Question

A charged particle goes undeflected in a region containing an electric and a magnetic field. It is possible that
(a) $\overrightarrow{E}\parallel \overrightarrow{B},$ $\overrightarrow{v}\parallel \overrightarrow{E}$
(b) $\overrightarrow{E}$ is not parallel to $\overrightarrow{B}$
(c) $\overrightarrow{v}\parallel \overrightarrow{B}$ but $\overrightarrow{E}$ is not parallel to $\overrightarrow{B}$
(d) $\overrightarrow{E}\parallel \overrightarrow{B}$ but $\overrightarrow{v}$ is not parallel to $\overrightarrow{E}$

Answer 1

(a) $\overrightarrow{E}\left|\right|\overrightarrow{B}$, $\overrightarrow{v}\left|\right|\overrightarrow{E}$
(b) $\overrightarrow{E}$ is not parallel to $\overrightarrow{B}$
In option (a) velocity, electric field and magnetic field are parallel to each other. So, the particle may accelerate but always continue to travel in the same straight path or go undeflected.
Another possibility of the particle to go undeviated is that magnetic force acting on it is counterbalanced by electric force. This is possible if all the three, i.e. velocity, magnetic field and electric field are perpendicular to each other, so that magnetic force is balanced by electric force. So option (b) can also be one possibility. But (c) and (d) are wrong statements.