Original Maxwell equations versus todays version

[Firefox123]

How does todays "modern" form of Maxwells equations differ from the original equations Maxwell developed and why?


If this should be in the physics section...please move it...

 

[yungman]

Do you have example? I am no expert in Maxwell's equations, but I have seen only one version. There are four main one and two others that are a continuity equation and force equation.

$$\nabla \cdot \vec E =\frac{\rho_v}{\epsilon}\;\hbox{ (1).}$$
$$\nabla \cdot \vec B=0\;\hbox{ (2).}$$
$$\nabla \times \vec E = -\frac{\partial \vec B}{\partial t}\;\hbox{ (3).}$$
$$\nabla \times \vec B = \mu \vec J + \mu \frac{\partial D}{\partial t}\;\hbox{ (4).}$$

$$\nabla \cdot \vec J = -\frac{\partial \rho_v}{\partial t}\;\hbox{ Continuity equation.}$$
$$\vec F=q(\vec E + \vec u \times \vec B)\;\hbox{ where u is the velocity. Lorentz force equation.}$$

Yes Classical Physics section is a better place. When I was studying EM and ED, I was there all the time. BUT I do like to follow up with this as I am very interested in EM or ED.

 

[phyzguy]

Since our modern notation of vector calculus had not been invented yet, Maxwell's original paper had a total of 20 equations which spelled out today's equations on a component-by-component basis. You can read his original paper at this link:

http://en.wikipedia.org/wiki/A_Dynamical_Theory_of_the_Electromagnetic_Field

 

[yungman]

Thanks for a history lesson. Books does not talk about this. I actually though those are originated from the modern Maxwell's equations that I posted.

I so wish they emphasize more on the

$$\vec J_{tot}= \vec J_{free} + \frac{\partial \vec D}{\partial t}\;\hbox { and } \nabla \times \vec H = \vec J_{tot}$$

Took me a long time to realize this. Maybe the professor emphasize in the class but I never attended a class and only study on my own. Actually I learn the first time from the video lecture of IIT ( India Institute of Technology) professor of the free charge, free current vs bounded charge.

This is really enlightening for me. I actually like the old form of 20 equations because it really is more detail and you can see the wave equations, total charges and current in a more physical way. It just give me a whole different light of where all these come from and I think it would be easier to understand than the modern form of the six equation and derive the 20 out of it. There comes a point that it is too condensed for people to really appreciate the total significance of the six equations in the modern form.

 

[phyzguy]

There comes a point that it is too condensed for people to really appreciate the total significance of the six equations in the modern form.

I agree with this. This is why it is important to work out real problems - so you can see how the different quantities work together and get a physical feel for what the equations mean.

 

[yungman]

This is really a "light bulb" moment for me. I even have all the 6 modern Maxwell's eq. written with the rest of the 20 in a two pages summary in my note book how to derive from the modern six to the 20 or so. Now I have to go back a revise that it's from the 20 derive back to the condensed 6. This is important stuff on how did they all began.

I love to studying EM ( I am not sick!). I followed San Jose State and studied book by Ulaby and worked out all the problems and their finals. Did not feel like I learn anything. Then I re-studied "Field and Wave Electromagnetics" by David K Cheng. It is a much more advance EE electromagnetics, but still I did not feel it. Finally I bite the bullet and studied Griffiths. After three go around, I think I start to get the feel of it.

Problem with EE EM books are they try not to get into the detail of the EM theory and Maxwell's eq. They all try to get by with minimal explanation. I have like 8 books on EM and none of the EE books do a good job. Griffiths get deeper into it. But Griffiths lack the phasors, transmission lines and Smith Charts that are so so important for EE. I my opinion, student don't really get the basics until they study at least one EE and one Physic EM book.

My dream is one day, I can conquer the "Classical Electrodynamics" by JD Jackson. But that is still quite far as I still need to study Complex Analysis, Numerical Analysis, a little Real Analysis and Green's Function to get ready.

 

[berkeman]

How does todays "modern" form of Maxwells equations differ from the original equations Maxwell developed and why?


If this should be in the physics section...please move it...

Please take care to post schoolwork questions in the Homework Help forums, and show your attempt at a solution (your work) before asking for help.

Thread moved to HH.

 

[Firefox123]

Please take care to post schoolwork questions in the Homework Help forums, and show your attempt at a solution (your work) before asking for help.

Thread moved to HH.

This is not a homework question...I am not a student.

Please refer to the PM I sent you a few moments ago.

 

[berkeman]

How does todays "modern" form of Maxwells equations differ from the original equations Maxwell developed and why?


If this should be in the physics section...please move it...

This is not a homework question...I am not a student.

Please refer to the PM I sent you a few moments ago.

Fair enough. But you have been at the PF long enough to know how we handle posts that sound like schoolwork:

https://www.physicsforums.com/showthread.php?t=373889

Your OP was too incomplete for its purpose. Please in the future spell out what your intention is in making a post like this. With the background you gave me in your PM, if that had been posted with your OP, there would have been no question where this belonged. I will move this thread back to the technical physics forums now.