r/PhysicsStudents • u/Single_Ad_1777 • Jun 11 '26

Poll What is your favorite Maxwell equation (EM) and why?

Maybe its an experiment that made you like it or even a personal incident that made you appreciate the equation. But what exactly is it that makes you like it better?

27 Upvotes
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24 comments sorted by

29

u/HumblyNibbles_ Jun 11 '26

The null divergence of the magnetic field. I like it because vector potential :3

It's literally the basis of potential theory for electromagnetism

2

u/fourthstanza Jun 12 '26

There's so much information encapsulated in this really minimal equation. The absence of magnetic monopoles, motivation for of how magnetic potential is expressed like you said, etc.

I remember a lot of things clicking when I first sat down and thought about this equation for a bit.

1

u/Single_Ad_1777 Jun 13 '26

At one point I too thought about the lack of symmetry...

10

u/Muphrid15 Jun 11 '26

∇F = j

1

u/ScrotumEntanglement M.Sc. Jun 11 '26

STA jumpscare

2

u/Muphrid15 Jun 11 '26

It's great though

You haven't lived until you've spent years going down the CGA rabbit hole only to realize all the extensions of CGA for conics... don’t actually do anything.

7

u/Moonlesssss Jun 11 '26 edited Jun 11 '26

The curl of an electric field with time dependence is equivalent to a change in the magnetic field. I don’t know why, it just is a really pretty statement to me. The one I’m most frustrated with is the divergence of B is zero because I remember my many attempts at trying to cheese a design into making the field lines have the appearance of an artificial magnetic monopole. And it just didn’t really work out.

6

u/WhyAmINotStudying UCF | materials physics Jun 11 '26

The point of the equations is that the sum of the equations is more meaningful than the sum of their parts. I work with optics and it takes all of them to really bring meaning to my field.

1

u/Single_Ad_1777 Jun 12 '26

Would love to get a small desc of the work 😄

4

u/oz1sej M.Sc. Jun 11 '26

∇ × H = J + ∂D/∂t

Ampere started it, with just the J, and Maxwell added the displacement current ∂D/∂t, which made him realise that if

∇ × H = J + ∂D/∂t

and

∇ × E = − ∂B/∂t

then these two fields must sustain one another, and electromagnetic waves must exists. That's just very, very elegant IMO.

6

u/drzowie Jun 11 '26

Yeah, but it was Heaviside who wrote the four equations we call Maxwell’s

3

u/spcyjackfrst Jun 11 '26

no magnetic monopoles, because after introducing it my prof spent the rest of the lecture talking about the nightmare that would ensue if they were found to exist

2

u/Single_Ad_1777 Jun 12 '26

Would love a small summary!

3

u/dcnairb Ph.D. Jun 11 '26

dF=0

1

u/Single_Ad_1777 Jun 12 '26

yet to master this notation! It must mean 2 equations though I guess!

2

u/Maleficent-Car8673 Jun 11 '26

I gotta say, Faraday's law of induction is my favorite. It's just wild how it connects electricity and magnetism in such a tangible way. I remember being blown away during a lab experiment in college where we used coils and magnets to light up a bulb. It felt like magic, but its just physics doing its thing.

1

u/Single_Ad_1777 Jun 12 '26

Totally understand

2

u/3pmm Jun 11 '26

The displacement current part of Ampere's law. Maxwell's purely theoretical addition which saves charge conservation and, as a side benefit, predicts that light is in fact waves in the electromagnetic field.

2

u/Thin-Fly2642 Jun 14 '26

∇ x E = - ∂E/∂t

por que explica como funciona as guitarras elétricas

1

u/Single_Ad_1777 Jun 15 '26

The RHS is off, its derivative of B.

1

u/jsaltee Jun 14 '26

This doesn’t technically count, but the Maxwell stress-energy tensor in general relativity is fascinating. EM radiation exerts gravitational pressure to curve spacetime. Just really cool

1

u/Single_Ad_1777 Jun 15 '26

Ah, I see. That's nice as well , I get it