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

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 &
$$\vec F=q(\vec v\times \vec B)$$
$$\Rightarrow \vec F=q[V\hat i\times B\hat k]\Rightarrow \vec F=qVB(\hat i\times \hat k)$$
$$\Rightarrow \vec F=qvB(-\hat j)$$
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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