question_answer

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

Correct Answer: D

Solution :

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 \[{{v}_{\bot }}=v\,\sin \theta \] perpendicular to B. The component \[{{v}_{||}}\] gives a linear path and the component \[{{v}_{\bot }}\] gives a circular path to the particle. The resultant of these two is a helical path whose axis is parallel to the magnetic field.