Helmholtz Coil

​
z
c
0.5
plot
3D
contour
field
A
θ
Φ
B
r
B
z
 B 
A Helmholtz coil consists of two circular coils of radius
R
with a common axis placed symmetrically in parallel planes at
z=-
z
c
and
z=+
z
c
, separated by the distance
h=2
z
c
. Both coils carry electrical currents
i
c
flowing in the same direction. To maximize the homogeneity of the magnetic induction
B
at the center of the coils, the separation distance is set equal to the radius of the coils,
h=R
.
In this Demonstration the coil radius
R
and the current
i
c
are both set equal to one. The constants
μ
0
/4π
in SI units or
1/c
in Gaussian units are also set to one. For the magnetic induction
B
at the center of the coils,
B(0)=4π
3/2
4
5
=8.992
.
The quantities calculated are the vector potential
A
θ
in the tangential
θ
direction, the flux
Φ=2πr
A
θ
, the radial and axial components of the magnetic induction
B
r
,
B
z
, and its norm
B
.
The contour lines of the flux
Φ
are in the direction of the magnetic induction field lines.

Details

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

External Links

Helmholtz-Coil Fields
Square Helmholtz Coils

Permanent Citation

Thomas Koeppel
​
​"Helmholtz Coil"​
​http://demonstrations.wolfram.com/HelmholtzCoil/​
​Wolfram Demonstrations Project​
​Published: March 7, 2011