How did Maxwell find the speed of light

[stephen8686]

According to this video I was watching Maxwell was looking for the speed of EM waves and just divided coulomb's constant by the magnetic constant and then took the square root and that was the speed of light.

√(K_e/μ₀)=√(9e⁹/1e^-7) = 3e⁸m/s

So why is this a thing? I just don't understand why it works, and how did Maxwell know it was the speed of light?

 

[Nugatory]

Which video? Until you tell us that, we don't know whether it's incomplete or whether you're missing something.

One of the solutions to Maxwell's equations is an electromagnetic wave moving at $3\times{10}^8$ m/sec; you will find some good derivations if you google for "Maxwell speed of light derivation". However they will require some vector calculus and solving a differential equation so I don't know if there's a better answer than "Trust us, that's what you get when you do the math" without understanding the math.

The speed of light had been measured and found to be $3\times{10}^8$ m/sec long before anyone had any idea what light was. So when Maxwell worked through the math and found that it predicted waves traveling at the already known speed of light he made an inspired guess - that the waves his equation predicted were light.

 

[stephen8686]

Which video? Until you tell us that, we don't know whether it's incomplete or whether you're missing something.

One of the solutions to Maxwell's equations is an electromagnetic wave moving at $3\times{10}^8$ m/sec; you will find some good derivations if you google for "Maxwell speed of light derivation". However they will require some vector calculus and solving a differential equation so I don't know if there's a better answer than "Trust us, that's what you get when you do the math" without understanding the math.

The speed of light had been measured and found to be $3\times{10}^8$ m/sec long before anyone had any idea what light was. So when Maxwell worked through the math and found that it predicted waves traveling at the already known speed of light he made an inspired guess - that the waves his equation predicted were light.

The video is here:
The part that I am referring to happens at about 11;30
It's a pretty simple video, so I don't think I am missing anything, and the video is on caltech's channel so I assume it is credible. I see that the speed of light can be determined from Ampere's Law (which I will not fully understand until the end of this year). I just don't understand why these two particular constants have any relationship to the speed of light.

 

[jtbell]

how did Maxwell know it was the speed of light?

See this post:
https://www.physicsforums.com/threads/determining-c-from-maxwells-equations.894375/#post-5627394

 

[stephen8686]

See this post:
https://www.physicsforums.com/threads/determining-c-from-maxwells-equations.894375/#post-5627394

Thank you