in physics, is it always possible to visualise what the equations mean physically? e.g. squared constants/variables, i can't imagine. is it just an abstract thing that describes the physical thing but you can't imagine the individual terms and what they mean physically?
Apparently you can't with really visualise string theory, but with the stuff we do in VCE, yeah definitely.
I'll use the example of Coulomb's Law:
Here's the fancy definition: "The magnitude of the Electrostatics force of interaction between two point charges is directly proportional to the scalar multiplication of the magnitudes of charges and inversely proportional to the square of the distances between them."
I haven't found a derivation of it that's really simple for it yet (didn't really care about derivations in units 1&2 lol). I've seen it derived from Maxwell's equation.
http://planetmath.org/encyclopedia/DerivationOfCoulombsLawFromGaussLaw.html. I think there was also a method about something to do with electric fields.
(copied this from some equation database, don't know if it's correct)
Gauss's Law states (in fancy terms): "The electric flux through any closed surface is proportional to the enclosed electric charge."
I have also seen this even fancier version: ""the divergence of the electric field equals charge density divided by ε_0" That fancier one is just the equation spelled out in words.
Also this fancy definition kind of combines the two: "The total of the electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity."
So you can see that equations are really just a fancy way of describing something that sounds even fancier. However, this even fancier thing (the words), really just describes an idea that's fairly straight forward a lot of the time.
Flux is sort of a measure of 'flow' through a surface. What we've been doing in Unit 4 is magnetic flux. A magnetic field can be modeled using magnetic field lines. If you take an area (e.g. a rectangular piece of paper), magnetic flux is the measure of how many magnetic field lines pass through the area. So flux can be considered to be the "amount of field in an area".
So in less fancy words, Gauss's Law states that "The amount of electric field in an area" is proportional to the "electric charge in that area". That's what I understood of it anyway.
Damn, I was supposed to be talking about Coulomb's Law. Flux is a concept that clicked for me when the teacher demonstrated it using a piece of paper. I assume you know what electric charge is. I guess it still shows my approach though, just start off with the fancy definitions you are given and then boil it down to the simpler terms. I have a feeling I didn't answer your question entirely.
Maybe this is kind of relevant (probably not, I just like xkcd):
http://xkcd.com/895/. I like the mouse-over text: "Space-time is like some simple and familiar system which is both intuitively understandable and precisely analogous, and if I were Richard Feynman I'd be able to come up with it."