 in physics, specifically electromagnetism, the biotâsavart law ( or )"biot-savart law". random house webster's unabridged dictionary. is an equation describing the magnetic field generated by an electric current. it relates the magnetic field to the magnitude, direction, length, and proximity of the electric current. the law is valid in the magnetostatic approximation, and is consistent with both ampÃ¨re's circuital law and gauss's law for magnetism. it is named after jean-baptiste biot and fÃ©lix savart who discovered this relationship in 1820. ==equation== ===electric currents (along closed curve)=== the biotâsavart law is used for computing the resultant magnetic field b at position r generated by a steady current i (for example due to a wire): a continual flow of charges which is constant in time and the charge neither accumulates nor depletes at any point. the law is a physical example of a line integral: evaluated over the path c the electric currents flow. the equation in si units iselectromagnetism (2nd edition), i.s. grant, w.r. phillips, manchester physics, john wiley & sons, 2008, isbn 978-0-471-92712-9 {|\mathbf{r}|^3} |cellpadding |border |border colour = #50c878 |background colour = #ecfcf4}} where r is the full displacement vector from the wire element to the point at which the field is being computed and \mathbf{\hat{r}} is the unit vector of r. using \mathbf{\hat{r}}, the equation can be equivalently written as: : \mathbf{b} = \frac{\mu_0}{4\pi}\int_c \frac{i d\mathbf{l} \times \mathbf{\hat r}}{|\mathbf{r}|^2} where dl is a vector whose magnitude is the length of the differential element of the wire, in the direction of conventional current, and Î¼0 is the magnetic constant. the symbols in boldface denote vector quantities. the integral is usually around a closed curve, since electric currents can only flow around closed paths. an infinitely long wire (as used in the definition of the si unit of electric current - the ampere) is a counter-example. to apply the equation, the point in space where the magnetic field is to be calculated is arbitrarily chosen. holding that point fixed, the line integral over the path of the electric currents is calculated to find the total magnetic field at that po
Aerodynamics Electromagnetism