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

To determine the path of a charged particle moving in a magnetic field with both parallel and perpendicular components of velocity, let's analyze each aspect of its motion:

1. Perpendicular Component of Velocity: v_{\perp}
   • When a charged particle moves perpendicular to a magnetic field B, it experiences a magnetic force that acts perpendicular to its velocity.
   • This results in circular motion due to the Lorentz force, which acts as a centripetal force.
   • Hence, the particle will revolve in a circle with a plane perpendicular to the magnetic field.
2. Parallel Component of Velocity: v_{\parallel}
   • The component of velocity parallel to the magnetic field does not get affected by the magnetic force as the force is zero in this direction.
   • This allows the particle to move freely along the magnetic field lines.
3. Combination of Both Components:
   • The combination of circular motion due to the perpendicular component and free motion along the magnetic field due to the parallel component results in a helical trajectory.
   • The helical path has its axis along the direction of the magnetic field, as the magnetic force acts perpendicular to both v_{\perp} and B.

Based on the above analysis, the correct answer is:

Helical path with the axis along magnetic field \( B \)

This is because the particle spirals around the magnetic field lines due to the perpendicular component and simultaneously moves along the field lines due to the parallel component.