Two identical charged particles enter a uniform magnetic field with same speed but at angles 30^o an

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4.Moving Charges and Magnetism

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Two identical charged particles enter a uniform magnetic field with same speed but at angles $30^o$ and $60^o$ with field. Let $a, b$ and $c$ be the ratio of their time periods, radii and pitches of the helical paths than

A

$abc = 1$

B

$a = bc$

C

$abc < 1$

D

Both $(A)$ and $(B)$

Solution

$r=T=\frac{2 \pi m}{q B} a=1$

$r=\frac{m V_{1}}{q B}, b=\frac{\sin 30^{\circ}}{\sin 60^{\circ}}=\frac{1}{\sqrt{3}}$

Pitch a $v \cos 0 c=\frac{\cos 30^{\circ}}{\cos 60^{\circ}}$

So abc $=1$

Standard 12

Physics

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