How to Determine the Magnetic Field of Helmholtz Coils?

[xxbigelxx]

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.

 

[gabbagabbahey]

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.

 

[xxbigelxx]

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

 

[xxbigelxx]

Hmm or would that not work since the 'z' values are different depending on the coil you are talking about at the time.

 

[bjnartowt]

Do you mean the distance between the coils is equal to the radius of the coils? You say diameter, and they told me "radius".

 

[xxbigelxx]

Oh yes, sorry.

 

[bjnartowt]

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 : )

 

[xxbigelxx]

So would I be correct in following that similar example I posted, but adding a factor of 2 out front?

 

[gabbagabbahey]

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?

 

[xxbigelxx]

Yeah I think I got it now. Thanks.