Why does surface area not directly affect normal force in friction?

[starablaze]

could you tell me why the surface area does not affect the surface area? isn't the normal force due to the electromagnetic interactions between the body and the surface? so the greater the surface area, the greater the normal force,right?

so the frictional force will depend on surface area,in the expression

friction=mu x normal force

no?

 

[jomoonrain]

In fact, I think we can define a force (areal) density f here.
And the frictional force is:
F(fric)=Nu=[f1 x A(area)]u=f2 x A, N is the pressure (the body give to the suface),u is friction coefficient,f1 is the pressure density, f2 is the frictional force density
for a given body, the pressure N is fixed, and the change of the area can only affect the pressure density and so the frictional force density.

So,although the area is changed, the force density is also changed, and fortunately they happen to cancel out.