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The force required to accelerate a radiating charge

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If we try to treat a non-relativistic point charge, what force do we need to accelerate it uniformly, when we take the fact that it radiates into account? I assumed the force would do the necessary extra work so that:

F dx = d(1/2 mv^2) + P dt;

where P is the Larmor power, but at any point where the velocity is 0 this would imply an infinite force. What am I missing?

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