Magnetic flux (and flux in general)

The general interpretation of flux as I understand it (and please correct me if I'm wrong) is that it represents how much something is going through another (surface or volume (and perhaps lines?)), I'll quote Khanacademy :

Considering that magnetism is a force, I very well understand that we only want the force that is pushing in the direction of the infinitesimal surface and keeping in mind the definition given before, it seems much logical to me to use this :
$$\iint_S \frac{\mathbf{B}\cdot\mathbf{dS}}{|\mathbf{dS}|}$$
We find the direction with the dot product but take off the surface and then we sum up the force. I probably am misunderstanding the flux definition and hope someone would have the kindness to clear this up.
I understand this integral can't be done since we no more have an infinitesimal to integrate with respect to it, but I think you see what I want to say through it.

My problem with this is that when I'm thinking that we're kind of distributing the force over that ##|\mathbf{dS}|## we'll be loosing "strength", ##|\mathbf{B}|*0.00000000.......1##, I hope you're getting what I mean.

BvU
Homework Helper
loosing "strength"
doesn't occur because of the integration: look what you get when ##\bf B## is constant and can be taken out in front of the integral

doesn't occur because of the integration: look what you get when ##\bf B## is constant and can be taken out in front of the integral
That would be ##|\mathbf{B}| \iint |\mathbf{dS}|(\hat{\mathbf u}\cdot\hat{\mathbf n})##, I can't see what you wanted to show me though, please do elaborate more.

I got it however, I was thinking wrong from the beginning by ignoring the units, a fractional number of surface would still actually represent something because of the meaning of a square meter which is a finite quantity (a collection of points dare I say) and thus fractions of it are still finite quantities (##n\to\infty\in \mathbb{N}## points forming an area) have escaped my thought, we are actually adding the strength "##n## times", I was blind to the unit.

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BvU