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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.
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 = 8.98e7 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
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