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Deduce an Expression for the Frequency of Revolution of a Charged Particle in a Magnetic Field - Physics

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Deduce an expression for the frequency of revolution of a charged particle in a magnetic field and show that it is independent of velocity or energy of the particle.

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When a charged particle with charge q moves inside a magnetic field `vecB`with velocity v, it experiences a force, which is given by:


Here, `vecv` is perpendicular to `vecB`,`vecF`is the force on the charged particle which acts as the centripetal force and makes it move along a circular path.

Let m be the mass of the charged particle and r be the radius of the circular path.


v and B are at right angles:



Time period of circular motion of the charged particle can be calculated as shown below:




 ∴ Angular frequency is



 Therefore, the frequency of the revolution of the charged particle is independent of the velocity or the energy of the particle.

Concept: Motion in Combined Electric and Magnetic Fields - Cyclotron
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