Orbital Magnetic Moment and Angular Momentum
For a point particle of charge q and mass m in orbital motion, mu_L = (q/2m)L. For an electron, q is negative, so magnetic moment and angular momentum point oppositely.
Why this shows up in the exam
Comparing magnetic moment with angular momentum · Electron orbital direction questions · Rotating charged-particle systems
Learn the idea
A charge moving in a circular orbit has magnetic moment proportional to its orbital angular momentum. The orbit is both a mechanical rotation and a tiny current loop. Radius and angular speed appear in both quantities, so they cancel from the ratio, leaving only charge and mass.
🧠 Memory hook: Orbit makes both L and mu; q over 2m links them.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- mu_L = (q/(2m)) L — orbital gyromagnetic relation including the charge sign
- |mu_L|/|L| = |q|/(2m) — magnitude ratio independent of orbit radius and speed
- I = q f — equivalent current for orbital frequency f
How to approach it
- 1Identify charge sign and mass
- 2Use mu/L = q/(2m)
- 3Separate magnitude from vector direction
Common slip-ups that cost marks
- •Dropping the electron's negative sign
- •Using q/m instead of q/(2m)
- •Assuming the ratio depends on radius or angular speed
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A charge of 2 microC moves perpendicular to a 3 T magnetic field at 4 x 10^5 m/s. Find the magnetic force.
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