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Jul27-10, 11:14 AM
P: 250
Quote Quote by htg View Post
Since the intensity of the beam falls off rapidly as we move away from its axis, I do not see how the Gauss' law may be satisfied.
It may be true that the intensity falls off as we move away from the x axis. But it increases perpendicular to that axis as the light energy disperses. The divergence entails derivatives in all 3 directions. Even the most collimated laser beams spread with distance. Laser beams pointed at the moon illuminate lunar surface areas much larger than the beam's cross section at its origination point. For what it's worth, I am sympathetic to your skepticism, perhaps because texts don't discuss the applicability/validity of Gauss' law in electrodynamic (especially relativistic) situations. But ultimately divE=rho/eps0 appears to apply in all cases, even though one of its ramifications (Gauss' law) is mostly invoked in electrostatics.