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  4. 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

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Q. 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

IIT JEEIIT JEE 2000Moving Charges and Magnetism

Solution:

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 $v=Aq E\hat{i}$
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.