Why does the diameter of a long solenoid have no influence on the magnetic Flux?

I am a german high school student and I have a question.

• My Questions is based on the Formular for the magnetic flux in a long solenoid: B=μ0⋅(N/L)⋅I (μ0 = Permeability; N = amount of windings; L = effectiv length of the solenoid; I = current) (https://en.wikipedia.org/wiki/Solenoid)

• The Magnetic flux around a wire decreases with 1/r due to the formular B=μ0⋅μr⋅I/(2πr)

So when we imagine a solenoid with a growing diameter while all other parameters like effective length, current and amount of windings stay the same, just the wire itself gets longer. And we know that the wire produces a magnetic field which decrases by 1/r its hard to imagine that the diameter of the solenoid has no influence on the magnetic flux. Why is it so that in the formular B=μ0⋅(N/L)⋅I is no diameter included, is this mathematical proveable that the diameter dosen´t matter?

Thanks for the answers already and sorry if there are some mistakes in my english writing.