Question

If a charged particle moves unaccelerated in a region containing electric and magnetic fields,
(a) $\overrightarrow{E}$ must be perpendicular to $\overrightarrow{B}$
(b) $\overrightarrow{v}$ must be perpendicular to $\overrightarrow{E}$
(c) $\overrightarrow{v}$ must be perpendicular to $\overrightarrow{B}$
(d) E must be equal to vB

Answer 1

(a) $\underset{E}{\to }$ must be perpendicular to $\underset{B}{\to }$
(b) $\underset{v}{\to }$ must be perpendicular to $\underset{E}{\to }$

As the charged particle is not accelerated, the field $\underset{E}{\to }$ cannot be parallel to velocity $\underset{v}{\to }$. Hence, the velocity $\underset{v}{\to }$ is perpendicular to the electric field $\underset{E}{\to }$.

The magnetic force, i.e. force due to the magnetic field, acts in a direction perpendicular to the plane containing $\underset{v}{\to }$ and $\underset{B}{\to }$. Hence, in order to counterbalance the magnetic force, an equal and opposite electric force must be applied along the same axis in which the magnetic force is acting. Hence $\underset{E}{\to }$ must be perpendicular to $\underset{v}{\to }$ and $\underset{B}{\to }$.
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