Finding B-Field Of Solenoid Slightly Off Axis?

1. Dec 2, 2012

jasonpatel

If you have a solenoid positioned along the z axis...

...how would one find the b-field at slight deviations of x and y???

I have been googling for hours and cant find anything other than the fact that it is very difficult!

Thanks guys!

2. Dec 3, 2012

bp_psy

Last edited: Dec 3, 2012
3. Dec 3, 2012

jasonpatel

Interesting read, but extremely complicated! Haha, i was wondering if there was a way to taylor expand around the z axis with infintely small deviations from the z axis (i.e. x+ε and y+ε)

Any thoughts?

4. Dec 3, 2012

bp_psy

What exactly do you want to expand?
Note that the magnetic field inside a sufficiently long solenoid is in fact homogeneous and there is no need to expand anything, Also the need for complicated math and numerical integration techniques arises even on axis for a short finite solenoid since the fields at the ends diverge.

http://en.wikipedia.org/wiki/Soleno...ctor_potential_for_finite_continuous_solenoid

Last edited: Dec 3, 2012
5. Dec 7, 2012

jasonpatel

Well, let me get a little more specific then.

My actual problem was to find the b-field of a helix coil along the axis of symmetry (z-axis), and I did. The B_x, B_y and B_z components are all a function of z and no other variables.

Then I was asked to find the b-field at very small deviations from the z-axis, x+ε and y+ε. I was also given the advice to do some "Taylor expansion of the field".

But i dont have a clue of how to do that! Any help??

6. Dec 8, 2012

jasonpatel

Just to make things very clear I have attached a pdf of the integrals I will be computing. So, I am wondering if I should expand ∅ with a taylor expansion because of the assumption that displacements of ∅ will be very small i.e. (∅ + ε) and (∅ - ε)

I am hoping this expansion of ∅ will create a simple integral and the answer of which will give the b-field in terms of (x,y,z) with the assumption that displacements in the (x,y,z) will be very small (x+ε,y+ε,z+ε).

Does this sound reasonable or am I totally off? Also, how many terms in the taylor expansion should I keep?

Attached Files:

• example of the integrals.pdf
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Last edited: Dec 8, 2012