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Why does a charged particle follow a helical path when it moves partly along a magnetic field?

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Diagram showing a circular loop of wire with an electric current, surrounded by curved blue lines representing magnetic field lines that loop around the wire and pass through its center. — magnetism Some lines of the magnetic field B (blue) for an electric current I (gold) in a loop.

When a charged particle moves through a magnetic field, it experiences a Lorentz force that acts perpendicular to both its velocity and the magnetic field lines.12

The helical path occurs because the particle's velocity can be decomposed into two components: one parallel to the magnetic field and one perpendicular to it.3

Perpendicular component: The magnetic force acts on this component to pull the particle into a circular orbit around the magnetic field lines.12
Parallel component: The magnetic force has no effect on motion parallel to the field lines, so the particle continues to move at a constant velocity in that direction.123

The combination of these two motions—uniform motion along the field lines and circular motion around them—results in a helical trajectory with an axis parallel to the magnetic field. If the particle's velocity is perfectly parallel to the field, it moves in a straight line; if it is perfectly perpendicular, it moves in a circle.123