Question

A charged particle is released from rest in a region of steady and uniform electric and magnetic fields, where magnetic field and electric field are parallel. The particle will follow -

• A. Straight line path
• B. Circular path
• C. Elliptical path
• D. Helical path

Answer 1

The correct option is A Straight line path

Initially,

Charged particle is at rest $i.e.V_o=0$

Forces acting on it,

${\overrightarrow{F}}_E=q\overrightarrow{E}$, and

${\overrightarrow{F}}_B=q{\overrightarrow{V}}_o\times \overrightarrow{B}=0$ as $V_o=0$

But because of ${\overrightarrow{F}}_E$, charge will gain velocity along $\overrightarrow{E}$.

Also, $\overrightarrow{E}||\overrightarrow{B}$, so, velocity of particle at any instant $\overrightarrow{V}\left(t\right)$ will be along $\overrightarrow{B}$.

$\therefore \theta$ between $\overrightarrow{V}\left(t\right)$ and $\overrightarrow{B}=0^{\circ }$

$\Rightarrow {\overrightarrow{F}}_B=qV\left(t\right)B\sin 0^{\circ }=0$

Thus, only one force $F_E$ acts on the charge at any time.

$\therefore$ Charge will move in straight line along $\overrightarrow{E}$.

Hence, option $\left(A\right)$ is the correct answer.