The following simulation shows trajectory for a charged particle in electric and/or magnetic field.

$\vec{F}=q\vec{E}+q\vec{v}\times\vec{B}$

The magnetic field B is always in Z direction in the simulation, however, you can change Ex,Ey or Ez with a slider.
The initial condition is $\vec{B}=B_0 \hat{z}, E=0 , \vec{v}=v_0 \hat{y}$ , so the result is a circular motion.

If you add E field, then you will find $\vec{V_d}=\frac{\vec{E}\times\vec{B}}{|\vec{B}|^2}$ (E cross B drift).
The particle will drift along $\vec{V_d}$

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