Orbital Current, Magnetic Moment, and Field
For orbital period T, the current magnitude is e/T. The orbital magnetic moment magnitude is eL/(2m), so Bohr quantization gives mu_n = n mu_B. At the centre of a circular orbit, B = mu_0 I/(2r), which scales as Z^3/n^5 in the simple Bohr model.
Why this shows up in the exam
Comparing magnetic fields of two orbits · Finding orbital magnetic moment · Connecting angular momentum with magnetism
Learn the idea
A revolving electron acts like a current loop whose magnetic effects follow its charge circulation. One electron passing a point once per orbit is a tiny current. Its loop creates a magnetic moment and a field at the nucleus.
🧠 Memory hook: One charge per period makes the current; L sets the moment.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- I_n = e/T_n = e f_n — magnitude of orbital current
- mu_n = e L_n/(2m) = n mu_B — orbital magnetic-moment magnitude
- B_center = mu₀ I_n/(2 r_n) — field at the centre of a circular current loop
- B_n proportional to Z³/n⁵ — Bohr-orbit central-field scaling
How to approach it
- 1Find the orbital period or frequency
- 2Convert charge circulation to current
- 3Use the loop field or mu = eL/(2m) as requested
Common slip-ups that cost marks
- •Using electron charge sign when only magnitude is asked
- •Assuming magnetic field scales as n alone
- •Forgetting that both current and radius change with n
🌟 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.
In hydrogen, an electron transitions from n = 2 to n = 1. Using E_n = -13.6/n^2 eV, find the emitted photon energy.
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