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Consider an electromagnetic wave propagating through free space.The Electric and magnetic components of the fields, vary as sinusoids. If I construct a sphere of radius $\lambda/4$ at any location; i don't see why the flux of Electric field through that sphere will always be $0$?

But it must be $0$ due to the fact that divergence of electric field(induced+static) is $0$ at every point. Where am i wrong?

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You have answered your question. $\nabla.\mathbf{E}=0$ means that flux through the whole sphere will be zero (if it contains no charge), if the electric field is real (physically realizible). However it is still possible for portions of the sphere to have non-zero electric field flux, but it will be compensated somewhere else (on the sphere)

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