🌀 Cyclotron — B into the page, a charge spiralling between two dees

A charge q of mass m in a field B moves on a circle of radius r = m·v / (q·B). Each gap crossing the dee voltage speeds it up so r grows — yet the revolution frequency f = q·B / (2·π·m) does not depend on v at all.

Walkthrough 1 / 4

Two hollow D-shaped electrodes sit in a magnetic field B that points into the page.

Magnetic field B 0.50 T

Dee voltage ΔV 120 kV

f = q·B / (2·π·m) = 7.63 MHz · T = 0.131 µs
r = m·v / (q·B) = 6.3 cm

v = 0.50 Mm/s · ΔV speeds the charge each crossing, so r & v grow — but f is unchanged.

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