Question

A uniform magnetic field is directed vertically upwards. In which direction in this field should an alpha particle (which are positively charged) be projected so that it is deflected southward? Name and state the rule you have used to find the direction in this case.

Answer 1

An alpha particle has positive charge.
The Lorentz force is given by
F→=qv→×B→
For simplicity, you can take a right hand thumb rule. Curl your right hand fingers from the direction of v to B. Stretch out the thumb, the thumb gives the direction of the force.
The force towards south (the particle is deflected towards south).
The magnetic field is directed vertically upward. So the velocity is directed towards the east.
Therefore the alpha particle should be projected towards east.
I have used the expression for Lorentz force and the rule for vector multiplication.

Answer 2

Answer:

By using the flaming left-hand rule.

Explanation:

Since the alpha particle is positively charged so the current will exists in the direction in which the alpha particle will be projected.

mathematically:

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

$(-\hat{j})=q(\vec{V} \times \hat{k})$

$(-\hat{j})=q(\hat{i} \times \hat{k})$

Therefore

$\hat{V}=\hat{i} ,$ eastward or right side

Also, by using the flaming left-hand rule.

The forefinger will point in the upward direction.

And thumb should point in the direction in which deflection will take place ie. southward so in this circumstance middle finger will point in the right direction ie. East

Hence, the alpha particle should exist projected on the east or right side.

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