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: Understanding Charged Particle Motion in a Magnetic Field
A charged particle in a magnetic field experiences a force described 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.
The magnetic force is invariably perpendicular to the particle's velocity.
Step 2: Analyzing Velocity Components
A velocity component parallel to the magnetic field \( B \) results in no force along that direction, allowing continued motion.
A velocity component perpendicular to the magnetic field induces a force, leading to circular motion in a plane orthogonal to the field.
The superposition of these components (parallel and perpendicular) produces a helical motion, manifesting as a spiral path around the magnetic field lines.
Step 3: Conclusion
The charged particle's trajectory will be a helical path aligned with the magnetic field. This arises from the parallel velocity component driving movement along the field, while the perpendicular component dictates circular motion around the field lines.

Final Answer: The charged particle's path will be a helical path with the axis aligned with the magnetic field \( B \).