Question:
A charge particle moving in magnetic field \(B\), has the components of velocity along \(B\) as well as perpendicular to \(B\). The path of the charge particle will be
A charge particle moving in magnetic field \(B\), has the components of velocity along \(B\) as well as perpendicular to \(B\). The path of the charge particle will be
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Resolve the velocity into \(v_\parallel\) (unaffected by \(B\)) and \(v_\perp\) (gives circular motion); together they give a helix along \(B\).
Updated On: Nov 2, 2026
- helical path with the axis along magnetic field \(B\)
- straight along the direction of magnetic field \(B\)
- circular path
- helical path with the axis perpendicular to the direction of magnetic field \(B\)
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The Correct Option is A
Solution and Explanation
Resolve the velocity: \(v_\parallel\) along \(\vec{B}\) and \(v_\perp\) perpendicular to \(\vec{B}\).
The magnetic force \(\vec{F}=q(\vec{v}\times\vec{B})\) has no component along \(\vec{B}\), so \(v_\parallel\) stays constant and the particle keeps moving uniformly along \(\vec{B}\).
The force due to \(v_\perp\) has magnitude \(qv_\perp B\), is perpendicular to both \(v_\perp\) and \(B\), and so makes the particle move in a circle of radius \(r=\dfrac{mv_\perp}{qB}\) in the plane perpendicular to \(\vec{B}\).
Uniform circular motion in the perpendicular plane combined with uniform motion along \(\vec{B}\) is a helix whose axis is along \(\vec{B}\).
Answer: (1) helical path with the axis along magnetic field \(B\)
The magnetic force \(\vec{F}=q(\vec{v}\times\vec{B})\) has no component along \(\vec{B}\), so \(v_\parallel\) stays constant and the particle keeps moving uniformly along \(\vec{B}\).
The force due to \(v_\perp\) has magnitude \(qv_\perp B\), is perpendicular to both \(v_\perp\) and \(B\), and so makes the particle move in a circle of radius \(r=\dfrac{mv_\perp}{qB}\) in the plane perpendicular to \(\vec{B}\).
Uniform circular motion in the perpendicular plane combined with uniform motion along \(\vec{B}\) is a helix whose axis is along \(\vec{B}\).
Answer: (1) helical path with the axis along magnetic field \(B\)
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