How to tell the magnetic flux a certian distance from a solenoid?

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How to tell the magnetic flux a certian distance from a solenoid??

This is about a coursework problem that i've been trying to figure out for the past few weeks.


This is my context, for those wanting to know
i'm trying to predict the high of the ring, in the jumping ring experiment. For those of you who have no idea what that is, it basically takes advantage of Lenz's law, see here: http://www.physics.brown.edu/physics/demopages/Demo/em/demo/5k2030.htm
The voltages that i am working with are no where near high enough to cause the ring to jump, the ring more levitates to a certian height along the extended iron core.
This happens when the force due to the magnetic field equals that of gravity.

My problem
I can't really get my head around working out the magnetic field strength a certian distance outside of the coil (not from the side of the coil but from the end)

The attempt at a solution

at first i thought that applying the siot-savart law would offer me an answer.

B=μ0Ilsinθ/4πr2

where r is the distance. sinθ the angle. I the current. And μ0 the permibibility of free space.

if i took θ to be 90 degrees. as the coil is 90 degrees the plane of the core, as its twisting around it. this would eliminate sinθ as it equals 1.

Therefore B = μ0Il/4πr2

my problem now is n defining l, is it the circumferance of the coil or the total length of line in the coil. i'm generally havng problems with this law, what is this length meant to mean. and can the number of turns be factored into the equation.Additionally, I would have to add a μr term to include the relative permeability of the core

I looked through my book and found an additional formula for a flat circular coil:

B = μ0IN/2 times r2/(r2times x2)3/2

where r is the radius of the coil. x the distance. N the number of turns. I the current. And μ0 the permibibility of free space.

This seems to make more sense but my coil is a long
solenoid, how do they differ? can this equation still work.

I would really appreciate any insight that anyone can give for this problem. Its really been getting to me, and my teacher seems more concerned over other things than over the problems i'm having with my coursework. despite that, i have to get to understand this.
 

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