Question

If a velocity has both perpendicular and parallel components while moving through a magnetic field, what is the path followed by a charged particle ?

• A. Circular
• B. Elliptical
• C. Linear
• D. Helical

Answer 1

Answer: (D)

Suppose, the velocity v of the particle entering the field B, instead of being perpendicular to B, makes an angle $\theta$ with it.

Then v may be resolved into two components, $V_{||}=v\cos \theta$ parallel to B and $v_{\perp }=v\sin \theta$
perpendicular to B. The component $V_{\Vert }$ gives a linear path and the component $V_{\perp }$ gives a circular path to the particle. The resultant of these two is a helical path whose axis is parallel to the magnetic field.