Charge in a Magnetic Field
Fire a charged particle into a magnetic field. Predict which way it bends, then find the radius of its circular path and where it lands.
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The magnetic force on a charge moving at right angles to the field is F = qvB. It is always at right angles to the velocity, so it changes the direction of the motion but never the speed: the magnetic force does no work. The path is a circle.
qvB = mv2/r, so r = mv/(qB)
The direction comes from the right-hand palm rule: the thumb points along v, the fingers along B, and the palm pushes in the direction of the force on a positive charge. For a negative charge, the force is the other way.
The particle goes round half a circle and lands on the plate at a distance 2r from the slit. This is how a mass spectrometer sorts ions by mv/q. The time for a full circle is T = 2πm/(qB), which does not depend on the speed.
The numbers are in relative units (1 q, 2 v, 3 m and so on), so you can compare shots without needing real values.
Learn more in the Charge in magnetic fields lesson.