Maxwell's Equations: Integral or Differential Form?

[romsofia]

Which form do you prefer, the integral form or differential form?

EDIT: Forgot to say I prefer the integral form.

 

[fluidistic]

You forgot the tensor form! :D

 

[Drakkith]

Where's the option for "Who's Maxwell and what do these two terms mean"?

 

[romsofia]

You forgot the tensor form! :D

I'm unfamiliar with the tensor form o.o! It would probably make little sense to me :P

Where's the option for "Who's Maxwell and what do these two terms mean"?

They're 4 equations, and that ain't in this poll :P.

 

[WannabeNewton]

I would have liked to see the differential forms version of Maxwell's equations, very elegant way of expressing them. But since they aren't up there I would have to go with the differential form because the del operator looks cool =D

 

[atyy]

Where's the option for "Who's Maxwell and what do these two terms mean"?

 

[yungman]

You need to use both.

 

[Drakkith]

WTF was that?

 

[Jimmy Snyder]

Which one of Maxwell's equations is your favorite? Mine is Faraday's equation.

 

[Saitama]

Like the differential form! Altough i have just started them. MIT lectures are great!

 

[clancy688]

Integral... how the hell am I supposed to calculate with the differential form without my head imploding?

Favourite one: Gauss's Law - the easiest concept to grasp imho. :shy:

 

[dextercioby]

What's more beautiful than [itex] dF= 0 [/itex] and [itex] \delta F=j [/itex] ?

 

[I like Serena]

I like this one best:
[tex]\square A^\alpha = \mu_0 J^\alpha[/tex]
That is, all of Maxwell's equations rolled into one simple equation!

 

[WannabeNewton]

What's more beautiful than [itex] dF= 0 [/itex] and [itex] \delta F=j [/itex] ?

Is [itex]\delta F [/itex] the same as [itex]d(\star F) [/itex]?

 

[dextercioby]

Essentially, up to a possible minus sign depending on the dimension of spacetime and metric signature , delta = * d * .

 

[dextercioby]

I like this one best:
[tex]\square A^\alpha = \mu_0 J^\alpha[/tex]
That is, all of Maxwell's equations rolled into one simple equation!

Well, not really, the fundamental gauge symmetry is missing in your equation.

 

[I like Serena]

Well, not really, the fundamental gauge symmetry is missing in your equation.

I'm not familiar with fundamental gauge symmetry yet.
What is it?

Is it part of Maxwell's equations?

 

[Antiphon]

The integral form is easier to visualize because the curls turn into line and surface integrals which naturally illustrate relationships between things like enclosed current and MMF.

 

[dextercioby]

I'm not familiar with fundamental gauge symmetry yet.
What is it?

Is it part of Maxwell's equations?

Yes, the reason we use potentials is quantum mechanics and quantum field theory. A quantum theory of the electromagnetic field cannot be built without dealing with the gauge symmetry first.

 

[cragar]

I like how we call them Maxwell's equations even tho it was Faraday and Heaviside that pretty much came up with them.

 

[Pengwuino]

I like this one best:
[tex]\square A^\alpha = \mu_0 J^\alpha[/tex]
That is, all of Maxwell's equations rolled into one simple equation!

As dexter was hinting at, Maxwell's equations can't be uniquely defined by that condition.

As far as the thread is concerned, the integral form of anything is noob-sauce.

 

[I like Serena]

What's more beautiful than [itex] dF= 0 [/itex] and [itex] \delta F=j [/itex] ?

Aha!
I had to read up on Maxwell's equations again before I understood (again).
There (wiki) I also found your equations, which were not familiar to me.

But now I understand that your 2 equations are an alternate form that represent all of Maxwell's equations!