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B.1 Magnetic field

The Biot-Savart law for a zero-thinkness wire is given by

μ0∫ ′ dl(r′) ×(r − r′) B(r) = 4π- I(r )---|r-−-r′|3---, (625)
where dl(r′) is a line element along the wire (the freedom of choosing which one of the two possible directions along the wire is up to users), I(r′) is the current in the wire (I is positive if the current in the same direction of dl, otherwise, negative).

In Cartesian coordinates, the vector r − r′ is written as

′ ′ ′ ′ r− r = (x− x )ˆex + (y− y )ˆey + (z − z)ˆez.
(626)

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