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.The Feynman Lectures on Physics Vol. II Ch. 14: The Magnetic Field in Various Situations Another approach involves a general solution of the inhomogeneous wave equation for the vector potential in the case of constant currents. David Tong. Lectures on Electromagnetism. University of Cambridge, Part IB and Part II Mathematical Tripos (2015). http://www.damtp.cam.ac.uk/user/tong/em.html. 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. Daniel Zile and James Overdui. Derivation of the Biot-Savart Law from Coulomb’s Law and Implications for Gravity. APS April Meeting 2014, abstract id. D1.033. https://doi.org/10.1103/BAPS.2014.APRIL.D1.33. 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.
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.The Feynman Lectures on Physics Vol. II Ch. 14: The Magnetic Field in Various Situations Another approach involves a general solution of the inhomogeneous wave equation for the vector potential in the case of constant currents. David Tong. Lectures on Electromagnetism. University of Cambridge, Part IB and Part II Mathematical Tripos (2015). http://www.damtp.cam.acuk/user/tong/em.html. The magnetic field can also be calculated as a consequence of the Lorentz transformations for t.he electromagnet.ic force acting from one charged particle on another particle. Daniel Zile and James Overdui. Derivation of the Biot-Savart Law from Coulomb’s Law and Implications for Gravity. APS April Meeting 2014, abstract id. D1033. https://doi.org/10.1103/BAPS.2014APRIL.D1.33. 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.