Larmor’s Formula Derivation

This is a derivation of Larmor's formula which describes the power contained in electromagnetic radiation. The steps followed are the ones from Walter Lewin's 8.03 class at MIT.
On the way to the formula, I derive the expression for the Poynting vector of electromagnetic radiation. The dependence on "sine squared" comes out in the wash. The Poynting vector expression shows that no power is radiated immediately ahead or immediately behind the charged particle; furthermore, it shows that the maximum power is radiated transversely.
This is an important result that is used in the study of antennas.

[@User-jr7vf]

It took me 3 days of hard work to derive Larmor's formula (not looking at derivations in the literature). Now I came to KZbin just to hear how "Larmor" is pronounced in English.

[@zsh7862]

Absolute legend this explanation saved me

[@quantumradio]

Thank you for the comment. BTW you may also find helpful the video lectures presented by Dr. Walter Lewin in his E&M 8.02 class at MIT. Best of luck in. your studies.

[@iffylunatic4035]

Thank you sir❤

[@quantumradio]

Thank you for the comment. Best of luck in your studies!

[@veronicanoordzee6440]

Very nice and clear writing.

[@quantumradio]

Thank you for the comment. Hope the derivation was helpful.

[@veronicanoordzee6440]

@@quantumradio Absolutely. From the book I wasn't so sure I got things right. But now I have. Thanks for the confirmation.

[@alipedram5720]

Superb!

[@quantumradio]

Thanks Ali. Have a great one!

[@azizfaozi7203]

ty

[@kasel1979krettnach]

this formula poses so many questions. 😅 first and foremost the violation of general relativity

[@quantumradio]

Thanks for the comment. The way I understand it, special relativity (SR) may be the bigger concern since General relativity (GR) would require large masses to affect the curvature of space-time; however, SR kicks in at high enough velocities so it could affect us. Recall that the assumption in the derivation is that r=ct >> ut so the lurch is a lot slower than the speed of light. So we should be OK to neglect SR. 73!

[@kasel1979krettnach]

@@quantumradio i think it violates the equivalence principle. a charge thats is gravitaionally accelarated should radiate but then a co-accelareted observer should be able to observe the radiation - and by that be able to tell free fall from weightlessness

[@quantumradio]

@@kasel1979krettnach Andreas, the equivalence principle refers to the equivalence of gravitational and inertial mass. In this case gravitational acceleration plays no part. Best of luck in your studies.

[@kasel1979krettnach]

I was referring to that elevator thought experiment. try falling alongside an electric charge and you have a way to determine whether you are free falling or in free space. charge radiates --> free falling (acceleration), does not radiate = free space. My studies are long past. @@quantumradio