Light, charge, and the field that holds the world together.
Maxwell's four equations — the most important four lines in physics — unify electricity, magnetism, and light into a single field theory. Every radio, screen, wire, and star depends on them.
MODULE 1 · ELECTROSTATICS
ELECTRIC CHARGE AND COULOMB'S LAW
The force between two charges — and why it looks so much like gravity.
THE ELECTRIC FIELD
When a force has a place of its own.
GAUSS'S LAW
The equation that turns symmetry into an answer.
ELECTRIC POTENTIAL AND VOLTAGE
Energy per charge, and the map every battery reads from.
CAPACITANCE AND FIELD ENERGY
Where the charge goes when you let go of the switch.
CONDUCTORS AND THE FARADAY CAGE
Why a metal box is the safest place in a lightning storm.
THE METHOD OF IMAGES
A trick that turns a hard problem into a symmetry.
MODULE 2 · ELECTRIC FIELDS IN MATTER
POLARIZATION AND BOUND CHARGES
What happens when the charges can't leave, but can lean.
DIELECTRICS AND THE D FIELD
The extra field that only notices what's free.
BOUNDARY CONDITIONS AT INTERFACES
What the field must do when the material changes.
PIEZOELECTRICITY AND FERROELECTRICITY
The crystals that remember which way they've been pushed.
MODULE 3 · MAGNETOSTATICS
CURRENTS AND THE LORENTZ FORCE
Why a moving charge feels what a still one doesn't.
THE BIOT–SAVART LAW
The magnetic analogue of Coulomb, one current element at a time.
AMPÈRE'S LAW
The shortcut when the current walks a straight line.
THE VECTOR POTENTIAL
The field behind the field.
MAGNETIC DIPOLES AND TORQUE ON LOOPS
Why a compass turns, in the language of fields.
MODULE 4 · MAGNETIC FIELDS IN MATTER
MAGNETIZATION AND THE H FIELD
Matter's answer to an applied magnetic field.
DIAMAGNETISM AND PARAMAGNETISM
The quiet magnets hiding in almost everything.
FERROMAGNETISM, DOMAINS, AND HYSTERESIS
Why iron remembers, and why the memory can be erased.
SUPERCONDUCTIVITY AND THE MEISSNER EFFECT
When the field is not just weakened — it is thrown out.
MODULE 5 · ELECTRODYNAMICS & INDUCTION
FARADAY'S LAW OF INDUCTION
A changing magnetic field brings an electric field with it.
LENZ'S LAW AND MOTIONAL EMF
Nature pushes back against the change that caused it.
SELF AND MUTUAL INDUCTANCE
Why a coil resists its own changing current.
ENERGY IN MAGNETIC FIELDS
Where the energy goes when the current ramps up.
EDDY CURRENTS AND MAGNETIC BRAKING
The invisible circuits that stop a falling magnet.
MODULE 6 · CIRCUITS
DC CIRCUITS AND KIRCHHOFF'S LAWS
The two sentences that solve almost every schematic.
RC CIRCUITS AND THE CHARGING CURVE
Why the capacitor never quite gets there, and always almost does.
RL CIRCUITS
The coil's version of hesitation.
RLC CIRCUITS AND RESONANCE
Two stores of energy, one frequency that loves them both.
AC CIRCUITS, PHASORS, AND IMPEDANCE
Rotation as the secret of every wall socket.
TRANSFORMERS AND POWER TRANSMISSION
How one coil teaches another what voltage to be.
TRANSMISSION LINES AND IMPEDANCE MATCHING
When the wire becomes long enough to matter.
MODULE 7 · MAXWELL'S EQUATIONS
DISPLACEMENT CURRENT
The missing term Maxwell put in, and the universe it unlocked.
THE FOUR EQUATIONS, TOGETHER
The most important four lines in physics.
GAUGE FREEDOM AND THE POTENTIALS
The parts of the potential the field can't see.
THE POYNTING VECTOR
Where the energy in a field is flowing, right now.
MOMENTUM AND THE MAXWELL STRESS TENSOR
Fields carry momentum — and push on what they touch.
MODULE 8 · EM WAVES IN VACUUM
DERIVING THE EM WAVE EQUATION
Four equations, two fields, and light falling out the other side.
PLANE WAVES AND POLARIZATION
The shape of a ray of light, written in two transverse fields.
ENERGY, MOMENTUM, AND RADIATION PRESSURE
Light pushes. Measurably.
THE ELECTROMAGNETIC SPECTRUM
One equation, every wavelength from radio to gamma.
MODULE 9 · WAVES IN MATTER & OPTICS
INDEX OF REFRACTION
What slows light down when it has somewhere to be.
SKIN DEPTH IN CONDUCTORS
How deep a radio wave can actually get into a metal.
THE FRESNEL EQUATIONS
What reflects, what goes through, and at what angle.
TOTAL INTERNAL REFLECTION
The mirror made of an angle.
OPTICAL DISPERSION
Why a prism splits white light — and why a rainbow has an order.
GEOMETRIC OPTICS
When the wavelength is small enough to forget.
INTERFERENCE
Two waves that know how to add — and how to cancel.
DIFFRACTION AND THE DOUBLE SLIT
What a wave does when a wall gets in the way.
POLARIZATION, BREWSTER, AND BIREFRINGENCE
When the direction the field points starts to matter.
WAVEGUIDES AND OPTICAL FIBERS
How to keep light inside a pipe for a thousand kilometers.
MODULE 10 · RADIATION
THE LARMOR FORMULA
Why every accelerating charge leaves light behind.
ELECTRIC DIPOLE RADIATION
The simplest antenna in the universe.
ANTENNAS AND RADIO
The difference between a wire and a broadcast.
SYNCHROTRON RADIATION
Light made on purpose by bending electrons in a circle.
BREMSSTRAHLUNG
The light that comes out when a charge gets in the way of itself.
RADIATION REACTION
The force that a charge exerts back on itself.
MODULE 11 · EM & RELATIVITY
CHARGE IS INVARIANT
The one quantity every observer must agree on.
E AND B UNDER A LORENTZ BOOST
What looks like a magnet to you looks like an electric field to someone moving past.
THE ELECTROMAGNETIC FIELD TENSOR
Six numbers, one object, the full relativistic story.
MAGNETISM AS RELATIVISTIC ELECTROSTATICS
The reveal: there is no second force.
THE FOUR-POTENTIAL AND EM LAGRANGIAN
Electromagnetism rewritten as a principle of least action.
MODULE 12 · FOUNDATIONS
GAUGE INVARIANCE AND THE BIRTH OF GAUGE THEORIES
The symmetry that became the template for every force.
THE AHARONOV–BOHM EFFECT
When the potential matters even where the field is zero.
MAGNETIC MONOPOLES AND DUALITY
The symmetric version of Maxwell, and the particle we haven't found.
THE CLASSICAL LIMIT OF QED
Where classical electromagnetism ends, and what replaces it.