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Main >> Applications >> Sample problems >> 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

**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.

**Task:**

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*) = 2*B*_{1}(*x*) = 2 · μ*n**I**R*^{2} / 2(*R*^{2} + *x*^{2})^{3/2}

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

* Reference: http://en.wikipedia.org/wiki/Helmholtz_coil