Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet

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b) CLrcular current loop
Let a and I be the radius and the current of the loop. The potential
has cylindrical syr~.nlctry,but can be expressed by means of simp1.e
functi.ons only on the. axis r =: 0. For t.he n~oment we assume that
the current loop is in the plane z = o. For symnetry reasons there
is only a H z component on the axis.
1 Biot-Savart's law yields
whence
- 1a2 A8
' I a h 6 a
c4 . . .
ILZ = -
4n (z2+a 2) 3/2
I a2
z 2 (z2-ka 2)3i2
- .
l\roli xZ = -av/az = + a2+e/az2. Kence integrating twice on using
Vcm) = 0 = ie(m) we obtain
Now we have to solve (2.35b) , i. e.
Looking up in a table of Laplace transforms:
Sf the plane of thc loop is z = -hI 1 - > 0, then a si1npl.e change
of origin yiel-ds
1 Circular current loop I
I
I