Question

An ionized gas contains both positive and negative ions. If it is subjected simultaneously to an electric field along the $+x-$direction and a magnetic field along the $+z$ direction, then

• A. positive ions deflects towards $+y-$direction and negative ions towards $-y$ direction
• B. all ions deflect towards $+y-$direction
• C. all ions deflect towards $-y-$direction
• D. positive ions deflect towards $-y-$direction and negative ions towards $+y-$direction

Answer 1

The correct option is C all ions deflect towards $-y-$direction

Case of positively charged particle: Two forces are acting on the positively charged particle (i) force due to electric field in the positive x direction, and (ii) force due to magnetic field &
$\overrightarrow{F}=q(\overrightarrow{v}\times \overrightarrow{B})$
$\Rightarrow \overrightarrow{F}=q[V\hat{i}\times B\hat{k}]\Rightarrow \overrightarrow{F}=qVB(\hat{i}\times \hat{k})$
$\Rightarrow \overrightarrow{F}=qvB(-\hat{j})$
This force will deflect the positively charged particle toward -y axis.
Case of negatively charged particle:
Two forces are acting on the negatively charged particle
(i) due to electric field on the negative X direction, and
(ii) due to magnetic field
$\Rightarrow \overrightarrow{F}=-q(\overrightarrow{v}\times \overrightarrow{B})\Rightarrow \overrightarrow{F}=-q\left[v\right(-\hat{i})\times B(\hat{k}\left)\right]$
$\Rightarrow \overrightarrow{F}=qvB[\hat{i}\times \hat{k}]\Rightarrow \overrightarrow{F}=qvB(-\hat{j})$
Same direction as that of positive charge.