the vortex and r is the perpendicular distance between the point and the vortex line. This is similar to the magnetic field produced on a plane by an infinitely long straight thin wire normal to the plane. This is a limiting case of the formula for vortex segments of finite length (similar to a finite wire): where A and B are the (signed) angles between the line and the two ends of the segment. The Biot–Savart law, Ampère's circuital law, and Gauss's law for magnetism In a magnetostatic situation, the magnetic field B as calculated from the Biot–Savart law will always satisfy Gauss's law for magnetism and Ampère's law: In a non-magnetostatic situation, the Biot–Savart law ceases to be true (it is superseded by Jefimenko's equations), while Gauss's law for magnetism and the Maxwell–Ampère law are still true. Theoretical background Initially, the Biot–Savart law was discovered experimentally, then this law was derived in different ways theoretically. In The Feynman Lectures on Physics, at first, the similarity of expressions for the electric potential outside the static distribution of charges and the magnetic vector potential outside the system of continuously distributed currents is emphasized, and then the magnetic field is calculated through the curl from the vector potential. Another approach involves a general solution of the inhomogeneous wave equation for the vector potential in the case of constant currents. The magnetic field can also be calculated as a consequence of the Lorentz transformations for the electromagnetic force acting from one charged particle on another particle. Two other ways of deriving the Biot–Savart law include: 1) Lorentz transformation of the electromagnetic tensor components from a moving frame of reference, where there is only an electric field of some distribution of charges, into a stationary frame of reference, in which these charges move. 2) the use of the method of retarded potentials. See also People André-Marie Ampère James Clerk Maxwell Pierre-Simon Laplace Electromagnetism Darwin Lagrangian Notes References Further reading Electricity and Modern Physics (2nd Edition), G.A.G. Bennet, Edward Arnold (UK), 1974, Essential Principles of Physics, P.M. Whelan, M.J. Hodgeson, 2nd Edition, 1978, John Murray, The Cambridge Handbook of Physics Formulas, G. Woan, Cambridge University Press, 2010, . Physics for Scientists and Engineers - with Modern Physics (6th Edition), P. A. Tipler, G. Mosca, Freeman, 2008, Encyclopaedia of Physics (2nd Edition), R.G. Lerner, G.L. Trigg, VHC publishers, 1991, ISBN (Verlagsgesellschaft) 3-527-26954-1, ISBN (VHC Inc.) 0-89573-752-3