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.