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Explanation for the damping of electromagnetic (EM) waves propagating in a plasma is given. Comparisons of the damping rates between a general plasma (with no dust grains) and a dusty plasma are given. It is found that, in a certain range of the EM waves, the damping rate in the dusty plasma is much larger than that in a general plasma. The damping rate mainly depends on the number density of the dust grains and the frequency of the EM waves.