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In my book it is shown that the frequency of revolution of the charged particle in a magnetic field is independent of its energy.

Now I understand that why if a particle is in a magnetic field then the frequency of revolution of charged particle is independent of the energy of the particle.

Now my question is that why it is important in order to build a cyclotron.

What happens if the frequency depends upon the energy of the particle? Is it not possible to build the cyclotron in this case?

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    $\begingroup$ That's only true for non-relativistic particles. In the relativistic case one has to vary the frequency or the magnetic field in the machine or both, and that comes with additional problems which, at some point, are better avoided by building a synchrotron, instead. $\endgroup$ – CuriousOne Jan 16 '16 at 4:19
  • $\begingroup$ frequency $n = \frac{q B}{2 \pi m}$ depends upon the energy reached ( m is the energy, q the charge, B the MF ). The super-cooled magnets must be activated smoothly , perhaps this explains that ... $\endgroup$ – user46925 Jan 16 '16 at 11:53
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    $\begingroup$ the introduction of the wikipage of Synchrocyclotron describes the differences with a cyclotron : "the frequency is varied to compensate for relativistic effects as the particles velocity begins to approach the speed of light. This is in contrast to the classical cyclotron, where this frequency is constant" . $\endgroup$ – user46925 Jan 16 '16 at 12:54
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Obviously it would require more effort to build a cyclotron that has to change the frequency of the alternating current while the particle accelerates. That the frequency doesn't depend on the particle's energy (in the non-relativistic regime) means you don't need to change it during operation.

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Then polarity of dees can not change at the instant when charge particle arrives between the gap of two dees. Then charge particle can't be accelerated.

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