violating gausss law for magnetism and electr induction

i dont know but i hv this doubt nagging me.......

we hv studed that according to gauss law magnetic flux through a closed surface is 0 as no single charge ever exists.....
now in electromagentic inudctuion the emf induced is rpopotional to the magnetic flux through that surface....

the only expaination which comes to my mind is that if it is that here we only cnsider a single surface that means we only consider a part of the closed surface and magnetic flux through this portion is unidirectional
is my thinking right
if not pls correct me

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