How to Calculate Magnetic Field Strength of Helmholtz Coils?

[jgrossm1]

I am currently working on a research project, and need an equation or method to find the magnetic field strength produced by any number of helmholtz coils, and not just on the central axis, but at any position in the space around them. Can anyone help me out?

Thanks

 

[ice109]

it's just the vector sum of the b field due to each coil.

 

[jgrossm1]

OK, i understand that, but how do you find the individual b field vectors for each coil, as all of the equations I've searched for so far will only do this for the central axis of a single coil, nowhere else

 

[ice109]

OK, i understand that, but how do you find the individual b field vectors for each coil, as all of the equations I've searched for so far will only do this for the central axis of a single coil, nowhere else

you have to do the integral of the biot-savart law for a point off axis. definitely someone has done it already though so it has to be somewhere. maybe look in an intermediate E&M book. or just do it yourself.

 

[clive]

Here is an analytical solution:
http://www.netdenizen.com/emagnet/offaxis/iloopoffaxis.htm

If not, do it numerically...(and you do not need those elliptic integrals any more)

 

[jgrossm1]

Here is an analytical solution:
http://www.netdenizen.com/emagnet/offaxis/iloopoffaxis.htm

If not, do it numerically...(and you do not need those elliptic integrals any more)

Do you know of a website that demonstrates and explains the method numerically with the elliptic integrals?

 

[clive]

In the numerical approach you do not need those elliptic integrals. You just consider each loop as a collection of small tail-to-tip oriented segments and sum the individual contributions at each point (of interest) of the space:
$$H_i=\frac{I\,\vec{dl}_i\times \hat{r}_i}{4\pi r_i^2}$$