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 deflect 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

Answer: (C)

We can write $E=E.\hat{i}$ and $B=B\hat{k}$
Velocity of the particle will be along $q.E$ direction.
Therefore, we can write $v=AqE\hat{i}$
In $E,B$ and $v.A,E$ and $5$ are positive constants while $q$ can be positive or negative
Now, magnetic force on the particle will be
$F_m=q(v\times B)=q\{AqE\hat{i}\}\times \{B\hat{k}\}$
$=q^{2}AEB(\hat{i}\times \hat{k})$
$F_m=q^{2}AEB(-\hat{j})$
Since, $F_m$is along negative y-axis, no matter what is the sign of charge' $q$. Therefore, all ions will deflect towards negative y-direction.