Magnetic perturbation due to a line current.
Magnetic perturbation due to a line current.

The geometry is shown in the figure. Using the Biot-Savart law the magnetic perturbation at point P due to a current element is:
But l = rcot and therefore dl = -rcosec2d. Hence we have:
Integration from to yields:
For a very long line current, -> 0, and -> and in the limit we have:
If this line current flows at a height H above the ground then the horizontal and vertical components of the ground magnetic perturbation vary along a path at right angles to the current as shown in panel A of the figure. Mathematically, this is given by:
where the magnetic perturbation that is directed at right angles to the current and the position vector has been resolved parallel and perpendicular to the ground plane.


BAS Homepage UASD Homepage Navigator