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It only means that the direction of give flux is opposite to some reference which we consider as positive.property of an electric field that may be thought of as the number of electric lines of force (or electric field lines) that intersect a given area. Electric field lines are considered to originate on positive electric charges and to terminate on negative charges. Field lines directed into a closed surface are considered negative; those directed out of a closed surface are positive. If there is no net charge within a closed surface, every field line directed into the surface continues through the interior and is directed outward elsewhere on the surface. The negative flux just equals in magnitude but of opposite direction.
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This helps in solving problems where the fluxes entering and leaving a surface is known and we have to calculate charge within the conductor.
Suppose a Gaussian surface encloses an unknown charge. Flux entering and leaving the surface are #1 and #2. We want to know the magnitude of charge enclosed by the Gaussian surface.
From Gauss Law
Net Flux = q/epsilon
Here Net flux = #1 - #2
So charge = (#1 - #2)*epsilon.
Hope u are clear.........