question about Speed of light

Everyone knows that c (speed of light ) equals 299,792,458 metres per second

please I want to know how could we get this value by means of Maxwell equations

thanks

Look at the definitions and dimensions of permeability and permittivity for free space.

Note that
c = +√1/(με)

Can you take it from here and is this homework?

dragon_electron said:

Everyone knows that c (speed of light ) equals 299,792,458 metres per second

please I want to know how could we get this value by means of Maxwell equations

thanks

Click to expand...

You need to derive a wave equation from Maxwell's equations for vacuum. When this is done, it becomes obvious that the speed of the wave is as given by studiot. Any good college level textbook on electromagnetics will show how to do this, or an on-line search will reveal it as well.

This is one area I'm really weak in. Didn't Maxwell's equations come before Einstein's Theory of Relativity? I am under the impression that Einstein's math predicted this, and the physicists of the time were kept busy verifying this prediction, long after Maxwell's equations.

Bill_Marsden said:

This is one area I'm really weak in. Didn't Maxwell's equations come before Einstein's Theory of Relativity? I am under the impression that Einstein's math predicted this, and the physicists of the time were kept busy verifying this prediction, long after Maxwell's equations.

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Bill,

I think you are referring to the issue of the constancy of light. This seems to be a separate issue from the original question about how to derive the value of speed from Maxwell's Equations. Although, it is an important point, and worth mentioning.

You are right that Maxwell's finalization of the electro-magnetic equations came before Einstein's theory. The major contribution from Maxwell was to add the displacement current term to Ampere's Law. Once he did this, he was able to simply derive a wave equation in standard form. It was then obvious that the electromagnetic wave speed was a simple function of permeability and permitivity of free space, as pointed out by studiot. The fact that this value was about equal to the measured speed of light, within the bounds of experimental uncertainty, seemed to confirm that light was electromagnetic in nature. So, basically, Maxwell hit a pretty big home run on this one, and knew it. Personally, I rank it among the top 10 greatest scientific feats.

Later, the issue became apparent that Maxwell's equations obeyed the Lorentz transformation, which is consistent with Einstein's later theory of relativity, but was inconsistent with the then accepted Galilean transformation consistent with Newton's work. This was a big mystery that was debated for quite a while, until Einstein helped resolve it. - Another of the top 10 home runs, in my personal ranking.

Perhaps your top ten would make a good thread, Steve?

Are they all physics are do you allow other sciences a look in?

studiot said:

Perhaps your top ten would make a good thread, Steve?

Are they all physics are do you allow other sciences a look in?

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I tend to be biased toward physiscs, but other sciences are allowed too. For example, I put Darwin's theory of natural selection in there too.

That is a good idea for a thread, since it's a good way to solicit other peoples ideas of the greatest discoveries. It wouldn't be a bad idea to reevaluate my own list in this way. I'll write out my list. I know the entries, but will have to think carefully about their order.

I suggest that the question be defined to distinguish between those inventions affecting humanity in a general sense (e.g., beer, wheel, fire, crops) from those most similar to what has already been presented here, i.e., those that were revolutionary for a particular field. You might also want to limit them to the nineteenth century or later.

To your growing list, I would add Pasteur for infectious diseases and to a lesser extent, chemistry.

John

Did you know that Michael Faraday (attributed for discovery of electromagnetism) actually assisted in the development of chemistry by creating a mechanism for demonstrating that gas/liquid forms of chemicals (in his case chloride I believe) are impacted by pressures?

I would also add Onnes for being the first to liquify Helium. Certainly wouldn't give any credit to Dewer (don't even care if I spelt his name correctly), the conceited arsewipe of a scientist. Bloody Dewer created an experiment that took one of his assistants eye, and even after the assistant STAYED with him, blamed his own failure on this very same assistant once Onnes beat him to it!