Helmholtz coil - QuickField simulation example
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.
How to calculate the uniformity of the magnetic flux density inside a Helmholtz coil?
Answer Typical applications Geometry
Given Task
Solution
The field at the center between Helmholtz coils is:
Results
Flux density distribution around the Helmholtz coils
* Reference: http://en.wikipedia.org/wiki/Helmholtz_coil
Engineering question
Solve the axisymmetric DC-magnetic model, map the nearly uniform field region, and compare the center flux density with the analytical approximation.
Helmholtz coils, laboratory reference coils, sensor calibration coils
Download
Simulation problem
Problem Type
Axisymmetric problem of DC magnetics
H = R = 1 m,
Each coil consists of 1 loop with total electric current of I = 1 A. Media around the coils is air.
Magnetic flux-density distribution and uniform-field region inside a Helmholtz coil, with the calculated field compared against the 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
B(x=R/2) = 2 · μnIR² / 2(R² + (R/2)²)3/2 = 0.83/2 · μnI/R.
Analytical solution for I=1 ampere, R=1 meter and n=1 gives B(x=0) = 8.98e-7 T.
QuickField calculates flux density value at the center between Helmholtz coils as B = 8.95e-7 T.
Video
Related examples