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Nuclear and Particle Physics

The cyclotron and the radius of a charged particle's path

  • 2 things to know
  • Papers 1 and 3

Overview

Recall questions on how a cyclotron is built, where the particle gains energy, why it spirals outwards, and the derivation and use of r = p/(BQ).

What you need to know

Answer each one before you reveal it.

Your recallNot started
Numbers

How is the equation r = p/(BQ) derived, and what happens to a particle's radius if the magnetic flux density is doubled?

Numbers

Where in a cyclotron does the particle actually gain energy, and what happens to it inside a dee?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    How is a cyclotron constructed?

    Model answer

    Two hollow D-shaped electrodes sit in an evacuated chamber with a uniform magnetic field applied perpendicular to their flat faces, and an alternating potential difference is applied across the gap between them.

  2. 2

    Where in a cyclotron does the particle actually gain energy?

    Model answer

    Only in the gap between the dees, where the electric field acts; inside a dee there is no electric field and the particle simply follows a semicircular path at constant speed.

  3. 3

    Why does a particle in a cyclotron spiral outwards?

    Model answer

    Its momentum increases each time it crosses the gap, and since r = p/(BQ) with B and Q fixed, each successive semicircle has a larger radius.

  4. 4

    Why can a cyclotron use an alternating supply of fixed frequency for non-relativistic particles?

    Model answer

    The time for a semicircle is independent of both speed and radius, so the particle always takes the same time to return to the gap and the polarity reversal stays in step.

  5. 5

    How is the equation r = p/(BQ) derived for a charged particle in a magnetic field?

    Model answer

    The magnetic force BQv provides the centripetal force, so BQv = mv²/r; cancelling v and rearranging gives r = mv/(BQ) = p/(BQ).

  6. 6

    What happens to the radius of a particle's path if the magnetic flux density is doubled at constant momentum?

    Model answer

    The radius halves, because r is inversely proportional to B.

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