Question

Show that the cyclotron frequency does not depend on the speed of the charged particle

Answer 1

Explanation:

The magnetic force to keep a charged particle moving a circle is given as

$F=qvB=\frac{mv^2}{r}$

Here, q is the charged particle v is its velocity perpendicular to uniform magnetic field B.

Above relation can also write,

$r=\frac{mv}{qB}$

Now we know, orbital period,

$T=\frac{2\pi r}{v}$

so.

$T=\frac{2\pi m}{qB}$

now cyclotron frequency,

$f=\frac{1}{T} =\frac{qB}{2\pi m}$

Not depend upon v.

Thus, the cyclotron frequency does not depend on the speed of the charged particle.

#Learn More: Cyclotron frequency.

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Answer 2

Answer:

the cyclotron frequency does not does depend on mcq