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Intuitive Guide to Maxwell's Equations

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Re: Intuitive Guide to Maxwell's Equations

#21

Post by l33tman »

tarsinge wrote: post #15

Interesting, I always thought of fields as the interface to measure underlying particles interactions instead of the "base thing" itself. My reasoning was that since it was impossible to model effects from individual particles behavior, we were modeling the aggregate effect using fields, but underneath it was just "small objects" interactions. Edit: reading the rest of the guide, I find it very enlightening and at th…

At this level of abstraction and energy scale it's modelled as a mathematical field, but things get more tricky "underneath" just as you suggest.

Re: Intuitive Guide to Maxwell's Equations

#22

Post by martincmartin »

chronolitus wrote: post #3

These kinds of visual, well thought out explanations of topics which are often taught with terse, obscure and uninviting methods are a gift. On a tangent: I remember asking my Calculus 101 professor what the "intuitive meaning" of divergence and curl was, outside of the formal math and equations. He was shocked that one could ask to sully these perfect mathematical concepts with dirty intuitive reductions. A guide li…

The book Geometrical Vectors does exactly that. In fact, it considers the gradient vector to be a different kind of vector than a normal distance vector. If I have a vector between two points, and I compress space so that the points move closer together, then the distance vector gets smaller. However, the gradient vector gets bigger. The gradient is basically a density, it's units are units-of-whatever-your-taking-the-gradient-of / meters.

And, or course, the vector you get from a cross product only has 3 degrees of freedom because we live in a 3D world. The cross product of two 2D vectors is a scalar, the cross product of two 4D vectors needs 6 numbers to describe it. Even in 3D, if you reflect the original vectors in a mirror, the cross product now points the opposite direction, i.e. it depends on the handednes of the coordinate system.

Re: Intuitive Guide to Maxwell's Equations

#23

Post by SAI_Peregrinus »

It's also interesting once you understand what Maxwell's equations mean to look at their geometric algebra formulation[1]. In particular it makes their use in special and general relativity somewhat more elegant, since the GA form explicitly includes a spacetime component. Of course that page isn't an elementary introduction, it assumes familiarity with GA and the divergence & curl operators, as well as some concepts of special & general relativity.

https://www.av8n.com/physics/maxwell-ga.htm

Re: Intuitive Guide to Maxwell's Equations

#24

Post by ChrisLomont »

antman wrote: post #5

As a side note there was a historical debate, and the shape of these equations is the end result of the chosen system. In geometric algebra which did not prevail, these are one equation.

In modern relativisitic formulations using tensors they are one equation also, derivable from the action of the electromagnetic field tensor. This formulation also shows that electric and magnetic fields are the same, simply rotated under a relativisitic transform, which is the modern view.

Start here for the ideas https://en.wikipedia.org/wiki/Electromagnetic_tensor

Re: Intuitive Guide to Maxwell's Equations

#25

Post by Aardwolf »

I'd be interested in an intuitive explanation of the units of electromagnetic quantities.

E.g. the unit of magnetic flux is equivalent to volt times seconds, and inductance is volt times seconds per ampere. But I can't find intuitive explanations for this

Re: Intuitive Guide to Maxwell's Equations

#26

Post by discordance »

Aardwolf wrote: post #25

I'd be interested in an intuitive explanation of the units of electromagnetic quantities. E.g. the unit of magnetic flux is equivalent to volt times seconds, and inductance is volt times seconds per ampere. But I can't find intuitive explanations for this

If I’m getting you right, take a look into ‘dimensional analysis’

Re: Intuitive Guide to Maxwell's Equations

#27

Post by augustt »

Aardwolf wrote: post #25

I'd be interested in an intuitive explanation of the units of electromagnetic quantities. E.g. the unit of magnetic flux is equivalent to volt times seconds, and inductance is volt times seconds per ampere. But I can't find intuitive explanations for this

Usually easier to move around the units to match the standard equations, e.g. voltage is rate of change of magnetic flux.

Re: Intuitive Guide to Maxwell's Equations

#28

Post by C4stor »

ghaff wrote: post #7
chronolitus wrote: post #3

These kinds of visual, well thought out explanations of topics which are often taught with terse, obscure and uninviting methods are a gift. On a tangent: I remember asking my Calculus 101 professor what the "intuitive meaning" of divergence and curl was, outside of the formal math and equations. He was shocked that one could ask to sully these perfect mathematical concepts with dirty intuitive reductions. A guide li…

Wikipedia is probably the most obvious modern exemplar of this. The editors of most mathematics articles clearly are much fonder of playing with the equations editor than they are of actually explaining things.

Well, it's not Wikipedia's fault if people producing intuitive content are not contributing to it. It's not like editors go out of their way to remove nice explanations.

Re: Intuitive Guide to Maxwell's Equations

#29

Post by [deleted] »

augustt wrote: post #27
Aardwolf wrote: post #25

I'd be interested in an intuitive explanation of the units of electromagnetic quantities. E.g. the unit of magnetic flux is equivalent to volt times seconds, and inductance is volt times seconds per ampere. But I can't find intuitive explanations for this

Usually easier to move around the units to match the standard equations, e.g. voltage is rate of change of magnetic flux.

[deleted]

Re: Intuitive Guide to Maxwell's Equations

#30

Post by adamnemecek »

pa7x1 wrote: post #9
antman wrote: post #5

As a side note there was a historical debate, and the shape of these equations is the end result of the chosen system. In geometric algebra which did not prevail, these are one equation.

Geometric algebra is a bit awkward notationally. Physicist prefer to use an alternative notation based on exterior calculus that does provide a compact representation of Maxwell equations: d F=J dF=0 Geometric algebra produces two equations too, by the way, not one.

It's one equation in geometric algebra. https://www.av8n.com/physics/maxwell-ga.htm#eq-max-ga

Also there is a new community for geometric algbera people https://bivector.net/.

Check out the demo https://observablehq.com/@enkimute/animated-orbits

Watch the SIGGRAPH talk https://youtu.be/tX4H_ctggYo

Join the discord https://discord.gg/vGY6pPk

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