Helmholtz coil
The term Helmholtz coils refers to a device for producing a region of nearly uniform magnetic field. It is named in honor of the German physicist Hermann von Helmholtz.
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[[==Description
A Helmholtz pair consists of two identical circular magnetic coils that are placed symmetrically one on each side of the experimental area along a common axis, and separated by a distance equal to the radius of the coil. Actually, a slightly larger separation improves the field uniformity. Each coil carries an equal electrical current flowing in the same direction. A cylindrical region extending between the centers of the two coils and approximately 1/5 of their diameter will have a nearly spatially uniform magnetic field.
Mathematics
The calculation of the exact magnetic field has mathematical complexities and involves the study of Bessel functions. An approximate calculation gives the correct value at the center point. If the radius is R, the number of turns in each coil is n and the current flowing through the coils is I, then the magnetic flux density, B at the midpoint between the coils will be given by
is the permeability constant (, or , for coils measured in meters, centimeters and inches, respectively)
Quadrupole Magnetic Field
This is a Magnetic Field produced by two electric coils; see for example: [1]