Practice portal › Moving Charges and Magnetism › Motion of a Charge in a Magnetic Field
Asked in GSEB Board March 2018 · Circular motion: radius, period and energy
Idea: in a uniform magnetic field the magnetic force supplies the centripetal force, qvB=(mv²)/r, so r=(mv)/(qB).
Angular speed: ω=v/r=v×(qB)/(mv)=(qB)/m.
The speed cancels: a faster particle simply travels on a proportionally larger circle and takes exactly the same time to go round.
So ω depends on the charge, the field and the mass, but not on the linear speed.
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