Magnetic Field of a Current Loop
Magnetic Field of a Current Loop
A electrical current moving around a circular loop of radius , 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 () are shown.
I
a
y=0
The strength of the magnetic field is indicated by the density of the lines of force. The magnitude is expressed in units of /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 , the ring behaves like a magnetic dipole , with vector potential . As (with I constant), this approaches the field of a point magnetic dipole.
μ
0
r≫a
m=πI
2
a
A=
μ
0
4π
mr
3
r
a0
2
a
It is shown in the Details section that a contour plot of the vector potential (x,z) in the plane coincides with the magnetic lines of force.
A
ϕ
y=0