An ionized gas contains both positive and negative ions. If it is subjected simultaneously to an electric field along the -direction and a magnetic field along the -direction, then [2000]

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 [2000]

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(3)

Given electric field along $+ x$ direction, $\vec{E} = E . \hat{i}$ and magnetic field along $+ z$ direction, $\vec{B} = B . \hat{k}$

Velocity of the ionised particle will be along the direction determined by $q . \vec{E}$

or velocity $\vec{v} = A q E \hat{i},$ where A is a positive constant.

Here, A, E, and B are positive constants.

Charge on ions $(q)$ may be positive or negative.

Magnetic force $\vec{F} = q (\vec{v} \times \vec{B})$

$∴$ $\vec{F} = q [(A q E \hat{i}) \times (B \hat{k})] = q^{2} A E B (\hat{i} \times \hat{k})$

$= q^{2} A E B (- \hat{j}) = {(\pm q)}^{2} A F B,$ along the negative $y$ -direction.

As magnetic force is along the negative $y$ -axis, hence all ions, whether positive or negative, will deflect towards the negative $y$ -axis.

Solution

Q.
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]

1 positive ions deflect towards $+ y$ -direction and negative ions towards $- y$ direction

2 all ions deflect towards $+ y$ -direction

3 all ions deflect towards $- y$ -direction

4 positive ions deflect towards $- y$ -direction and negative ions towards $+ y$ -direction.

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Solution

Q. 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]

1 positive ions deflect towards +y-direction and negative ions towards −y direction

2 all ions deflect towards +y-direction

3 all ions deflect towards −y-direction