Lorentz force
F = q·v·B·sin α · charge in a magnetic field
Angle α between the velocity vector and the magnetic field vector. Elementary charge e = 1.6·10⁻¹⁹ C.
The Lorentz force is always perpendicular to both the velocity and the field — so it bends the charge onto a circular path (it changes neither its speed nor its energy). Maximum at α = 90°, zero when the motion is along the field lines.
The Lorentz force acts on a charge moving through a magnetic field:
where is the charge, its velocity, the magnetic flux density and the angle between the velocity vector and the field vector. The force is greatest when the charge moves perpendicular to the field () and zero when it moves along the field lines.
A key feature: the Lorentz force is always perpendicular to the velocity, so it does not change the speed of the charge — it only bends its path (into a circle in a uniform field). This is the operating principle of the cyclotron, the cathode-ray tube and the aurora.
Examples
Frequently asked questions
Why doesn't the Lorentz force change the charge's energy?+
Because it is perpendicular to the velocity — it does no work. It only changes the direction of motion, bending the path, without speeding the charge up or slowing it down.
When is the Lorentz force zero?+
When the charge is not moving (v = 0) or moves parallel to the field (α = 0°, sin 0° = 0). It is greatest when the motion is perpendicular to the field.
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