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Helmholtz coil

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


Helmholtz coil

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.

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

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


The field within Helmholtz coils at the axis may be estimated as*:
B(x) = 2B1(x) = 2 · μnIR2 / 2(R2 + x2)3/2

The field at the center between Helmholtz coils is:
B(x=R/2) = 2 · μnIR2 / 2(R2 + (R/2)2)3/2 = 0.83/2 · 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.

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Download Download simulation files helmholtz_coil.zip.