JEE Main · 2023 · 08 Apr 2023 · Shift 1 · Magnetic Effects of Current

Resolve the velocity into a component $v_{\parallel }$ along $\vec{B}$ and a component $v_{\perp }$ perpendicular to $\vec{B}$. The parallel component experiences no magnetic force, because $\vec{F}=q\vec{v}\times \vec{B}$ vanishes for motion along the field, so the particle advances uniformly in that direction. The perpendicular component experiences a force $q{v}_{\perp }B$ that is always directed towards a centre, producing uniform circular motion in the plane perpendicular to $\vec{B}$. Combining steady translation along the field with circular motion across it traces a helix whose axis lies along the magnetic field $\vec{B}$.