Finding B-Field Of Solenoid Slightly Off Axis?

  • Context: Graduate 
  • Thread starter Thread starter jasonpatel
  • Start date Start date
  • Tags Tags
    Axis B-field Solenoid
Click For Summary

Discussion Overview

The discussion centers around finding the magnetic field (B-field) of a solenoid when positioned slightly off-axis, specifically at small deviations from the z-axis. Participants explore theoretical approaches, mathematical techniques, and the complexity involved in calculating the B-field in this context.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant inquires about the method to find the B-field at slight deviations from the z-axis, noting the difficulty in finding resources on the topic.
  • Another participant suggests that the problem involves elliptic integrals and provides links to relevant papers that may assist in the calculations.
  • A participant expresses interest in using Taylor expansion around the z-axis for small deviations, questioning the feasibility of this approach.
  • Another participant points out that the magnetic field inside a sufficiently long solenoid is homogeneous, suggesting that expansion may not be necessary, and highlights the complexity of the problem even for finite solenoids.
  • A participant clarifies their specific problem involves a helical coil and that they have already determined the B-field components along the z-axis, seeking assistance with the Taylor expansion for small deviations.
  • One participant proposes expanding the angle ∅ with a Taylor expansion due to the assumption of small displacements, questioning the reasonableness of this approach and how many terms to include in the expansion.

Areas of Agreement / Disagreement

Participants express differing views on the necessity and feasibility of using Taylor expansion for this problem. There is no consensus on the best approach to take, and the discussion remains unresolved regarding the application of mathematical techniques to calculate the B-field off-axis.

Contextual Notes

Participants note the complexity of the problem, including the potential need for numerical integration techniques and the behavior of the magnetic field at the ends of finite solenoids. The discussion highlights the dependence on specific assumptions regarding the size of deviations and the nature of the solenoid.

jasonpatel
Messages
32
Reaction score
0
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 can't find anything other than the fact that it is very difficult!

Thanks guys!
 
Science news on Phys.org
This is kind of a hard problem that involves elliptic integrals.
Here is paper that shows you how to do it .

http://ntrs.nasa.gov/search.jsp?R=19980227402

Also this might help.
http://www.netdenizen.com/emagnettest/offaxis/?offaxisloop
 
Last edited:
Interesting read, but extremely complicated! Haha, i was wondering if there was a way to taylor expand around the z axis with infinitely small deviations from the z axis (i.e. x+ε and y+ε)

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

Any thoughts?
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:
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 don't have a clue of how to do that! Any help??
 
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?
 

Attachments

Last edited:

Similar threads

Undergrad Magnetic field at a point along the solenoid's axis but outside the solenoid
  • · Replies 5 ·
Replies
5
Views
2K
Calculating magnetic field outside a solenoid
  • · Replies 15 ·
Replies
15
Views
2K
Electron in a time variable magnetic field
  • · Replies 5 ·
Replies
5
Views
2K
Field transformations in the z-direction
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Magnetic field strength at point P around a solenoid
  • · Replies 1 ·
Replies
1
Views
2K
What is the Magnetic Field of a Long Solenoid?
  • · Replies 3 ·
Replies
3
Views
2K
Deciding the direction of magnetic field of a solenoid
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Current induced from a changing magnetic field
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Electric and magnetic field lines in a plane wave of finite extent
  • · Replies 1 ·
Replies
1
Views
2K
What Force is Needed to Pull a Solenoid in a Magnetic Field?
  • · Replies 3 ·
Replies
3
Views
5K