Deriving speed of light using Maxwell's equations | EM waves | Physics | Khan Academy

In this video, we derive the speed of light using Maxwell's equations and realize the importance of all four Maxwell's equations coming together to explain the nature of light as an EM wave!
00:00 Introduction
01:28 Assumptions
02:27 Testing if the EM fields satisfy Gauss' law of electricity and magnetism
05:47 Testing if the EM fields satisfy Faraday's law
13:56 Testing if the EM fields satisfy Ampere's law
19:09 Summary
Master the concept of EM waves and EM spectrum through practice exercises and videos - www.khanacademy.org/science/i...
Check out more videos and exercises on Electromagnetic waves - www.khanacademy.org/science/i...
To get you fully ready for your exam and help you fall in love with Physics, find the complete bank of exercises and videos for Class 12 Physics here - www.khanacademy.org/science/i...
Khan Academy is a free learning platform for Class 1-12 students with videos, exercises, and tests for maths, science, and more subjects. Our content is aligned to CBSE syllabus and available in Hindi, English, and many more regional languages.
Experience the joy of easy, seamless, accessible learning anywhere, anytime with Khan Academy.
Subscribe to our KZbin channel - / khanacademy
As a 501(c)(3) nonprofit organization, we would love your help!
Donate here: www.khanacademy.org/donate?ut...
Created by Vibhor Pandey

[@jaishivshambhu1008]

To get the qualitative knowledge in small time , we must prefer this platform ❤

[@shaikhahmed6562]

I always admire this channel for making me a person who I am now....thanks for filling up voids....

[@chinmayelastname3544]

Great video as always

[@feelingzhakkaas]

Absolutely wonderful explanation

[@RajAryanMYSTRY-MAN]

Wow ... This explains my all time favorite problem ... Thank you

[@williamwalker39]

No, it does not. See my post at the top of the comments.

[@anilsurjewala3606]

Always love your videos

[@user-vy5hf4ei1x]

Thank you so much sir

[@joanfontanalsmartinez8934]

I have a doubt, the requirement for E and B fields to be 0 beyond the wave front, how is it expressed in the solution of the EM wave in the vacuum where E = E0cos(kx-wt) and B = B0cos(kx -wt)? In these expressions, fot t=1, the fields are not 0 beyond ct right?

[@chunlangong2214]

You are an awesome Teacher and explainer!

[@feelingzhakkaas]

Only small correction in end part.. B is written as 'b'...

[@4m0d]

bruh

[@OP-do7rt]

Come mahesh sir please

[@williamwalker39]

This analysis is wrong! And was wrong when Maxwell first presented this argument. Setting the wave equation = 0 is only valid at infinite distance from a source, which does not exist. One must set the wave equation equal to a source term. This is because Maxwell"s equations have source terms. If one uses a sinusoidal source, and plots the resultant phase shift vs distance (dispersion curve) from the source, one finds that the nearfield is very non linear and becomes linear only in the farfield. The phase speed of the field can then be determined from the inverse of the slope of the dispersion curve and the group speed can be determined from the inverse curvature of the dispersion curve. The results show something amazing, that the speed of light is instantaneous in the nearfield and reduces to about speed c at about one wavelength from the source, and never becomes exactly c even at astronomical distances from the source. This was experimentally confirmed by measuring radio waves propagating between 2 antennas and separating the antennas from the nearfield to the farfield, which occurs about 1 wavelength from the source. This behavior of gravity and light occurs not only for the phase and group speed, but also the information speed. This instantaneous nature of light and gravity near the source has been kept from the public and is not commonly known. The reason is that it shows that both Special Relativity and General Relativity are wrong! It can be easily shown that Instantaneous nearfield light yields Galilean Relativity and farfield light yields Einstein Relativity. This is because in the nearfield, gamma=1since c= infinity, and in the farfield, gamma= the Relativistic gamma since c= farfield speed of light. Since time and space are real, they can not depend on the frequency of light used. This is because c=wavelength x frequency, and 1 wavelength = c/frequency defines the nearfield from the farfield. Consequently Relativity is an optical illusion. Objects moving near the speed of light appear to contract in length and time appears to slow down, but it is just what you see using farfield light. Using nearfield light you will see that the object has not contracted and time has not changed. For more information: Search William Walker Relativity. Since General Relativity is based on Special Relativity, General Relativity must also be an optical illusion. Spacetime is flat and gravity must be a propagating field. Researchers have shown that in the weak field limit, which is what we only observe, General Relativity reduces to Gravitoelectromagnetism, which shows gravity can be modeled as 4 Maxwell equations similar in form to those for electromagnetic fields, yielding Electric and Magnetic components of gravity. This theory explains all gravitational effects as well as the instantaneous nearfield and speed of light farfield propagating fields. So gravity is a propagating field that can finally be quantized enabling the unification of gravity and quantum mechanics. The current interpretation of quantum mechanics makes no sense, involving particles that are not real until measured, and in a fuzzy superposition of states. On the other hand, the Pilot Wave interpretation of Quantum Mechanics makes makes much more sense, which says particles are always real with real positions and velocities. The particles also interact with an energetic quantum field that permeates all of space, forming a pilot wave that guides the particle. This simpler deterministic explanation explains all known quantum phenomena. The only problem is that the Pilot Wave is known to interact instantaneously with all other particles, and this is completely incompatible with Relativity, but is compatible with Galilean Relativity. But because of the evidence presented here, this is no longer a problem, and elevates the Pilot Interpretation to our best explanation of Quantum Mechanics. *KZbin presentation of above argument: kzbin.info/www/bejne/qZazlX1tq7iErLM *Paper it is based on: William D. Walker and Dag Stranneby, A New Interpretation of Relativity, 2023: vixra.org/abs/2309.0145 *Electromagnetic pulse experiment paper: www.techrxiv.org/doi/full/10.36227/techrxiv.170862178.82175798/v1 Dr. William Walker - PhD in physics from ETH Zurich, 1997