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P: 38
i totally consider the fact that electric field lines are merely (rather continuous) the tangential representations of force acting on unit charge at that point which is definitely a vector and flux measures the flow of electric field lines through a particular defined surface δs and that is somewhat similar to heat flow or amount of heat flow through a well defined surface hence scalar rather the flux density is somewhat we define at particular point just considering the temperature gradient at point which has a direction indicating heat flow at a pt hence becomes vector..but the thing that still confusing is :-
 in case of parallel plate capacitor which i have considered here the Da=q where D : flux density a: surface area q: total charge on one plate and we also know that surface charge density is defined as : charge density is a measure of electric charge per unit volume of space, in one, two or three dimensions. More specifically: the linear, surface, or volume charge density is the amount of electric charge per unit length, surface area, or volume, respectively. The respective SI units are C·m−1, C·m−2 or C·m−3 from: http://en.wikipedia.org/wiki/Charge_density so here in case of parallel plate capacitor we have charge density σ=q/a ( surface charge density charge per unit area) and we also have the relation bet flux density D with E electric field intensity D=εE and E=σ/ε ( one can find this from gauss law for parallel plate capacitors) so both D and σ are here equal and but we know that charge density is definitely NOT a vector but flux density is a vector so both being equal in magnitude one has defined as scalar and other as vector..??