Helical Motion In A Magnetic Field

As explained in NCERT Class 12, Chapter 4 (Moving Charges and Magnetism), when a charged particle enters a magnetic field at an angle $\theta$ that is neither $0^{\circ }$ nor $90^{\circ }$, its velocity is resolved into two parts. The component perpendicular to the field, $v\sin \theta$, produces uniform circular motion because it feels a magnetic force. The component parallel to the field, $v\cos \theta$, experiences no magnetic force and so continues unchanged, carrying the particle steadily along the field direction. The combination of steady drift plus circular motion produces a helix, and since the parallel speed is constant, the pitch (advance per turn) is constant. A straight line would require the force to be zero, which is false here. A single-plane circle occurs only at exactly $90^{\circ }$. A parabola arises for a constant force like gravity, not the velocity-dependent magnetic force. Plausibility check: superposing uniform linear drift on uniform circular motion geometrically yields a helix, confirming the answer. As a limiting test, setting $\theta =90^{\circ }$ makes the parallel component zero so the pitch collapses to zero and the helix degenerates into a plane circle, while $\theta =0^{\circ }$ removes the circular part entirely and leaves a straight line; the general oblique case correctly interpolates between these two extremes, which is exactly the behaviour a helix of constant pitch should show.