Helical motion in a magnetic field
Fire a particle into a magnetic field at an angle, and it traces out a spring.
When a charged particle's velocity makes an angle with the magnetic field, it can be resolved into components parallel and perpendicular to the field. The Lorentz force acts only on the perpendicular component, producing uniform circular motion; the parallel component feels no force and continues in uniform straight-line motion. Together they give a helix. The cyclotron period T = 2πm/(qB) does not depend on speed, which is the basis of the cyclotron and of magnetic focusing.
Gyroradius and pitch vs. angle
The larger the angle, the larger the radius and the smaller the pitch; at α = 90° the path is a circle.
Think about it
What shape does the path take when the angle between the velocity and the field is 90°?
The parallel component is zero, so the pitch is zero and the path degenerates into a circle. Try setting the angle to 90°; the smaller the angle, the more stretched out the helix.
Model assumptionsParticle is a proton · uniform magnetic field · gravity and radiation ignored · one revolution every 2 s on screen
Data log
Set the parameters and click “Record data”. Record several rows with different parameters to plot their relationship and fit a straight line; pause and record at different times to study how a reading changes with time.