Ten articles that take you from the idea of a field to the four equations behind every antenna, cable and circuit board — with derivations, diagrams and worked RF examples in every part.
By the end of the series you will be able to read each of these and explain what it means for an RF design. Each card links to the article that develops it.
Electric charges are the sources of electric flux. Gives capacitance and the fields on conductors.
Part 2 → 2 · Gauss's law for magnetism ∇·𝐁 = 0There are no magnetic charges, so magnetic flux always flows in closed loops.
Part 3 → 3 · Faraday's law ∇×𝐄 = −∂𝐁/∂tA changing magnetic field creates a circulating electric field — induction, transformers, coupling.
Part 4 → 4 · Ampère–Maxwell law ∇×𝐇 = 𝐉 + ∂𝐃/∂tCurrents and changing electric fields create magnetic fields. Together with Faraday's law, this gives waves.
Parts 5–6 →Each article builds on the one before it. Read them in order, or jump to the stage you need.
Charges, currents and the two divergence laws.
What electric and magnetic fields are, how charges and currents create them, and why they combine into waves.
Electric fieldMagnetic fieldField linesLorentz forceEM wavesElectric flux and the first Maxwell equation, used to find the fields of spheres, conductors and a coaxial cable.
Electric fluxGaussian surface∇·𝐃 = ρConductorsCoax capacitanceMagnetic flux, why the net flux out of any closed surface is zero, and what that means for transformers and inductors.
Magnetic flux∇·𝐁 = 0MonopolesFlux linkageTransformer coresInduction, Ampère's law and the displacement current.
A changing magnetic flux induces voltage: generators, transformers, NFC, wireless charging and EMI pickup.
Induced EMFLenz's law∇×𝐄 = −∂𝐁/∂tMutual inductanceNFC & WPTCurrents create circulating magnetic fields — wires, solenoids, toroids, and the inductance and 50 Ω impedance of coax.
Right-hand rule∇×𝐇 = 𝐉Solenoid & toroidCoax inductanceZ₀Maxwell's fix to Ampère's law: a changing electric field acts as a current, which makes radio waves possible.
Capacitor paradox∂𝐃/∂tAmpère–MaxwellContinuityLoss tangentThe complete equations, waves, interfaces and real RF hardware.
All four equations side by side, in integral and differential form, with materials and an RF example for each.
Integral vs differentialConstitutive relationsε, μ, σPhasor formHistoryDerive the wave equation step by step and get the speed of light, 377 Ω, wavelength and skin depth from it.
Wave equationSpeed of lightη₀ = 377 ΩLossy mediaSkin depthWhat fields do at an interface, and how much of a wave reflects from substrates, radomes and metal shields.
Tangential & normalSurface currentΓ and τλ/4 matchingShieldingThe equations at work: transmission lines, waveguide modes, microstrip, antenna radiation and EM simulation.
Transmission linesTE/TM modesMicrostrip ε_effAntennasFEM / FDTDFour equations that describe all classical electric and magnetic phenomena: Gauss's law (charges produce electric fields), Gauss's law for magnetism (there are no magnetic charges), Faraday's law (a changing magnetic field produces an electric field) and the Ampère–Maxwell law (currents and changing electric fields produce magnetic fields).
Every RF structure is a solution of them. Characteristic impedance, waveguide cut-off, microstrip effective permittivity, reflections, shielding and antenna radiation patterns all come directly from Maxwell's equations and their boundary conditions, and EM simulators such as HFSS and CST solve them numerically.
Algebra, basic trigonometry and an idea of what derivatives and integrals mean. Vector operations such as divergence and curl are explained as they appear, and every article includes worked numerical examples.
In order from Part 1 to Part 10 if you are new to electromagnetics. If you already know the four laws, start at Part 7 for the complete equations, then continue to waves (Part 8), boundary conditions (Part 9) and applications (Part 10).
Part 1 takes about 16 minutes and needs no prior electromagnetics.