Enunciating the Biot-Savart Law

Jean Baptiste Biot and Félix Savart are the two precursors of the calculation of the magnetic field in a wire.

Hans Christian Oersted was a physical scholar who was born in the year 1777. It was he who created the theory of electric currents and also made some discoveries involving the properties of magnetic fields. Because of his discoveries, he was very important for the growth of science from the 19th century onwards.
Thanks to his experiments, Oersted was able to show the direct relationship involving electrical and magnetic phenomena. Even without being able to give an explanation using mathematical calculations, he showed that electric currents create magnetic fields around them.

His experiment was announced at a meeting that took place at the French Academy of Sciences in the year 1920, in France. In search of new explanations for this phenomenon, Jean Baptiste Biot and Félix Savart presented more convincing reports, leaving their conclusions known as the Biot-Savart Law.

Let us imagine a charge q of positive value and that is moving with a speed v . Let us now consider the plane formed by the vectors v (velocity) and P (point where we want to measure the magnetic field). By the right-hand rule, we have the possibility to establish the magnetic field ( B ) that the positive charge q creates at a point P that is at a distance r from it. Looking at the figure, we see that the magnetic field is perpendicular to the plane and to find the magnitude of the magnetic field ( B ) we have the following equation:

Where k m is the magnetic constant whose value in the international system of units (SI) is given by k m = 10 -7
we have a wire carrying an electric current i. To determine the value of the magnetic field produced by the current at a point P, we simply divide the wire into small pieces (ΔL). In this way, we have that the magnetic field produced by each of the small pieces of wire is given by the equation:

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