Question

A charge particle moving in magnetic field \( B \), has components of velocity along \( B \) as well as perpendicular to \( B \). The path of the charge particle will be:

• A. Helical path with the axis perpendicular to the direction of magnetic field \( B \)
• B. Straight along the direction of magnetic field \( B \)
• C. Helical path with the axis along magnetic field \( B \)
• D. Circular path

Hint:

In the presence of a magnetic field, the motion of a charged particle can be analyzed in terms of components:
Parallel component: causes linear motion along the field.
Perpendicular component: causes circular motion, resulting in helical motion when combined with the parallel component.

Answer 1

The Correct Option is C

Step 1: Force on a Charged Particle in a Magnetic Field
A charged particle in a magnetic field experiences a force defined by: \[ F = q \vec{v} \times \vec{B} \] Where:
\(q\) represents the particle's charge,
\(\vec{v}\) is the particle's velocity,
\(\vec{B}\) is the magnetic field.
This magnetic force is consistently orthogonal to the particle's velocity.
Step 2: Velocity Component Analysis
A velocity component parallel to the magnetic field \( B \) results in no force in that direction, allowing continued motion.
A velocity component perpendicular to the magnetic field induces a force, leading to circular motion in a plane perpendicular to the field.
The superposition of these parallel and perpendicular velocity components results in helical motion, forming a spiral path around the magnetic field lines.
Step 3: Conclusion on Particle Path
The charged particle's trajectory will be a helical path, with its axis aligned with the magnetic field's direction. This arises from the parallel velocity component driving motion along the field and the perpendicular component causing circular motion around it.Final Answer: The trajectory of the charged particle is a helical path aligned with the magnetic field \( B \).