Edexcel A-Level Physics 9PH0
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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.
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
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
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
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
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
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
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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