Why is the speed of light what it is? Maxwell equations visualized
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Published 2020-03-25
Not only do they describe every electrical and magnetic phenomenon, but hidden within these equations is a fundamental truth about the nature of light, and why it is the ultimate speed of the universe. We are going to visualize the equations with graphics.
Objects have something called a charge. This is a property of matter like mass is a property of matter. If you have a static object with a charge, it will affect only other charges. And if you have a static magnet, it will affect only other magnets. But if you have a moving charge, it will affect a magnet. And if you have a moving magnet, it will affect a charge. That's what the four equations are telling us.
A charge is the source of an electric field. If I have another charge, you can understand exactly what force it will feel. The first equation is a formula that tells us how electrical charges create electrical fields. It is based on concepts developed by Carl Friedrich Gauss. Permittivity of free space is required in the equation. It is the resistance of free space against the formation of electric fields.
The second equation is called Gauss’s law for magnetism. It says that if you had the same sphere but it was a magnet, you will never find a configuration where the magnetic lines of force always point outward, or always point inwards. In other words, a magnet will always have two poles. There are no magnetic monopoles.
The third equation is called faraday’s law. This law says that if move a magnet, you will create an electric field. This equation tells engineers how to generate electricity from a generator.
The fourth equation is Ampere’s law. It says that if you have moving charge through a wire, or an electrical current, you generate a magnetic field. This requires a constant of nature called mu naught. This is the permeability of free space. This is the ability of free space to allow magnetic lines of force to go through it. Note that there are two terms in this equation, one term tells you the moving electrical charges can create magnetic fields, and the second term tells you that moving electrical fields can also create magnetic fields. This idea of magnetic fields being created from electric fields was Maxwell’s addition to Ampere’s law.
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Both of these constants have to be measured, since they are inherent properties of nature. They are not derived from anything. What does this have to do with light?
If I take an electric charge and put it on a pole, and I just move it up and down, what will this cause? According to ampere’s law, if an electric field moves or changes with time, it would create a magnetic field perpendicular to that.
And because of the changing movement, the magnetic field would also be changing with time. And according to Faraday’s law the moving magnetic field lines would create another new set of electric field lines.
Now, since the same thing is happening to these new electric field lines, that is, they are changing over time, they would in turn create new magnetic field lines. And the new moving magnetic field lines would create yet more electric field lines. You have just created a self propagating wave.
What is the speed of this wave? You find this using advanced multivariable calculus which Maxwell was very good at. He comes up with is 1/V^2 = epsilon naught * Mu naught. Solving you get Velocity = Sq root (1/epsilon naught * Mu naught). So what the equations are saying is the velocity of this wave is inversely proportional the permittivity and permeability of free space. It makes sense that the velocity of any wave would be inversely proportional to the resistance of the substance it is traveling in.
You might ask, well why are mu naught and epsilon naught those exact values? No one knows why. These are just the constants of nature.
Now we take the measured values of these two constants, and do some simple math. The speed of the wave is about 300,000 km per second. Maxwell realized that light must be an electromagnetic wave.
About 40 years later another great scientist by the name of Einstein did his own thought experiments inspired by Maxwell’s equation. And his thought experiment was based on one simple assumption. He asked if the speed of light is an inherent property of space, why would this speed be any different based on the speed of the observer?
And it was from this simple assumption, that he came up with the special theory of relativity in 1905 which changed our ideas about the nature of time.
All Comments (21)
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For those of you wanting to know exactly how Maxwell derived velocity using, here is a source that shows the details of that derivation: www.wikihow.com/Derive-the-Speed-of-Light-from-Max…
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I teach electrical theory at university and I’ve never seen such a brilliantly clear explanation of the Maxwell equations and their consequences - Many Thanks.
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Watching this made my jaw drop, imagine that Eureka moment, when Maxwell realised the approximate measured speed of light matched his equation. Epic.
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Just imagine how Maxwell felt when he realized that he arrived at the speed of light... What epiphany! I wouldn't be able to take another breath from excitement. This is a great video. Thank you. Amazing to see that the speed of light can be derived from those two constants -- vacuum permittivity and permeability of free space. It actually makes sense.
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There is a statue to Maxwell in Edinburgh where he was born , most people just pass by without realising what an important contribution Maxwell made to our understanding of how the universe works.
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I've learned more about electromagnetism and the meaning behind Maxwell's equations in these 13 minutes than in 5 years of studying electrical engineering.
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"There was a point in time when Maxwell was the only person in the world who realized this." That is pretty amazing.
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wow, as a physics enthusiast, I’ve been looking for this level of understanding of “c” and how it can be derived for years, and this video nails it. Thank you, Arvin Ash!!!
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Just imagine the thrill that Maxwell must have felt in that moment when the two speed limits matched.
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Thanks for the collaboration! Thanks for expanding our understanding of Maxwell’s contributions!
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As a former undergrad in physics and grad in oceanography, I wish all educators were required to be at this level of understanding, enthusiasm and preparedness. Its nice to see you to explain serious material so simply, as well as capture the attention of thousands of people in subject matter deemed widely as boring and drab. Thank you for doing this, I'm subscribing to your channel.
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I have zero background in physics, yet you explain things in a way I can actually understand. It's fascinating. Thanks!
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I was an electronic engineer in research and development for 35 years. I developed extremely sensitive detectors for gas chromatographs. The last 5 years of my career I was designing a Liquid Quadrupole Ion Trap Mass Spectrometer. I never used Maxwell's equations through out my whole career. The equations that I did use were E=I*R, ohms law, P=I*E, watts law, Q=C*V, charge of a capacitor is the capacitance times the voltage on a capacitor, Q=I*T, charge of a capacitor is the current times the time of a capacitor and I*T=C*V. This leads to V= 1/C int(i dt), the voltage of on a capacitor is equal to 1/C times the integral of the current over time and I=C * dv/dt, the current out of a capacitor is equal to the change in voltage with respect to time. Yes, there are other common formulas like XC= 1/(2*pi*F*C) and XL=2*pi*F*L, to measure the capacitance and inductance reactance with frequency. We can't forget about T=RC, time constant of an capacitance-resistance circuit and T=L/R, time constant of an inductance-resistance circuit. Yes, I learned about Kirchhoff's law, Thevenin and Norton theorems too.
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This presentation of Maxwell’s equations is the best I’ve ever seen.
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I can barely add, subtract or multiply and have zero understanding of equations, but I just LOVE this stuff.
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Unlike most of the people commenting here, I’m not an engineer or have any connection with engineering, in fact I teach marketing at a university. So I have no background in engineering whatsoever, but the way you have explained this, even a layman like me understood it so well. You are a great teacher!
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People look up to Einstein, but Einstein looked up to Maxwell.
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This is superb. Maxwell has always been one of my favorites, but I’ve never understood how his mind made such a leap to see the relationship between electromagnetism & light. Your explanation Arvin is so clear and simple that now I feel like I truly have an intuitive understanding. Love History Guy too! Good to see 2 of my favorite channels collaborating!
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Thanks. I learned more in 13 minutes then in a semester of Fields and Waves when I was in college 25 years ago.
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Imagine if we could go back in time and show these great minds the technology that their great works led to. I wonder what they would say about it.
