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malikwizard
Icarian Member

 Posted: Sat Oct 15, 2005 8:58 pm    Post subject: 1 Hi, I am a high school student, and I have been studying Electromagnetism in school. I have heard of Maxwell's equations that describe any electromagnetic phenomenon. I have been interested in figuring out how he derived these equations. I however have not been able to find any resources that are detailed enough to explain to me how he derived such an equation. Could anyone point me to an online resource that might help me figure out how to derive these equations? Thanks again.
Courk
Daedalian Member

 Posted: Sat Oct 15, 2005 9:24 pm    Post subject: 2 This is way out of my league, but http://en.wikipedia.org/ (you'll have to type "Maxwell's equations" into the search, I can't make it a nice link) seems to say that the equations already existed, he just was the first to put two-and-two together.
old grey mare
Guest

 Posted: Sun Oct 16, 2005 2:48 am    Post subject: 3 I don't think of Maxwell's equations as being "derived" in the sense that they would be the result of some mathematical manipulation. I think those four equations simply describe the observed phenomena. For example, Newton's second law is F=ma. The concepts of force, mass, time, and distance are first defined in a non-mathematical way. Then F = m d(ds/dt)/dt describes their observed relationship. An interesting thing about electricity and magnetism is that, in Maxwell's time, they were thought to be two different, but inter-related forces. After relativity came along, it could be shown that they are really two different observed perspectives on the same force. (At least that's what I've heard. I never did tensor calculus myself!)
Leptonn
Guest

 Posted: Sun Oct 16, 2005 6:04 am    Post subject: 4 Howdy, The previous poster is correct: the four Maxwell Equations are experimental artifacts. You can play around with them, if you'd like, but you will end up at an axiom for each. I know that I wasn't up to vector calculus when I was in high school (this is the language that the equations are written in), but if you're interested, here's one of my favourites: The Equations div(E)= p/e curl(E) = -dB/dt div(B) = 0 curl(B) = ue dE/dt Take curl(curl(E)) = grad(div(E)) - laplace(E) = - laplace(E) curl(curl(E)) = curl(-dB/dt) = -d(curl(B))/dt = -ue d^2E/dt^2 So laplace(E) = ue d^2E/dt^2 This is the equation that describes a 3-dimensional wave that progates at the fixed speed (ue)^-0.5, or about 3e8 m/s... the speed of light! The same thing can be done for the magnetic field B. Thus lies the suggestion that light is an electromagnetic disturbance. Further, it is worth noting the beautiful symmetry with time. This is the heart of special relativity.
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