On-Axis Field Due to a Current Loop

This simple formula uses the law of Biot Savart, integrated over a circular current loop to obtain the magnetic field at any point along the axis of the loop.

Current loop in cross section view.

B is the magnetic field, in teslas, at any point on the axis of a current loop. The direction of the field is perpendicular to the plane of the loop.

is the permeability constant (1.26x10-6 H/m)

i is the current in the wire, in amperes.

r is the radius of the current loop, in meters.

x is the distance, on axis, from the center of the current loop, in meters.

  Special Case: x = 0

  Special Case: x >> r

Note that this is equivalent to the expression for on axis magnetic field due to a magnetic dipole:

where A is the area of the current loop, or

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