Charged particles in a magnetic field $\vec{B}$ usually perform some type of circular motion, unless they move parallel to the field lines, due to the Lorentz force $\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$.

However, in the case where $\vec{E} = -\vec{v} \times \vec{B}$, a charged particle will translate uniformly. Given the link between special relativity and electrodynamics, is there some 'deeper' meaning behind this special case?