Magnetics 1 Question 13
13. 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
(2000, 2M)
(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
Show Answer
Answer:
Correct Answer: 13. (c)
Solution:
- We can write $\mathbf{E}=E \cdot \hat{\mathbf{i}}$ and $\mathbf{B}=B \hat{\mathbf{k}}$
Velocity of the particle will be along $q$. E direction. Therefore, we can write
$$ \mathbf{v}=A q E \hat{\mathbf{i}} $$
In $\mathbf{E}, \mathbf{B}$ and $\mathbf{v}, A, E$ and $B$ are positive constants while $q$ can be positive or negative.
Now, magnetic force on the particle will be
$$ \begin{aligned} \mathbf{F} _m & =q(\mathbf{v} \times \mathbf{B})=q{A q E \hat{\mathbf{i}}} \times{B \hat{\mathbf{k}}} \\ & =q^{2} A E B(\hat{\mathbf{i}} \times \hat{\mathbf{k}}) \\ \mathbf{F} _m & =q^{2} A E B(-\hat{\mathbf{j}}) \end{aligned} $$
Since, $\mathbf{F} _m$ is along negative $y$-axis, no matter what is the sign of charge $q$. Therefore, all ions will deflect towards negative $y$-direction.
