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 +ydirection and negative ions towards y direction
B
all ions deflect towards +ydirection
C
all ions deflect towards ydirection
D
positive ions deflect towards ydirection and negative ions towards +ydirection

Solution

## The correct option is C all ions deflect towards $$-y-$$directionCase 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 &$$\vec F=q(\vec v\times \vec B)$$$$\Rightarrow \vec F=q[V\hat i\times B\hat k]\Rightarrow \vec F=qVB(\hat i\times \hat k)$$$$\Rightarrow \vec F=qvB(-\hat j)$$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$$\Rightarrow \vec F=-q(\vec v\times \vec B)\Rightarrow \vec F=-q[v(-\hat i)\times B(\hat k)]$$$$\Rightarrow \vec F=qvB[\hat i\times \hat k]\Rightarrow \vec F=qvB(-\hat j)$$Same direction as that of positive charge.Physics

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