If a charged particle goes unaccelerated in a region containing electric and magnetic fields
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If a charged particle goes unaccelerated in a region containing electric and magnetic fields, force due to electric and magnetic field is equal
$|q \vec{E}|=q|\vec{v} \times \vec{B}|$
$\Rightarrow|\vec{E}|=|\vec{v} \times \vec{B}|$
$\vec{E} \perp \vec{B}$ and $\vec{E} \perp \vec{v}$
$\Rightarrow E=v B \sin \theta,$ not necessarily to $v B$ since sin $\theta$ is not necessarily equal to one.
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