{α}}{d τ} = \frac{q}{m} F^{α}_{β} u^{β}

\frac{d u^{0}}{d τ} = \frac{q}{m} \frac{E_{y}}{c} u^{2} \frac{d u^{1}}{d τ} = \frac{q}{m} \frac{B_{z}}{c} u^{2} \frac{d u^{2}}{d τ} = \frac{q}{m} (\frac{E_{y}}{c} u^{0} - B_{z} u^{1}) \frac{d u^{3}}{d τ} = 0

\frac{E_{y}}{c} γ c - B_{z} γ v_{x} = 0 ⟹ v_{x} = \frac{E_{y}}{B_{z}}