Question

A sodium ion moving from north to south enters a magnetic field directed vertically upwards. The force acting on the ion will be in a direction (a) Vertically downwards (b) (c) From east to west (d) From south to north From west to east
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Answer 1

Given:

A sodium ion moving from north to south enters a magnetic field directed vertically upwards.

To find:

Direction of force experienced?

Calculation:

In this kind of questions, we will try to use VECTOR CROSS PRODUCT to solve them.

• First try to assign the proper annotations, refer to digram.

Since sodium ion (positive ion) is moving from north to south, it's velocity vector will be :

$\rm \vec{v} = v \: ( \hat{k})$

Now, magnetic field intensity vector will be (directed vertically upwards):

$\rm \vec{B} = B \: (\hat{j})$

Now, force experienced will be :

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

$\rm \implies \vec{F} = q( v \hat{k} \times B \hat{j})$

$\rm \implies \vec{F} = qvB ( - \hat{i})$

Since $(-\hat{i})$ is directed along -X axis, the force direction will be from

EAST TO WEST .