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Electromagnetics Knowledge Map
Physical intuition in 30 secondsMost electromagnetic technologies can be described by the same recurring questions: What fields exist? How do they propagate? How do they interact with matter? What device converts that interaction into a useful signal or force? How does the complete system use it?
The organizing chain for this site is
\[\boxed{\text{fields}\rightarrow\text{waves}\rightarrow\text{interaction with matter}\rightarrow\text{devices}\rightarrow\text{systems}\rightarrow\text{applications}.}\]1. Foundations: the field description
2. Classical engineering branches
3. Classical-to-quantum bridge
For a semiclassical atom–field description,
\[\mathbf E(t)\rightarrow H_E=-\mathbf d\cdot\mathbf E(t),\qquad \mathbf B(t)\rightarrow H_B=-\boldsymbol\mu\cdot\mathbf B(t).\]4. From Maxwell to complete systems
Maxwell → wireless link
Maxwell → AESA radar
Maxwell → MRI
Maxwell → Rydberg RF sensor
RF $\mathbf E$→$-\mathbf d\cdot\mathbf E$→Rabi coupling→EIT / AT / Floquet→photodetector→field estimate
Charged particle → measured current
$q(\mathbf E+\mathbf v\times\mathbf B)$→trajectory→$q\mathbf v\cdot\mathbf E_w$→TIA→oscilloscope / spectrum
5. Electrical-size regimes
A useful dimensionless parameter is
\[ka=\frac{2\pi a}{\lambda}.\]| Regime | Common model class | Typical applications |
|---|---|---|
| $ka\ll1$ | electro/magneto-quasistatics | capacitors, inductors, small sensors |
| $ka\sim1$ | full-wave Maxwell solution | antennas, resonators, scattering |
| $ka\gg1$ | full-wave or high-frequency asymptotics | electrically large spacecraft, reflectors, radar scenes |
See Scaling Laws & Dimensionless Numbers for a larger regime map.
The map is intentionally recursive: a sophisticated system usually contains several simpler electromagnetic problems nested inside one another.