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 :
all ions deflect towards $$-y$$ -direction
Solution :
Case of positively charged particle :
Two force are acting on the positively charged particle
(a) due to electric field in the positive $$x$$-direction.
(b) Force due to magnetic field.
$$\eqalign{
& \overrightarrow F = q\left( {\overrightarrow v \times \overrightarrow B } \right) \cr
& \Rightarrow \overrightarrow F = q\left( {v\hat i \times B\hat k} \right) \Rightarrow \overrightarrow F = qvB\left( { - \hat j} \right) \cr} $$
This forces will move the positively charged particle towards Y-axis.
Case of negatively charged particle.
Two forces are acting on the negatively charged particle
(a) due to electric field in the negative $$X$$-direction.
(b) due to magnetic field
$$\eqalign{
& \overrightarrow F = - q\left( {\overrightarrow v \times \overrightarrow B } \right) \cr
& \overrightarrow F = - q\left[ {v\left( { - \hat i} \right) \times B\left( {\hat k} \right)} \right] \cr
& \overrightarrow F = - qvB\left[ {\hat i \times \hat k} \right],\overrightarrow F = qvB\left( { - \hat j} \right) \cr} $$
Same direction as that of positive charge.
(C) is the correct answer.