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Circular Kinematics

A uniform mag...

Question

A uniform magnetic field acts right angles to the direction of motion of electrons.As a result, the electron moves in a circular path of radius 2 cm, if the speed of electrons is doubled, then the radius of the circular path will be.

A

2.0 cm

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B

0.5 cm

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C

4.0 cm

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D

1.0 cm

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Solution

The correct option is D 4.0 cm
The radius of the electron moving in a magnetic field is given by:
$r = \frac{m v}{q B}$

$\Rightarrow r \propto v,$

So, when the speed of the electron is doubled, the radius will also be doubled for the electron.
$\Rightarrow r_{2} = 2 r_{1} = 2 \times 2 = 4 c m$

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