Question

The pitch of the helix described by a charged particle in a magnetic field is given by:

Options

• \[p = v \cdot T = \frac{2\pi m v}{qB}\]

• \[p = \frac{mv_\parallel}{qB}\]

• \[p = v_\parallel \cdot T = \frac{2\pi m\, v_\parallel}{qB}\]

• \[p = v_\perp \cdot T = \frac{2\pi m\, v \sin\theta}{qB}\]

Answer 1

The pitch is the distance traveled along \[\vec B\] in one complete revolution: \[p = v_\parallel \cdot T = \frac{2\pi m\, v_\parallel}{qB}\]. Since only the parallel component \[v_\parallel = v \cos\theta\] contributes to motion along the field, it alone determines the pitch.