The geometry is shown in the figure in which the current sheet is made up of many line currents
of elemental cross-section. Using the equations for a line current that extends to
a finite length yo into and out of the plane of the figure, we have
 =  -
 = tan-1(r/yo) and the
magnetic perturbation at point P due to the elemental line current, dI, is:
But dI = jhdx where j is the current density and h is the height of the thin ionospheric
current layer. Also Hence we have:
Writing o = tan-1(H/yo) we get:
which upon integration gives:
For the case of an infinite plane current sheet we find:
This is the formula that relates a magnetic perturbation Bx to the equivalent current, jy. |
and therefore 
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