photonlines / intuitive-guide-to-maxwells-equations

An intuitive and visual guide to understanding Maxwell's equations.

Description

This is a guide to Maxwell's equations which focuses on providing an intuitive / geometric review of some of the main concepts.

The main inspiration for this guide was a video by 3Blue1Brown and it can be found here:

Divergence and Curl: The language of Maxwell's equations, fluid flow, and more

The images illustrating vector fields, as well as the concepts included in the curl and divergence sections were taken directly from the video.

The images shown when explaining the heat equation and partial differential equations were also taken from the video series by 3Blue1Brown called ‘Solving the Heat Equation’ which can be found using the link below:

Solving the Heat Equation

Also, by no means is this a thorough reference! For those wanting a more in depth view of the equations, I'd suggest taking a look at A Student's Guide to Maxwell's Equations by Dan Fleisch, which not only goes into a much more detailed view of the equations, but also includes valuable examples and practice problems!

Credits

• Divergence and Curl: The language of Maxwell's equations, fluid flow, and more
• Solving the Heat Equation
• The Feynman Lectures on Physics (Vol 2)
• A Student’s Guide to Maxwell’s Equations
• Why is Maxwell’s theory so hard to understand?
• A Visual Tour of Classical Electromagnetism
• The Physics Hypertexbook: Electromagnetic Waves

Many thanks to Grant Sanderson / 3Blue1Brown for the outstanding material he's made available on his channel, as well as for allowing me to use the images from his videos in presenting some of the topics available within the guide!

intuitive-guide-to-maxwells-equations's Issues

Nit: Typo of temperature

The heat equation has a typo. "The rate of change of temparature..." -> "The rate of change of temperature..."

Page 7: incorrect Laplacian symbol

The Laplacian in the heat equation on page 7 should either be written as ∇^2 or Δ, but not Δ^2.

Atoms & volume

I don't think that atoms are considered elementary particles and thus have no volume. They are definitely not fundamental particles since they are made up of other particles (electrons, protons, neutrons). I also think that the radius for several atoms has been measured which implies that they do have a volume.
The statement that atoms have no volume is made in the fifth paragraph of the Fields/What is a field? section.

Typo

Page 26: "who's" (are we want to measure) should be "whose".

Provide hints on derivation of wave equations on page 52?

Page 52 just says to apply the vector identity curl(curl(F)) = grad(div(F)) - div(grad(F)) to equations 3 and 4 to derive the electromagnetic wave equations, but doesn't give any hint about how to do this. It baffled me for a while... but the great thing was that it stimulated me to search on the Internet and find a better explanation elsewhere.

Maybe a couple hints would be helpful? Perhaps in an appendix?

Misspelling of "discrete"

On page 4:

These ‘things’ furthermore have mass and volume, and they have discreet boundaries.

Missing punctuation mark

On page 5, the full stop at the end of this sentence is missing:

Below, we’ll show a few examples of fields and illustrate what they mean

Typo in heat equation figure

The rate of change of temparature..