Question

A charged particle moves in a magnetic field \(B\) with velocity components both along and perpendicular to \(B\). What is its path?

• A. Circular path
• B. Straight line
• C. Helical path
• D. Parabolic path

Hint:

A quick rule:
• \(v \perp B\) → Circular motion
• \(v \parallel B\) → Straight line
• \(v\) partly parallel and partly perpendicular → Helical motion

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We need to describe the trajectory of a charged particle entering a magnetic field with an arbitrary velocity that is neither strictly parallel nor strictly perpendicular to the field lines.
Step 2: Key Formula or Approach:
The magnetic force is \(\vec{F} = q(\vec{v} \times \vec{B})\). Resolve the velocity \(\vec{v}\) into two components:
1. \(v_{\perp}\) (Perpendicular to \(B\)): This component experiences a force that provides centripetal acceleration, leading to circular motion.
2. \(v_{\parallel}\) (Parallel to \(B\)): This component experiences zero magnetic force (\(\sin 0^\circ = 0\)), leading to constant linear motion along the field.
Step 3: Detailed Explanation:
The particle undergoes two simultaneous motions:
- Circular motion in the plane perpendicular to the magnetic field.
- Uniform linear motion along the direction of the magnetic field.
Combining a circle with a forward translation results in a spiral or helical path.
Step 4: Final Answer:
The path followed by the particle is helical.