How to Determine the Magnetic Field of Helmholtz Coils?

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Homework Help Overview

The discussion revolves around determining the magnetic field along the z-axis between two Helmholtz coils, which consist of two circular loops of radius R carrying current I in the same direction. The loops are positioned along the z-axis with their centers at z=+/-s/2.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the relationship between the magnetic field of a single loop and that of two loops, questioning whether a factor of two should be included due to the presence of both coils. There is also discussion about the implications of the different z-values for each coil when calculating the magnetic field.

Discussion Status

The discussion is ongoing, with participants sharing their thoughts on how to approach the problem. Some guidance has been provided regarding the need to consider the positions of the coils when applying formulas, but no consensus has been reached on the exact method to use.

Contextual Notes

Participants note confusion regarding the distance between the coils, specifically whether it should be considered as the radius or diameter of the coils, which has implications for their calculations.

xxbigelxx
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Homework Statement



We have 2 circular loops, each of radius R with current I in same direction. This is called a Helmholtz coil. The loop axes are along the z axis and the centers are at z=+/-s/2.

Find the magnetic field along the z axis between the 2 loops.



Homework Equations





The Attempt at a Solution


I'm having a little trouble starting this because every problem I could find that was similar would always have the distance between the coils equal to the diameter of the coils. It was throwing me off. Thanks.
 
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xxbigelxx said:

Homework Statement



We have 2 circular loops, each of radius R with current I in same direction. This is called a Helmholtz coil. The loop axes are along the z axis and the centers are at z=+/-s/2.

Find the magnetic field along the z axis between the 2 loops.



Homework Equations





The Attempt at a Solution


I'm having a little trouble starting this because every problem I could find that was similar would always have the distance between the coils equal to the diameter of the coils. It was throwing me off. Thanks.

You basically have two circular current loops and are asked to find the magnetic field of the axis between them...surely you've calculated the magnetic field along the axis of a single circular current loop before? It is a very common example.
 
Oh ok that's what I was wondering. I found this example in the book and thought about closely following it. Would it be the same value, but have a factor of two out front since there are now 2 coils?




http://i52.tinypic.com/309sxhi.jpg
 
Hmm or would that not work since the 'z' values are different depending on the coil you are talking about at the time.
 
every problem I could find that was similar would always have the distance between the coils equal to the diameter of the coils.[/QUOTE said:
Do you mean the distance between the coils is equal to the radius of the coils? You say diameter, and they told me "radius".
 
Oh yes, sorry.
 
xxbigelxx said:
Oh yes, sorry.


No problem, my friend. I'd just hate for you to be off by a factor of 2, or 1/2, or...whatever kind of frustration would await : )
 
So would I be correct in following that similar example I posted, but adding a factor of 2 out front?
 
xxbigelxx said:
Hmm or would that not work since the 'z' values are different depending on the coil you are talking about at the time.

Exactly, the two loops are at z=\pm \frac{s}{2}, not the origin... if you are at z=d (and x=y=0 ), how far are you from the bottom coil? how far are you from the top coil? Can you see what you should use instead of 'z' in the formula for each coil?
 
  • #10
Yeah I think I got it now. Thanks.
 

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