Name: Conversion of a Galvanometer Into a Voltmeter
Uploaded: 2019-07-19
Duration: 7 min 18 s
Description: This video helps us understand the working of a galvanometer. It also teaches us how to convert it into a voltmeter of the desired range both theoretically a...

Question

With the help of a diagram, explain the principle and working of a cyclotron. Show that cyclotron frequency does not depend on the speed of the particles.

Accepted Answer

Cyclotron :

It is a device used to accelerate charged particles like protons, deuterons, α-particles, etc, to very high energies. Principle : A charged particle can be accelerated to high speeds (energies) by passing it through electric field many number of times and at the same time magnetic field makes the charged particle to move in a circular path.

Let a particle of charge $q$ and mass $m$ enters a region of magnetic field vector B with a velocity vector $v$ , normal to the field vector B. The particle follows a circular path, the necessary centripetal force is provided by the magnetic field.

Therefore,

Magnetic force on charge $q$ = Centripetal force on charge $q$

Clearly, this frequency is independent of both the velocity of the particle and the radius of the orbit and is called cyclotron frequency or magnetic resonance frequency. This is the key fact which is used in the operation of a cyclotron.This condition in which frequency of applied voltage is equal to the frequency of revolution of charged particle is called the cyclotron’s resonance condition.

With the help of a diagram, explain the principle and working of a cyclotron. Show that cyclotron frequency does not depend on the speed of the particles.

Important Questions on Moving Charges and Magnetism

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