A charged particle in constant gravitational field

AI Thread Summary
A paradox in classical electrodynamics arises when analyzing a charged particle falling under gravity, as the Larmor formula indicates that the power radiated is proportional to the square of the acceleration, leading to a non-zero value. However, the Abraham-Lorentz formula, which accounts for radiation reaction, yields zero because it depends on the time derivative of acceleration, which is constant in this scenario. This discrepancy raises questions about the external power needed to counteract radiation reaction, which is also zero. Clarification is sought on why the Abraham-Lorentz formula does not apply to constant acceleration situations. Understanding this distinction is crucial for resolving the paradox.
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In classical electrodynamics a paradox arises when we compare the power radiated by a charge falling under gravity using larmor formula (proportional to square of the acceleration, hence g^2) but the radiation reaction , given by abraham lorentz formula gives zero.(since it depends on the time derivative of the acceleration) ie. the external power required to counteract the radiation reaction is zero. I haven't come across any good explanation. Can someone please help me out? Thanks.
 
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The abraham lorentz formula does not apply to constant acceleration.
 
i see ..thanks.
 

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