The Maxwell Series

Maya & Jared work through electromagnetism — from bench gear to the speed of light, one experiment at a time.

9 episodes · ~64 minutes total

1–2 Tools & measurement 3–6 The four laws 7 One wave 8 The numbers 9 The proof

Jared — a physics TA with a tuxedo and a chalkboard — and Maya — finance lead with a spreadsheet and healthy skepticism — start with the practical question of how to buy and use instruments, walk through each of Maxwell's four equations with a bench-top demo, then close the loop: the wave equation, the two constants, and Hertz's spark-gap experiment that confirmed it all in 1888. Each episode below explains its topic in the text; the video goes into the full derivation and demo.

EP 01

Why we spent $14k on a spectrum analyzer instead of $9k

total cost > sticker price

The series opener. A $9k analyzer and a $14k analyzer measure the same frequencies — but not the same signals. Jared and Maya break down total cost of ownership: phase noise, rework, and the time you lose when the cheap instrument can't see the problem. The episode that establishes the duo's dynamic: Maya counts the dollars, Jared counts the decibels.

4:12 · 22 MB
▶ Watch
EP 01
total cost > sticker price
▶ Watch
EP 02

How to measure the distance to the moon with a laser and corner cubes

d = c · Δt / 2

Lunar ranging in one demo: fire a laser pulse at the Apollo-era corner-cube retroreflectors, time the round trip, multiply by the speed of light. The corner cubes return light exactly the way it came in — the reason a few photons out of a quadrillion make it back, and why the Earth–Moon distance is known to millimeters.

4:56 · 20 MB
▶ Watch
EP 02
d = c · Δt / 2
▶ Watch
EP 03

Maxwell 1: What flows out of a charge

∮ E · dA = Qenc / ε₀

Gauss's law for electricity. Electric flux through any closed surface counts the charge inside — Coulomb's 1/r² law in disguise. The demo: a charged sphere, an electroscope, and the proof that where you draw the surface never matters, only how much charge it traps.

8:34 · 54 MB
▶ Watch
EP 03
∮ E · dA = Qenc / ε₀
▶ Watch
EP 04

There are no magnetic orphans

∮ B · dA = 0

Gauss's law for magnetism. Cut a magnet in half and you don't get an isolated north and an isolated south — you get two complete magnets. Field lines never begin or end; every B-field loop closes on itself. The episode where the universe declines to produce a magnetic monopole, no matter how hard Jared tries.

7:44 · 34 MB
▶ Watch
EP 04
∮ B · dA = 0
▶ Watch
EP 05

Change is the only source

∮ E · dl = −dΦB/dt

Faraday's law. A changing magnetic flux through a loop induces a circulating electric field — no battery, no wire, just motion. The demo is the physics behind every generator and transformer on the grid: move a magnet, watch the electroscope move with it.

7:02 · 37 MB
▶ Watch
EP 05
∮ E · dl = −dΦB/dt
▶ Watch
EP 06

The universe sends interdepartmental mail

∮ B · dl = μ₀ ( Ienc + ε₀ dΦE/dt )

Ampère's law plus Maxwell's fix. Put a compass inside a charging capacitor's gap — where no current flows — and it still deflects. Maxwell's displacement current closes the symmetry: a changing E-field makes a B-field, just as a changing B-field makes an E-field. This is the equation that predicts light.

7:54 · 25 MB
▶ Watch
EP 06
∮ B · dl = μ₀ ( Ienc + ε₀ dΦE/dt )
▶ Watch
EP 07

Curl is a thing

∇²E = μ₀ε₀ ∂²E/∂t²

The math episode: no lab demo, just a blackboard, two pieces of chalk, and a one-dollar budget. Take the curl of Faraday's law, the curl of Ampère-Maxwell, substitute, and the B-fields cancel — the wave equation falls out, with wave speed 1/√(μ₀ε₀). Light was hiding in the math since 1865. Two equations. Two curls. One substitution.

8:14 · 26 MB
▶ Watch
EP 07
∇²E = μ₀ε₀ ∂²E/∂t²
▶ Watch
EP 08

What you measure on a bench

c = 1 / √(μ₀ε₀) = 2.998 × 10⁸ m/s

Two pieces of apparatus define the constants: parallel wires carrying current give μ₀ = 4π × 10⁻⁷ H/m; a parallel-plate capacitor gives ε₀ = 8.854 × 10⁻¹² F/m. Multiply, square-root, invert — three hundred million meters per second, agreeing with Fizeau, Foucault, and Michelson. The speed of light from two chunks of metal and ceramic.

7:28 · 20 MB
▶ Watch
EP 08
c = 1 / √(μ₀ε₀) = 2.998 × 10⁸ m/s
▶ Watch
EP 09

Spark gap, three meters, the speed of light

c = λf

Karlsruhe, 1888. Hertz's induction coil fires a spark across two brass spheres; three meters away, a wire loop sparks in sync. Move the receiver and find the standing-wave maxima — every λ/2 ≈ 33 cm. Multiply λ by the oscillator frequency and you get c. Maxwell died believing the waves were real. Hertz's spark gap proved him right — and every radio since is this experiment, running.

7:14 · 33 MB
▶ Watch
EP 09
c = λf
▶ Watch

Blender animation clips

One 10-second "hero visual" per episode, rendered with Cycles on an RTX GPU — the field lines, the coil, the spark gap, the wave. The last card is the ep7 clip spliced into the episode itself, narration included.

ANIM 01

Spectrum sweep

6–12 GHz log sweep

The analyzer's trace builds in real time: noise floor first, then three signal peaks rise as the sweep passes them, and the camera pushes in on the tallest — the $14k instrument earning its keep.

0:10 · 0.6 MB · Cycles GPU
▶ Watch
ANIM 01
6–12 GHz log sweep
▶ Watch
ANIM 02

Corner cube

three reflections → antiparallel

A photon enters a corner-cube retroreflector, bounces off three mutually perpendicular mirrors, and exits exactly the way it came in — the geometry that lets one photon in a quadrillion find its way home from the Moon.

0:10 · 0.4 MB · Cycles GPU
▶ Watch
ANIM 02
three reflections → antiparallel
▶ Watch
ANIM 03

The ice pail

field outside: unchanged

A charged sphere moves to three positions inside Faraday's ice pail while the field lines outside — and the electroscope reading — never budge. Where the charge sits doesn't matter; only how much of it there is.

0:10 · 0.5 MB · Cycles GPU
▶ Watch
ANIM 03
field outside: unchanged
▶ Watch
ANIM 04

Snapping a magnet

∮ B · dA = 0

A bar magnet is snapped in two. Both halves instantly regrow full dipole field lines and the compasses swing to the new poles — there are no magnetic orphans, only smaller magnets.

0:10 · 0.8 MB · Cycles GPU
▶ Watch
ANIM 04
∮ B · dA = 0
▶ Watch
ANIM 05

The coil and the magnet

EMF ∝ dΦ/dt

A magnet drops through a coil, rests inside, then gets yanked out. The galvanometer needle reads velocity, not position — it kicks when the flux changes and goes dead while the magnet sits still.

0:10 · 0.5 MB · Cycles GPU
▶ Watch
ANIM 05
EMF ∝ dΦ/dt
▶ Watch
ANIM 06

Current through the gap

I = ε₀ · dΦE/dt

A capacitor charges, holds, and discharges while the compass flicks in sync — no wire crosses the gap, but a changing E-field carries the current anyway. Maxwell's addendum, on a bench.

0:10 · 0.5 MB · Cycles GPU
▶ Watch
ANIM 06
I = ε₀ · dΦE/dt
▶ Watch
ANIM 07

The electromagnetic wave

c = 1/√(μ₀ε₀)

E and B arrows oscillate in perpendicular phase as the wave sweeps down the board. Two measured constants, multiplied and square-rooted, give the speed of light — before anyone had seen one.

0:06 · 1.1 MB · Cycles GPU
▶ Watch
ANIM 07
c = 1/√(μ₀ε₀)
▶ Watch
ANIM 08

The μ₀ bench

F/L = μ₀I²/2πd

Two parallel wires share a current: magnetic loops grow around each wire, the force arrows pull them together, and the balance tips — the experiment that puts a number on μ₀.

0:10 · 0.4 MB · Cycles GPU
▶ Watch
ANIM 08
F/L = μ₀I²/2πd
▶ Watch
ANIM 09

Hertz's spark gap

λ·f = c

The transmitter spark fires; wavefront rings cross the bench at the speed of light and the receiver loop answers with its own spark, three meters away — Maxwell's waves, caught in the act.

0:10 · 0.6 MB · Cycles GPU
▶ Watch
ANIM 09
λ·f = c
▶ Watch
ANIM 07 · DEMO

The clip in the episode

8s episode + 6s wave

The ep7 animation spliced into the episode itself — eight seconds of Maya and Jared, then the rendered wave takes over. This is how every clip above will sit in its final episode.

0:14 · 2.2 MB · with narration
▶ Watch
ANIM 07 · DEMO
8s episode + 6s wave
▶ Watch