What are Maxwell's Equations?

Question

What is the significance of Maxwell's Equations? I know they have to do with electromagnetism but how would you use them and why? I've taken calc I and II and still have no idea what they mean or how they unite electricity and magnetism. I know this is a rather difficult question to answer, but I would greatly appreciate any information you can give.

Also, what does each one mean and what would be a typical scenario where you would need these equations?

Answer 1

I understand your difficulty. The problem is that Maxwell's Equations are not easily understood (in my opinion) from a mathematical point of view. But they are simple and beautiful once you look at them from the physics p.o.v. and see what they mean.

The first Maxwell's Equation is known as Gauss's Law, and it (roughly) states that the electric field multiplied times the a surface around it is equal to the charge enclosed by the surface, divided by a constant (called the permitivity of free space). Now, this first equation does not actually link electricity with magnetism, it's just an electric-only equation.

The second is law is known as the "no magetic monopoles" law by many, or Gauss's Law for Magnetism by others. Nor does this one link electricity and magnetism, but rather just says that all magnetic fields need to have both a source and sink. (Unlike electrical fields, that are quite happy having only a source, and no sink.) You could compare electrical fields to a lightbulb, which just shoots light off in all directions, and it could care not a whit that the light doesn't come back to it. However magnetic fields are more like fountains in a park ... they shoot out water, but the water has to fall back down the drain and get recirculated to shoot out again.

The Third Law is where the good stuff starts ... this one is known as Faraday's Law, and this one binds electricity with magnetism. Specifically, it says that if you move a magentic field through a loop of wire, a current (i.e. electromagnetic force, or voltage) will be created in that wire, as long as you keep moving the magnetic field thorugh the loop. This law is the basis of all electric generators and electric motors; I can use moving magnets to make electricity, or I can use electricity to make magnets move.

The last Maxwell's Equation is Ampere's Law, which Maxwell modified with an additional term and thus secured his position in the history of physics by making it compatible with a future that didn't even exist at the time ... Relativity.

With just a simple line integration, Ampere's Law connects the magnetic field of a current-carying wire with the electric current in the wire. It's what allows your television coaxial cable to work, along with solonoids, rail guns, particle accelerators, etc..

The amazing thing about Maxwell's Laws is that they can all be verified, played with, enjoyed, and studied with just a battery, some wire, a toy compass and a mulitmeter.

Radio Shack used to have some good kits, they may still have them.

http://ezinearticles.com/?Teaching-Kids-About-Electricity&id=509585

Answer 2

Together with the Lorentz force, they provide a complete mathematical description of the interaction of charges and the electric and magnetic fields in the classical limit. A first course in calc is just the start. The normal educational process leading up to their understanding involves a heuristic derivation from Coulomb's law and how it must be modified by special relativity. You'll need to understand the definitions of the various vector operators used and a couple of critical theorems pertaining to the operators' integral forms. Basically, you need to take courses in undergraduate classical mechanics and electromagnetism. It's very difficult to self-learn such stuff without the benefit of a teacher to ask questions of.