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The BiotSavart Law
The Engineer
posted on November 10, 2006 
 11944 views
Shortly after Oersted's discovery in 1819 that a compass needle is deflected by a currentcarrying conductor, Jean Baptist Biot and Felix Savart reported that a conductor carrying a steady current exerts a force on a magnet.
From their experimental results, Biot and Savart arrived in an expression that gives the magnetic field at some point in space in terms of the current that produces the field. The BiotSavart law says that if a wire carries a steady current I, the magnetic field d
B
at a point P associated with an element of the wire ds has the following properties:
The vector d
B
is perpendicular both to ds (which is a vector units of length and in the direction of the current) and to the unit vector r directed from the element to P.
The magnitude of d
B
is inversely proportional to r
^{2}
, where r is the distance from the element to P.
The magnitude of d
B
is proportional to the current and the length ds of the element.
The magnitude of d
B
is proportional to
, Where
is the angle between the vectors ds and r.
The BiotSavart law can be summarized
Where k
_{m}
is a constant that in SI is exactly 10
^{7}
T.m/A.
This constant is usually written
, where
is another constant, called the permeability of free space:
Hence,
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