# Helmholtz Coil

Helmholtz Coil

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, .

R

z=-

z

c

z=+

z

c

h=2

z

c

i

c

B

h=R

In this Demonstration the coil radius and the current are both set equal to one. The constants /4π in SI units or in Gaussian units are also set to one. For the magnetic induction at the center of the coils, .

R

i

c

μ

0

1/c

B

B(0)=4π=8.992

3/2

4

5

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 .

A

θ

θ

Φ=2πr

A

θ

B

r

B

z

B

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

Φ