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WOLFRAM|DEMONSTRATIONS PROJECT

Magnetic Field of a Current Loop

​
ring radius
6
current
2.75
A electrical current
I
moving around a circular loop of radius
a
, shown in yellow from a lateral point of view, produces a magnetic field, with lines of force shown as blue loops. For clarity, only lines of force in the vertical plane bisecting the ring (
y=0
) are shown.
The strength of the magnetic field is indicated by the density of the lines of force. The magnitude is expressed in units of
μ
0
/4π
. The field is cylindrically symmetrical about the axis of the ring. By a right-hand rule, a counterclockwise current produces magnetic lines of force that point upward inside the ring, downward outside the ring. At distances
r≫a
, the ring behaves like a magnetic dipole
m=π
2
a
I
, with vector potential
A=
μ
0
4π
mr
3
r
. As
a0
(with
2
a
I
constant), this approaches the field of a point magnetic dipole.
It is shown in the Details section that a contour plot of the vector potential
A
ϕ
(x,z)
in the
y=0
plane coincides with the magnetic lines of force.
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