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

Concept: When a charged particle enters a magnetic field, it experiences a magnetic force given by the Lorentz force law: \[ F = q(\vec{v} \times \vec{B}) \] Key cases:
• If velocity is perpendicular to \(B\) → particle moves in a circular path.
• If velocity is parallel to \(B\) → particle moves in a straight line.
• If velocity has components both parallel and perpendicular to \(B\) → particle follows a helical path.

Step 1: Identify the components of velocity. The particle has velocity components: \[ v_{\parallel} \text{ (along } B), \quad v_{\perp} \text{ (perpendicular to } B) \]

Step 2: Analyze the motion.
• The perpendicular component \(v_{\perp}\) causes circular motion.
• The parallel component \(v_{\parallel}\) causes uniform motion along the field.

Step 3: Combine the two motions. The combination of circular motion and forward motion produces a: \[ Helical path \]