Maxwell's Equations Visualized (Divergence & Curl)

Maxwell's equation are written in the language of vector calculus, specifically divergence and curl. Understanding how the electromagnetic field works requires we also understand that language. Unfortunately, symbols can be ugly, so let's try some dynamic visuals instead.

Advanced Theoretical Physics (Paperback):

Advanced Theoretical Physics (eBook):
________________________________
VIDEO ANNOTATIONS/CARDS

Electrodynamics Series:
________________________________
RELATED YOUTUBE VIDEOS

3blue1brown on Divergence and Curl:

Eugene on Divergence and Curl:

Khan Academy on Divergence and Curl:
________________________________
SUPPORT THE SCIENCE ASYLUM

Patreon:

Merchandise:
________________________________
HUGE THANK YOU TO THESE PATRONS

Warden of the Asylum:
YDT

Asylum Counselors:
Matthew O'Connor

Asylum Orderlies:
Daniel Bahr, William Morton, LT MarshMan, TheBonertronicPeewormExtravaganza

Einsteinium Crazies:
Albert B. Cannon, Wacky, Ken Davis, Ilya Yashin, Eoin O'Sullivan

Plutonium Crazies:
JKLMN Anderson, Al Davis, Kevin MacLean

Platinum Crazies:
Stephen Blinn, Fletch, Felipe Cruz, Eugene Boone, Vittorio Monaco, Mikayla Eckel Cifrese
________________________________
OTHER SOURCES

Code used for fluid flow animations:
________________________________
LINKS TO COMMENTS

[ScienceAsylum]

*Correction:* In the third equation (Faraday's law), those "d" symbols should be curly like they are in the fourth equation (Ampere's law). My bad! It doesn't actually matter much for the video, but it bothers me that I can't seem to get through a video without a typo. 😞

*Note:* Yes, there are similarities/overlap between my video and 3blue1brown's video from last year. That's one of the hazards of making educational content... but our videos have a slightly different focus and reach slightly different audiences, so I think it's OK.

[maskdalxx]

Please keep making visualization videos! I know that they might be harder for you to make but they really do help everyone understand physics better.

[akhil]

I'm a Ph.D. in Physics but I've never been taught like this. During my college, these equations seem like a nightmare to me, but your videos will really help Under Grad. and Grad. students to visualize the real things happing there. Best wishes.

[TheAmbientMage]

"Should I do more videos like this?"

Me: "YES. DUH. GIMME ALL THE MATHS!!!!"

[Ayshafr]

But seriously, I really appreciate videos like this. A lot of times in college I felt like I was just doing math without really understanding what it meant, and even when I was told in words, it didn't really stick. The math is essential to understanding the physics, but the physics sure helps in understanding the math. Would love to see more videos explaining equations and visualizing them.

[CaravaggioRoma]

Man, I should have known you 20 years ago when studying at the college!

[crouchingtigerhiddenadam]

It's math... But it's not scary.
You're breaking all the rules! I love the animations!

[alaynagrover]

Thank you! You are educating future engineers, physicists, and mathematicians so we can produce fruitful results to benefit society later on.

[dmullinsTWM]

You asked "should I do more like this?" My answer is a resounding "yes, please!"

[aniaddict]

Definitely need more videos explaining equations like Visualizing makes the whole concept a lot more clear in a very short time

[jimzweighaft]

Much better explanation than I got in Engineering school 40 years ago. The animations help a lot.

[Private_Duck]

This is insane.
Ive learned vector calculus before. but no one was perfect like you, when it comes to explanations.

[Enrique_Osorio]

Please make more videos like this. I am a 3rd year electrical engineering major and your videos have helped me visualize concepts in a way that makes it much more satisfying than simply applying and solving equations. I truly am on the edge of my seat while viewing your videos. Thank you so much for what you do, it means a lot.

[stevenbateson]

😂 I’m retired and spent a couple of months working through text books, teaching myself vector calculus for the express purpose of understanding Maxwell’s equations. You just condensed the fruits of all that labour into a couple of minutes 👍 All that work has had side benefits though, such as understanding Schrodinger’s equation and the Navier-Stokes equation etc. I look forward to your video on the NS equation when you’ve finish teaching yourself fluid mechanics 🙂

[AndrewDotsonvideos]

"which most people just call the maxwell equations... don't get me started" lmao!

[Mickolas]

Where were you when I was taking electromagnetism for my EE program? Well done.

[VikramGT]

Keep doing visualisation videos, younger generation will get interest in science.. Its a service to society.

[declanwk]

This is the best summary explanation of the Maxwell (Heaviside) equations I have ever see, Thank you

[veerakuusela]

Good to hear you are still learning new things. Means more things you can teach us in the future. :)

[joshuazeidner]

hats off to this amazing youtuber who turns stale dull scientific material into obnoxious irritating material filled with ads.