  We calculate the energy radiated coherently by a system of $N$ charged non
relativistic particles. It disagrees with the energy loss which is obtained if
one employs the Lorentz Abraham Dirac (LAD) equation for each particle, and
sums up the contributions. This fact was already clearly stated in the
classical literature long ago. The reason for the discrepancy is the omission
of the mixing terms in the Poynting vector. For some simple systems we present
a generalized equation for the radiation reaction force which cures this
defect. The counter examples show that the LAD equation cannot be generally
valid and that all "proofs" must fail somewhere. We demonstrate this failure
for some popular examples in the literature.
