Describe qualitatively the path of a charged particle moving in a region with uniform electrosatic and magnetic fields parallel to each other, with initial velocity (i) parallel (ii) perpendicular (iii) at an arbitrary angle with common direction of the fields.

Explanation

(i) When a charged particle moves parallel to both electrostatic and magnetic fields then the force on charged particle due to magnetic field is zero but due to electric field, the force on the charged particle will act along the direction of field and the charged particle will continue to move along the original straight line path.
(ii) When a charged particle moves perpendicular to both electric and magnetic fields, then due to electric field, the charged particle describes a parabolic path the due to magnetic field, it will describe a circular path. As a result of it, the particle will follow a resultant path in electric and magnetic fields. If electric and magnetic fields are perpendicular to each other as well as perpendicular to the motion of charged particle, the particle will continue moving along the same path if force on particle due to electric field is equal and opposite to the force on it due to magnetic field.
(iii) If we resolve `vecv` into two rectangular components, along B and perpendicular to `vecB`. Then due to component velocity perpendicular to `vecB`, the particle will describe a circular path and due to component velocity along `vecB` or `vecE`, it gets accelerated or retarded due to `vecE`, along the same path.