Helmholtz coil magnetic field, uniform magnetic field generation, homogenous magnetic field, coil FEA analysis

A Helmholtz coil is a device for producing a region of nearly uniform magnetic field. This construction is formed by the two identical circular coils, placed symmetrically along a common axis, and separated by the distance H equal to the coil radius R. Both coils carry the same electric current I. Area of the quasi uniform field is located inside the coils.

Problem type: Axisymmetric problem of DC magnetics

Geometry:

Given: H = R = 1 m,
Current I = 1 A.
Each coil consists of 1 loop with electric current I placed. Media between the coils is air.

Problem: Calculate the flux density distribution within the Helmholtz coil. Find the area of uniform field. Compare with analytical approximation.

Solution: Model may be defined and solved as a DC Magnetic Analysis problem.

Results: The field within Helmholtz coils at the axis may be estimated as*:
B(x) = 2B_{1}(x) = 2 · μnIR^{2} / 2(R^{2} + x^{2})^{3/2}

The field at the center between Helmholtz coils is:
B(x=R/2) = 2 · μnIR^{2} / 2(R^{2} + (R/2)^{2})^{3/2} = 0.8^{3/2} · μnI/R.

For our model parameters (I=1 ampere, R=1 meter, n=1 loop) this gives B = 8.98e-7 T. QuickField results are close to this approximated value.

Plot of the flux density along the radius between the coils.

Flux density distribution around the Helmholtz coils.