(a brief reminder of electromagnetism)

Prezentace na téma: "(a brief reminder of electromagnetism)"— Transkript prezentace:

1 (a brief reminder of electromagnetism)
Maxwell Equations (a brief reminder of electromagnetism)

2 Maxwell’s equations of electromagnetism
All relationships between electric and magnetic fields and their sources summarized by four equations. James Clerk Maxwell

3 Faraday’s Coil

4

5 Basic Facts – Maxwell Equations
obtained by generalizing of observations intrinsically relativistic can be made compatible with QM- quantum electrodynamics this lecture: “classical” electric and magnetic field

6 Maxwell Equations electric charge “source” magnetic charge (monopole)
“vector”

7 Maxwell Equations 12 variables .... 8 equations

8 Maxwell Equations 12 variables .... 8 equations “material relations”

9 Potentials scalar potential vector potential satisfied automatically:

10 Look at the cross section
Called: “Electromagnetic Waves” Accelerating electric charges give rise to electromagnetic waves E and B are perpendicular (transverse) We say that the waves are “polarized.” E and B are in phase (peaks and zeros align)

11 General solutions (retarded) potentials,
j(r’) field sources (e.g. molecules) observer (r) A(r) (retarded) potentials, in chemistry we do not care about relativity at this point

12 Multipole Expansions molecules dimension ~ r’ << observation distance r

13 Multipole expansion of electrostatic field
elektric monopole elektric dipole quadrupole octupole etc.

14 Magnetic field - similarly
magnetic dipole , Discrete charges: .

15 Electrodynamics @ Schrödinger equation:
p  p + qA V  V + q.

16 Molecule @ Electric Field
 = -r.E E = E - p0.E - E..E + ... molecular electric dipole molecular polarizability

17 Molecule @ Magnetic Field
(static field) E = E - m0.B - B..B + ... .

18 Molecule @ Magnetic Field
(static field) E = E - m0.B - B..B + ... molecular magnetic dipole . molecular magnetic susceptibility

19 Dependence of magnetic properties on coordinate origin
- observable variables (should not) depend on the origin

20 Dependence of magnetic properties on coordinate origin
- observable variables (should not) depend on the origin Solution: - infinite basis of AOs computation in molecular origin GIAO gauge invariant atomic orbitals (London or Field-Dependent AOs) special methods Important : NMR, VCD!!

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