Accelerated charges radiate energy

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Accelerated charges indeed radiate energy, a concept rooted in Maxwell's equations. To prove this, one can start by examining the Larmor formula, which describes the power radiated by a non-relativistic accelerating charge. Understanding the derivation of electromagnetic waves can also provide insights, as it relates to how changing electric and magnetic fields propagate energy. Resources such as lecture slides from reputable physics departments can offer valuable equations and frameworks for further exploration. Engaging with these materials will enhance comprehension of the relationship between acceleration and radiation in electromagnetic theory.
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Hi! Accelerated charges radiate energy. I've always just taken that to word, but my exams are coming, and I would really like to broaden my understanding a little. How can we go about proving that using Maxwell's theories? I'm not asking for a complete derivation because I know that might be too involved. I just need some hints, how I may approach the problem, or if possible a link to some website with relevant information. I know the derivation for plane EM wave, so if there's anyway that relates to the present question, pls let me know. Thansk very much.
 
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Here area few lecture slides i fond freely available on the web. I had a quick look through and all relevant equations seem to be there and they're not all derived if you want to have a go yourself.

http://www.physics.usyd.edu.au/~kuncic/lectures/HEA_L5.pdf
 
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Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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