# 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.

## 1 Answer

To obtain that equation, the diameter is assumed to be much smaller than the length of the solenoid, so it ends up not being relevant. Go look at the part of the article you link to talking about the finite solenoid; there the field does depend on the diameter, and if you look at the regime for when the solenoid is much longer than its diameter the equation for the infinite solenoid falls out.