Why does the magnetic flux in a solenoid depend on the number of loops?

[yosimba2000]

In a solenoid of N loops and uniform magnetic field B, the magnetic flux is B*N*A, where A represents the area surrounded by each loop.

I see that the N comes from the fact that you have one A for each turn, and you have N turns, so the total "area" is NA, but why do we use this? Why isn't magnetic flux just equal to B times only one cross-sectional area A?

Is it just definition?

 

[BvU]

Note that this is for a solenoid in an external field B. That the windings are stacked doesn't matter. If they were placed beside each other would you also have trouble with the expression ?

THere is some law that says that an emf is induced when the flux changes. In a coil all the emfs from the individual turns are added up, hence the factor N.

 

[ZapperZ]

In a solenoid of N loops and uniform magnetic field B, the magnetic flux is B*N*A, where A represents the area surrounded by each loop.

I see that the N comes from the fact that you have one A for each turn, and you have N turns, so the total "area" is NA, but why do we use this? Why isn't magnetic flux just equal to B times only one cross-sectional area A?

Is it just definition?

A solenoid is equivalent to a stack of loops of wire on top of each other. So if you have a flux for ONE loop, if you stack up N loops, why shouldn't the total flux be the sum of each individual flux?

Zz.