A charged particle q is moving in the presence of a magnetic field B which is inclined at an angle 30∘ with the direction of motion of the particle. Draw the trajectory followed by the particle in the presence of the field and explain how the particle describes this path.
Solution
Resolve the velocity into a component along the field, vcos30∘, and one perpendicular to it, vsin30∘. The parallel component feels no magnetic force, so the particle drifts uniformly along B. The perpendicular component gives a force qvsin30∘B that is always perpendicular to the motion, bending that part of the motion into a circle of radius
r=qBmvsin30∘.
The uniform drift along the field combined with the circular motion across it makes the particle trace a helix whose axis is along B.
