Is There a More Accurate Equation for the Magnetic Moment of a Solenoid?

[Kydharis]

Does anyone have an equation that describes the magnetic moment of a solenoid that does not actually use number of turns as an input?

I'm trying to validate a solenoid I have made with something like 11000 turns, but I'm not sure how accurate my number of turns in, so I need a second input that I can validate through testing (In this case, I can measure the magnetic flux at the poles of the solenoid).

I'm told that using a dipole equation for it is a decent approximation, but I'm really looking for a better approximation than that, since ideally a solenoid only becomes like a dipole at infinity.

 

[Meir Achuz]

The B field on the axis at one end of a solenoid is 1/2 what is given by the standard formula for the B field at the middle of a long solenoid.

 

[Kydharis]

Yes, but unfortunately the standard formula for the B field of a long solenoid has a
dependence on N (turns).

I actually can measure B of my solenoid - its the magnetic moment I'm concerned about. I want to use the B field I measured to get a magnetic moment.

 

[Meir Achuz]

In Gaussian units, the magnetic moment of a solenoid of length L with a field B at its center is m=BL/4pi.

 

[Meir Achuz]

I left out the cross-sectional area of the solenoid.
The mag moment should be m=BAL/4pi.

 

[Kydharis]

The units on that equation are a little weird. Right now, BAL/4pi is Tm^2 (or gauss*M^2). In my experience, magnetic moment is usually given in Am^2. I think the missing link is the magnetic constant - but adding it in with the 4pi leaves us with Am^3.