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AP Physics 2
12.2 Magnetism and Moving Charges
AdvancedMCQMathematical22.8k
A top-down schematic diagram of a cyclotron. Two semi-circular hollow metal conductors, labeled Dee 1 on the left and Dee 2 on the right, are separated by a narrow vertical gap. A particle of charge +q starts near the center gap and follows an expanding spiral trajectory composed of semicircular arcs of increasing radius within the dees. Uniform magnetic field vectors represented by dots inside circles (directed out of the page) are evenly spaced across the region. An alternating voltage source labeled \Delta V is connected across the gap between the two dees. The outer radius of each dee is labeled R from the center to the outer curved boundary. No other labels, lines, text, or axes appear.
Top-down view of a particle accelerating in a cyclotron.
A particle of mass \(m\) and positive charge \(q\) is released from rest near the center of a cyclotron. The cyclotron consists of two hollow D-shaped conductors (dees) of outer radius \(R\) situated in a uniform magnetic field of magnitude \(B\) directed perpendicular to the plane of the dees. An alternating electric potential difference of magnitude \(\Delta V\) accelerates the particle each time it crosses the narrow gap between the dees. Assuming the particle exits the cyclotron when its circular trajectory reaches radius \(R\), which of the following expressions correctly represents the minimum number of gap crossings \(N\) required for the particle to reach the exit?

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