Question

A charged particle with some initial velocity is projected in a region where non-zero electric and/or magnetic fields are present. In column I, information about the existence of electric and/or magnetic field and direction of initial velocity of charged particle are given, while in Column II the probable path of the charged particle is mentioned. Match the entries of Column I with the entries of Column II

Answer 1

Case A:
$\overrightarrow{E}=0$
$\Rightarrow \overrightarrow{F_E}=0$
If initial velocity $\overrightarrow{v}$ is at an angle to $\overrightarrow{B}$, there will be a component along $\overrightarrow{B}$ and a component $\perp \overrightarrow{B}$
The $\perp$ component is responsible for circular motion in the plane $\perp$ to $\overrightarrow{B}$.
The parallel component to $\overrightarrow{B}$ is responsible for motion along $\overrightarrow{B}$.
If $\overrightarrow{v}\parallel \overrightarrow{B}$, the motion will be along $\overrightarrow{B}$ only.
Case B:
If $\overrightarrow{v}\parallel to\overrightarrow{E}$, there will be acceleration if charge is positive, deceleration if the charge is negative.
If $\overrightarrow{v}\nparallel to\overrightarrow{E}$, the trajectory will be a parabola.
Case C:
$\overrightarrow{E}\ne 0$
$\overrightarrow{B}\ne 0$
$\overrightarrow{E}\parallel \overrightarrow{B}$
Path will be helical since component $\parallel \overrightarrow{B}$ and $vecE$ will move the particle along this direction.
Component $\perp \overrightarrow{B}$ will make the particle move in a circle.
Hence, the combined motion will be helical.
Case D:
$\overrightarrow{E}\ne 0$
$\overrightarrow{B}\ne 0$
$\overrightarrow{v}\perp \overrightarrow{E}$
$\overrightarrow{v}\perp \overrightarrow{B}$
$\overrightarrow{F_{mag}}\parallel \overrightarrow{E}$ or $\overrightarrow{F_{mag}}\parallel (-\overrightarrow{E})$
Hence, path will be a parabola in general.
If $\overrightarrow{F_{mag}}\parallel (-\overrightarrow{E})$ and both magnitudes are equal, the path will be a straight line.
Hence,
$A\to 1,3$
$B\to 1,2$
$C\to 4$
$D\to 1,2$