Building upon Biot-Savart Law: Behavior of Surfaces and Curves of Magnetic Field around Electrical Segments

The Biot-Savart law defines the magnetic field vector around an electrical segment. Its calculation involves a cross product, but certain physical properties of this operation are not fully satisfactory. This article proposes a modification to the Biot-Savart formula by replacing the vector field with a scalar field. The revised magnetic field concept is then applied to both short and long electrical segments.