But Why Do Moving Charges Have a Magnetic Field?
Physical Intuition
13,217 views
Why do moving charges have a magnetic field? In this video we derive the magnetic field and the Lorentz force from nothing but Coulomb's law and special relativity, using time dilation, length contraction, relativity of simultaneity and energy-momentum mixing. Then we use it to find the magnetic half of light: the magnetic field of an electromagnetic wave from an accelerating charge, the vector potential, and why E = cB.
Along the way we look at why a current-carrying wire shows magnetism at all, why light is a null field, and how light carries energy and momentum. No Maxwell's equations needed, just intuition and visual arguments.
This is Part 2 of "Why Accelerating Charges Radiate": Why Accelerating Charges Radiate
CHAPTERS
0:00 Hook
1:26 Setup
5:11 Derivation: x direction
7:20 Derivation: y direction
9:59 Putting it together
15:44 Magnetic dominant
18:41 Back to light
21:11 Derivation: Magnetic radiation
24:21 Light
28:58 Going relativistic
29:47 Conclusion
Next video: special relativity built properly from its two postulates.
Manim animation source code for this video:
https://github.com/denisgisbrecht74/m...
Reference:
E. M. Purcell & D. J. Morin, Electricity and Magnetism, 3rd Edition, Cambridge University Press (2013), Chapter 9 and Appendix H.
#physics #magnetism #specialrelativity
20 Comments
Great video.
The hardest parts for me are visualising the 3D waves. Anything you could do to make that easier would be really appreciated
This makes it sound as though magnetism is just there as a necessary part of the coulomb/electric field.
But ... is magnetism about ... metallic magnets, independent of the coulomb field?
This makes it sound almost as though magnetism isn't its own thing, just a philosophical necessity of relativity.
This is extraordinary.
So is magnetism caused by relativity???
https://www.youtube.com/watch?v=8MNcxa_Gk5U&t=21s
Your content is superb BTW!
But it seems like you supposed the magnetic force to exist in such a way that observers agree. It's still a separate force you have to discover/invent. "It has to exist to satisfy agreement between observers, therefore it exists."
Similar to Relativity as a whole, the rules (length contraction, time dilation) must be true following from the previous postulates (constant c, 1 reality different observers can agree on). It doesn't show how these things happen in any mechanistic way.
But Why Do Moving Charges Have a Magnetic Field?
Physical Intuition
13,217 views
Why do moving charges have a magnetic field? In this video we derive the magnetic field and the Lorentz force from nothing but Coulomb's law and special relativity, using time dilation, length contraction, relativity of simultaneity and energy-momentum mixing. Then we use it to find the magnetic half of light: the magnetic field of an electromagnetic wave from an accelerating charge, the vector potential, and why E = cB.
Along the way we look at why a current-carrying wire shows magnetism at all, why light is a null field, and how light carries energy and momentum. No Maxwell's equations needed, just intuition and visual arguments.
This is Part 2 of "Why Accelerating Charges Radiate": Why Accelerating Charges Radiate
CHAPTERS
0:00 Hook
1:26 Setup
5:11 Derivation: x direction
7:20 Derivation: y direction
9:59 Putting it together
15:44 Magnetic dominant
18:41 Back to light
21:11 Derivation: Magnetic radiation
24:21 Light
28:58 Going relativistic
29:47 Conclusion
Next video: special relativity built properly from its two postulates.
Manim animation source code for this video:
https://github.com/denisgisbrecht74/m...
Reference:
E. M. Purcell & D. J. Morin, Electricity and Magnetism, 3rd Edition, Cambridge University Press (2013), Chapter 9 and Appendix H.
#physics #magnetism #specialrelativity
Since the video became so packed, there are two assumptions I never got to discuss, and I want to mention them here for completeness:
1. Field line density gives field strength. This is Gauss's law: the number of field lines is fixed by the charge, so squeezing the lines together by length contraction makes the field stronger.
2. Charge is the same for all observers. This is not derived from relativity but is an experimental fact. For example, atoms stay neutral even though their electrons and nuclei move differently.