Physics · Moving Charges And Magnetism · NEET
Split the velocity into two parts. The part across the field, v_perp = v sin(theta), gives the circular motion (force qv_perp B provides the center-pulling force). The part along the field, v_parallel = v cos(theta), feels NO magnetic force because force = qvB sin(angle) and the angle between v_parallel and B is 0. So v_parallel keeps the particle drifting straight along B at constant speed. A circle plus a steady straight drift equals a helix.
The perpendicular part sets the radius: r = m*v_perp/(qB) = m*v sin(theta)/(qB). The parallel part sets the pitch (forward distance per one full turn): p = v_parallel * T = 2*pi*m*v cos(theta)/(qB). Radius uses sin(theta), pitch uses cos(theta). Mixing these up is the most common mistake.
No. T = 2*pi*m/(qB) is fixed by m, q and B only. It does not depend on speed or on the angle. That is why the same T is used to find pitch. The angle only changes how the total speed splits into circular (sin) and forward (cos) parts, not the time for one loop.
At theta = 0 or 180 (parallel or antiparallel to B): v_perp = 0, so no circle, the charge goes in a straight line (force = 0). At theta = 90 (perpendicular): v_parallel = 0, so pitch = 0 and the path is a pure circle. Only for angles in between do you get a real helix.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Pitch is the straight distance the charge moves along B during one complete circle. Formula: p = v_parallel * T = 2*pi*m*v cos(theta)/(qB), where theta is the angle between v and B.
The magnetic force on the parallel part is qv_parallel B sin(0) = 0. With no force along B, that component stays constant, giving uniform forward drift.
Yes. The magnetic force is always perpendicular to velocity, so it does no work. The total speed v (and hence kinetic energy) stays constant; only the direction keeps turning.
In both, the time period T = 2*pi*m/(qB) is independent of speed. A cyclotron uses this fixed T to keep re-accelerating a charge; helical motion is the natural 3D path when the injected velocity has a component along B.
