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According to the BiotSavart law, the magnetic field generated at position vector
by a current
circulating around a thin loop, an element of which is located at position
vector
, is

(613) 
Suppose that a second current loop carries the current
. The net magnetic force exerted on an element,
, of this loop, located at position
vector
, is

(614) 
Hence, the net magnetic force exerted on loop 2 by loop 1 is

(615) 
where
.
Richard Fitzpatrick
20140627