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 the Motion of the Charged Particle
A charged particle moving in a magnetic field experiences a force given by: \[ F = q \vec{v} \times \vec{B} \] Where:
\(q\) is the charge of the particle,
\(\vec{v}\) is the velocity of the particle,
\(\vec{B}\) is the magnetic field.
The force due to the magnetic field is always perpendicular to the velocity of the particle.
Step 2: Analyzing the Components of Velocity
When the velocity has a component parallel to the magnetic field \( B \), the particle will experience no force along that direction, and will continue to move in the same direction.
When there is a component of velocity perpendicular to the magnetic field, the particle will experience a force and undergo circular motion in a plane perpendicular to the magnetic field.
The combination of these two components of velocity (along and perpendicular to the magnetic field) results in a helical motion. The particle moves in a spiral path around the magnetic field lines.
Step 3: Conclusion
The path of the charge particle will be a helical path with the axis along the direction of the magnetic field. This is because the component of velocity along \( B \) causes the particle to move parallel to the field, while the perpendicular component causes circular motion around the field lines. Final Answer: The path of the charge particle will be a helical path with the axis along magnetic field \( B \).