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)

all ions deflect towards y-direction

Answer 2

We can write $E=E .\widehat{i}$ and $B=B\widehat{k}$
Velocity of the particle will be along E direction. Therefore, we can write
\hspace15mm v=Aq E\widehat{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
$F_m=q(v \times B)=q\\{AqE\widehat{i}\\}\times\\{B\widehat{k}\\}$
\hspace15mm =q^2 AEB(\widehat{i}\times\widehat{k})
\hspace15mm F_m=q^2 AEB (-\widehat{j})
Since, $F_m$is along negative y-axis, no matter what is the sign of charge' Therefore, all ions will deflect towards negative y-direction.