Electric and Magnetic Fields, Maxwell equations
Gaussian units; as mentioned before, there are only E and B; D and H are derived , unmeasurable quantities
Maxwell equations are based on earlier empirical laws : Faraday's Law; Ampere's law (but only the "displacement current" mentioned here)
Visualized by fieldlines - which do not have any real physical basis ( "field strength is given by the density of fieldlines" is not precise enough )
But the shapes of fieldlines are very instructive. By the way - how do you find the fieldlines?
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Huygens' Principle again - and the Green's function analogy
Huygens -> waves -> reflection, refraction -> correct
Newton --> Snell's law completely wrong
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Maxwell explained the electromagnetic waves, which nobody have seen for another 30 years
and found that the spead of propagation is "the same" as the speed of light in air
(historical physics)
Light thus assumed / postulated to be electromagnetic wave
Simple dimension analysis which we shall often revisit ...
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The electric field ( and magnetic field ) strength squared gives the ENERGY DENSITY
It all nicely fits
because the "charge" and "charge(d) current" only appear in second powers in anything observable
Electricity is unobservable without electricity - and thus no need for Ampere or Coulamb - or Farad
as fundamental quantities
They are however, VERY IMPORTANT derived quantities, even measurable, e.g. in terms of
number and density of elementary charges
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Last comment above: Pressure has the same dimension as energy density. Now wonder then that PV = RT ( energy = Energy )
More about SI vs PHYSICS
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There is one more problem - the 4 pi choice. This factor appears either in the forces or in the divergence
and definitions of macroscopic quantities
Probably the nicest system is the Heaviside-Lorentz (see last time), which is the Gauss with 4 pi moved
(see the Jackson Table)
Vector potential, waves, radiation Gauge
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One should discuss further Faraday law, and the Faraday disk
Faraday disk NO CHANGE IN THE magnetic "FLUX", still EMF generated
The origin traced back to Lorentz force (missing here; must be revisited before we end this)
https://en.wikipedia.org/wiki/Homopolar_generator
see there https://en.wikipedia.org/wiki/Homopolar_generator#Disk-type_generator
Have a look at https://en.wikipedia.org/wiki/Faraday_paradox
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Mathematicians love the vector field - curls and fluxes ....
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For physical optics the interfaces are interesting - i.e. abrupt discontinuous changes of material properties
(continuous changes are optically less dramatic, not easy to study
wave propagations - geometry, sources
plane waves, spherical waves (point source) cylindrical waves (either line source - or 2-dim; plane problems with point source)
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Boundaries - these relations follow from "infinitesimal pillboxes" and tiny rectangle closed circuites
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The same relations with less mathematics and more intuition
Next time - more of the same - approaching reflection and refraction