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energy due to a charge is infinite??

hello..

My professor said "Law of conservation of energy is not applicable to waves." This puzzled me a lot and trying to think otherwise i have a doubt regarding energy due to electric field. It seems that if energy due to electric field and magnetic combined, this might turn out to be true for light.
Let us have a charge Q at rest, whose electric field exists in the whole space. If a test charge,q i.e. Q>>q, is placed in this region, then due to repulsion it will move away from the charge Q. It will continue this motion till it is at infinite distance. This suggests that the total energy gained by the charge q from Q is infinite, further suggesting that the energy due to the electric field is not getting used up.... i.e. i can bring as many test charges as i want but this repulsion will exist, no matter how much energy the previous one has taken. So how is that so?

What kind of energy is possessed by the electric field created by a charge? Is it never ending, and suggesting that it never got created (may be when the charge or the electric field was formed)? in that sense this need not obey the laws of conservation of energy!

may be what i have asked is very silly, but any help is appreciated..