A charged particle with charge q is moving in a uniform...

A charged particle with charge $q$ is moving in a uniform magnetic field. If this particle makes any angle with the magnetic field then its path will be
(a) circular
(b) straight line
(c) helical
(d) parabolic

Key Concepts

Uniform Magnetic Field

A uniform magnetic field is one in which the field lines are parallel and the magnetic field strength is constant throughout the region of interest. This consistency means that any charged particle moving within the field experiences forces that depend solely on the particle's velocity relative to the fixed, uniform direction of the field.

Lorentz Force

The Lorentz force is the force experienced by a charged particle moving in a magnetic field and is given by the cross product of the velocity and the magnetic field (F = q(v x B)). This force acts perpendicular to both the particle's velocity and the magnetic field, causing the particle’s trajectory to bend.

Decomposition of Velocity

When a charged particle enters a magnetic field at an angle, its velocity can be decomposed into two components: one parallel to the magnetic field and one perpendicular. The parallel component remains unchanged because the magnetic force does not act along the magnetic field, while the perpendicular component results in circular motion.

Helical Motion

Helical motion arises when the charged particle’s path is a combination of circular motion (due to the perpendicular component of velocity) and linear motion (due to the parallel component of velocity). These combine to form a helical or spiral trajectory as the particle moves forward along the direction of the magnetic field while simultaneously circling around the field lines.

Please give Ace some feedback