Helmholtz Coil

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A Helmholtz coil consists of two circular coils of radius with a common axis placed symmetrically in parallel planes at and , separated by the distance . Both coils carry electrical currents flowing in the same direction. To maximize the homogeneity of the magnetic induction at the center of the coils, the separation distance is set equal to the radius of the coils, .

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In this Demonstration the coil radius and the current are both set equal to one. The constants in SI units or in Gaussian units are also set to one. For the magnetic induction at the center of the coils, .

The quantities calculated are the vector potential in the tangential direction, the flux , the radial and axial components of the magnetic induction , , and its norm .

The contour lines of the flux are in the direction of the magnetic induction field lines.

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Contributed by: Thomas Koeppel (March 2011)
Open content licensed under CC BY-NC-SA


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For more information on Helmholtz coils, see the following references.

Helmholtz Coil on Wikipedia

J. D. Jackson, Classical Electrodynamics, 3rd ed., New York: Wiley, 1998

E. M. Lifshitz and L. D. Landau, The Classical Theory of Fields, Vol. 2, 4th ed., Oxford: Butterworth-Heinemann, 1980

E. M. Lifshitz, L. D. Landau, and L. P. Pitaevskii, Electrodynamics of Continuous Media, Vol. 8, 2nd ed., Oxford: Butterworth-Heinemann, 1984

Helmholtz Coil Manual from ETS-Lindgren



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