Biot-savart Law

$d\backslash mathbf\{B\}\; =\; K\_m\; \backslash frac\{\backslash mathbf\{I\}\; d\backslash mathbf\{l\}\; \backslash times\; \backslash mathbf\{\backslash hat\; r\}\}\{r^2\}$

$K\_m\; =\; \backslash frac\{\backslash mu\_0\}\{4\backslash pi\}$ is the magnetic constant

I is the current, measured in amperes

$\backslash mathbf\{\backslash hat\; r\}$ is the unit displacement vector from the element to the field point

$\backslash mathbf\; B\; =\; K\_m\; I\; \backslash int\; \backslash frac\{d\backslash mathbf\; l\; \backslash times\; \backslash mathbf\{\backslash hat\; r\}\}\{r^2\}$

$v\; =\; \backslash frac\{\backslash Gamma\}\{4\backslash pi\; d\}$

Γ is the strength of the vortex

d is the perpendicular distance between the point and the vortex line.

$v\; =\; \backslash frac\{\backslash Gamma\}\{8\; \backslash pi\; d\}-\; cos(B)$

See also

• Jean Baptiste Biot
• Felix Savart
• magnetism
• vorticity

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