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 \bigskip

Hint:

A quick rule: \begin{itemize} \item \(v \perp B\) → Circular motion \item \(v \parallel B\) → Straight line \item \(v\) partly parallel and partly perpendicular → \textbf{Helical motion} \end{itemize}

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: \begin{itemize} \item If velocity is perpendicular to \(B\) → particle moves in a circular path. \item If velocity is parallel to \(B\) → particle moves in a straight line. \item If velocity has components both parallel and perpendicular to \(B\) → particle follows a helical path. \end{itemize} Step 1: {\color{red}Identify the components of velocity.} The particle has velocity components: \[ v_{\parallel} \text{ (along } B), \quad v_{\perp} \text{ (perpendicular to } B) \] Step 2: {\color{red}Analyze the motion.} \begin{itemize} \item The perpendicular component \(v_{\perp}\) causes circular motion. \item The parallel component \(v_{\parallel}\) causes uniform motion along the field. \end{itemize} Step 3: {\color{red}Combine the two motions.} The combination of circular motion and forward motion produces a: \[ Helical path \] \bigskip