Question

A point charge is projected in a uniform magnetic field such that its velocity vector makes an angle of 30° with magnetic field. Then path followed by particle will be

• A. Straight line
• B. Circle
• C. Helix
• D. Parabola

Answer 1

Answer: (C)

Helix

Answer 2

The magnetic force on a charged particle is given by $\vec{F} = q(\vec{v} \times \vec{B})$. This force is always perpendicular to both velocity $\vec{v}$ and magnetic field $\vec{B}$. When $\vec{v}$ makes an angle $\theta$ with $\vec{B}$, $\vec{v}$ can be resolved into $v\cos\theta$ (parallel to $\vec{B}$) and $v\sin\theta$ (perpendicular to $\vec{B}$). The parallel component is unaffected, while the perpendicular component causes circular motion. The combination of linear motion along $\vec{B}$ and circular motion perpendicular to $\vec{B}$ results in a helical path.