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PhysicsUK interactive

Magnetic fields

Learning goal

Why does a charged particle curve without speeding up?

A magnetic force acts at right angles to the particle’s velocity. It changes the direction of motion, but not the speed or kinetic energy.

Set the situation

A particle enters moving to the right

v ⟂ B
Charge
Magnetic field
× means into the page · • means out of the page velocity, vforce, F
AngleF ⟂ v
Speedconstant
Kinetic energyconstant

Extension: how a cyclotron uses this circular motion
dee dee alternating p.d. across gap magnetic field bends the path inside each dee

Two fields have different jobs

  1. An electric field accelerates the particle each time it crosses the gap.
  2. The magnetic field bends the particle inside each dee but does no work.
  3. As speed increases, the orbit radius increases and the path spirals outwards.
f = B|Q| / 2πm
In the non-relativistic model, the orbit frequency is independent of speed and radius.

Point-particle, uniform-field model. Direction mode fixes v perpendicular to B. Radius mode changes one variable at a time and draws path radii in their correct ratio; real particle sizes are not shown.