Why does a charged particle follow a helical path around a magnetic field line?

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A charged particle follows a helical path around a magnetic field line due to the Lorentz force, which is the force exerted on a charged particle moving through a magnetic field.12

The magnetic component of this force acts in a direction perpendicular to both the particle's velocity and the magnetic field lines. When a particle moves at an angle relative to the magnetic field, its velocity can be decomposed into two components: one parallel to the field and one perpendicular to it.123

  • Parallel component: Because the magnetic force is zero when the velocity is parallel to the field, the particle continues to move undeflected along the field line.12
  • Perpendicular component: The magnetic force acts as a centripetal force, causing the particle to move in a circular orbit around the field line.12

The combination of constant motion along the field line and circular motion around it results in a helical trajectory. If the angle between the velocity and the field is 90°, the path becomes a perfect circle; if the angle is 0°, the particle moves in a straight line.132