A charged particle follows a helical path of unequal pitch...

A charged particle follows a helical path of unequal pitch in a magnetic field. This means that:
(a) the magnetic field is non-uniform
(b) the velocity vector is not parallel to the magnetic field
(c) the velocity vector is not perpendicular to the magnetic field
(d) all of the above

Key Concepts

Helical Motion of Charged Particles

Charged particles moving in a magnetic field follow a helical path when their velocity has components both parallel and perpendicular to the magnetic field. The perpendicular component causes circular motion due to the Lorentz force, while the parallel component results in uniform linear motion along the field lines, combining to form a helix.

Velocity Component Orientation

The orientation of the velocity relative to the magnetic field is crucial. If the velocity is entirely parallel to the field, the path is a straight line, and if it is completely perpendicular, the path is a circle. A combination of both components produces a helix, with the pitch of the helix determined by the magnitude of the parallel component.

Magnetic Field Uniformity

A uniform magnetic field produces a constant pitch in the helical path because the magnetic force acting on the particle remains constant. In contrast, a non-uniform magnetic field can alter the particle’s motion by changing the magnitude of the force along the path, which may result in variations in the pitch of the helix.

Magnetic Lorentz Force

The magnetic Lorentz force, given by the cross product of the velocity of the charged particle and the magnetic field, governs the curvature of the particle's trajectory. This force acts perpendicular to both the velocity and the field, influencing the circular part of the motion, while any variations in the field or velocity components can modify the overall helical trajectory.

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