# Start EM Ch.5: Magnetostatics finish Modern Physics Ch.7: J=L+S Methods of Math. Physics, Thus. 24 Feb. 2011, E.J. Zita Magnetostatics: Lorentz Force and.

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Start EM Ch.5: Magnetostatics finish Modern Physics Ch.7: J=L+S Methods of Math. Physics, Thus. 24 Feb. 2011, E.J. Zita Magnetostatics: Lorentz Force and Biot-Savart Law Divergence and Curl of B; Ampere’s Law Modern Physics Spin, Energy levels, Zeeman effect Fine structure, Bohr magneton, J=L+S

Ex.5.2: Cycloid motion: B=Bx, E=Ez, find particle motion if it starts from rest at the origin. 1. Draw. 2. Qualitative analysis. 3. Quantitative analysis.

Ex.5.4: (a) A current I is uniformly distributed over a wire of circular cross section with radius a. Find J.

Ex.5 (b) Suppose the current density in the wire is proportional to the distance from the axis: J=ks (for some constant k). Find the total current in the wire.

Finding field B from current I Biot Savart law in general (5.32, p.215) Ampere’s law, when symmetry permits (p.221) Draw Ampere’s law:

Apply Stokes’ Thm. to Magnetostatics

Using Ampere’s law 1.Draw, 2. Qualitative analysis, 3. Quantitative Find B for an infinite uniform surface current K=Kx over the xy plane. (I=dK/dlength)

Using Ampere’s law 1.Draw, 2. Qualitative analysis, 3. Quantitative Find B for a solenoid with n closely wound turns per unit length on a cylinder of radius R and carrying a steady current I.

We’ll finish Ch.5 next week. Choose some HW problems…

Continuing Modern Physics Ch.7: H atom in Wave mechanics Spin, Energy levels Zeeman effect Fine structure Bohr magneton J=L+S

H-atom wavefunctions ↔ electron probability distributions: l = angular momentum wavenumber Discussion: compare Bohr model to Schrödinger model for H atom.

m l denotes possible orientations of L and L z (l=2) Wave-mechanics L ≠ Bohr’s n 

Stern-Gerlach showed line splitting, even when l=0. l = 1, m=0,±1 ✓ l = 0, m=0, s= ±1/2 Normal Zeeman effect Anomalous Zeeman effect

Magnetic moments shift energies in B fields

Spin S and orbit L couple to total angular momentum J = L + S

Spin-orbit coupling: spin of e - in orbital magnetic field of p Fine-structure splitting (e.g. 21-cm line) (Interaction of nuclear spin with electron spin (in an atom) → Hyper-fine splitting)

Total J + external magnetic field → Zeeman effect

History of atomic models: Thomson discovered electron, invented plum-pudding model Rutherford observed nuclear scattering, invented orbital atom Bohr quantized angular momentum, improved H atom model. Bohr model explained observed H spectra, derived E n = E/n 2 and phenomenological Rydberg constant Quantum numbers n, l, m l (Zeeman effect) Solution to Schrödinger equation shows that E n = E/l(l+1) Pauli proposed spin (m s = ±1/2), and Dirac derived it Fine-structure splitting reveals spin quantum number

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