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AP Physics 2
12.2 Magnetism and Moving Charges
IntermediateMCQMathematicalProportional AnalysisConceptual16.5k
A schematic top-down view of a cyclotron's circular region of uniform magnetic field B directed perpendicular to the page. A spiral path starts at the center and expands outward to a circular boundary of radius R, where a tangential arrow shows an ion exiting the boundary.
Top view of particle trajectories in a cyclotron extracted at radius R.
A cyclotron uses a uniform magnetic field of magnitude \(B\) to accelerate ions in circular paths until they reach a fixed extraction radius \(R\). Three different ions are accelerated individually in the device under identical magnetic field conditions:

- Ion \(X\): charge \(+e\), mass \(m\)
- Ion \(Y\): charge \(+e\), mass \(2m\)
- Ion \(Z\): charge \(+2e\), mass \(3m\)

Which of the following correctly ranks the maximum kinetic energy \(K\) of the ions when they reach the extraction radius \(R\)?

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