Question

A beam of electron passes, un-deflected through mutually perpendicular electric and magnetic fields. If the electric field is switched off, and the same magnetic field is maintained, the electrons moves

• A. in a circular orbit
• B. along a parabolic path
• C. along a straight line
• D. in an elliptical orbit.

Answer 1

The correct option is A in a circular orbit

Total force acting on the electron when switch is on
$${\overrightarrow{F}}_{net}={\overrightarrow{F}}_B+{\overrightarrow{F}}_E=q(\overrightarrow{V}\times \overrightarrow{B})+q\overrightarrow{E}$$Where,
$q=$charge
$\overrightarrow{V}$=velocity of charge $q$


When switch is off then $\overrightarrow{E}$ becomes zero and only $\overrightarrow{B}$ exists.

$\therefore$ only ${\overrightarrow{F}}_B$ is applied on $e^{-}$ beam,
$F_{net}={\overrightarrow{F}}_B=q(\overrightarrow{V}\times \overrightarrow{B})$

$\Rightarrow {\overrightarrow{F}}_B=-e(\overrightarrow{V}\times \overrightarrow{B})$

This force${\overrightarrow{F}}_B$ will make the $e^{-}$ beam to move in circular orbit as magnetic force doesnot increase the speed of the particle.

$\text{Alternate solution:}$

Since, direction of motion of electron must be perpendicular to the both electric and magnetic fields.When electric field is switch off then the magnetic field is perpendicular to the direction of motion of charge particle and therefore, the electrons starts exibiting circular motion.

Hence, option (a) is the correct answer.