A charged particle enters a region of uniform magnetic field of magnitude B with speed v, making an angle α with the field direction.
a. (i) Explain why the subsequent trajectory of the particle is a helix rather than a straight line or a circle.
b. (ii) Keeping the speed v and field magnitude B fixed, describe qualitatively how the radius of the circular part of the motion and the pitch of the helix vary when the entry angle α is changed from 0∘ to 90∘. State whether each quantity increases, decreases or remains unchanged with increasing α.
c. (iii) Sketch the paths corresponding to α=0∘, 30∘ and 90∘, clearly indicating the relative sizes of radius and pitch in each case.