K. Idris-Bey, M. Dehbaoui, S. Haireche, M. Ahmed Ammar UYFM You logo goes here K. Idris-Bey, M. Dehbaoui, S. Haireche, M. Ahmed Ammar Laboratory of Physics Experimental Techniques and Applications University of Medea, idrisbeykamel@gmail.com 2.2 - The ferrimagnetism 𝐻 𝑥, 𝑦, 𝑧 = 𝐼 𝜇 𝑟 𝑧 𝐿𝑛 𝑦 𝑦 0 −𝐿𝑛 𝑥 𝑥 0 Abstract/Introduction The ferrimagnetic susceptibility is 𝑥 0 and 𝑦 0 are the coordinates at the origin, The magnetization is also in the Oz axis orientation This article studies the different magnetic behaviors that can appear in a material. In the first place, the description of macroscopic magnetism, or macromagnetism, is essential in order to understand the functioning of the device and the work equipment. This step is treated by modeling the macroscopic magnetic field created by the electromagnet at any point in space. Through this step we get to know better the magnetization and magnetic susceptibility that are generated by the external magnetic field. In a second step, the modeling is dedicated to the micromagnetism which describes the magnetic behavior within the materials, by the knowledge of the distribution of the spins and the magnetic moments in all the space of the interior of the materials to be studied. Some bodies are attracted to magnetic fields, others are repulsed. So there are two signs for the magnetic effect. One can easily put these two signs show with a strong electromagnet including a pole pitch part is sharp and the other flat. The magnetic field is much stronger near the pitch sharp piece than of the piece pole pitch flat. If we suspend a small piece of material to a long rope so that the piece occupy the place between the two poles, low force will act on it. The piece of material will move in one direction or the other depending on the material used. Thus a small piece of Bismuth is weakly repelled by the sharp pole and a piece of aluminum is attracted. Substances that are repelled by the pointed pole are diamagnetic materials and substances that are attracted by the pointed pole are paramagnetic materials [1] and [2]. 𝑀 𝑥, 𝑦, 𝑧 =−𝐼 𝐿𝑛 𝑦 𝑥 −𝐿𝑛 𝑦 0 𝑥 0 . 1 𝑧 − 1 𝑧 0 𝑧 0 is the coordinate at the origin and I is the intensity of the courant, The expression of the magnetic susceptibility is written as 𝜒 𝑧 = 𝜇 𝑟 𝑧 𝑧 0 −1 Expression of the magnetic induction B (x,y,z) 𝐵 𝑥, 𝑦 = 𝜇 0 𝜇 𝑟 +𝜒 𝑧 𝐻= 𝜇 0 𝐼 𝑧 0 𝐿𝑛 𝑦 𝑦 0 −𝐿𝑛 𝑥 𝑥 0 B is independent of the z coordinate, this implies that the magnetic induction field B ⃗ respect the first equation of magnetism, ∇ . 𝐵 =0. This figure shows the two curves corresponding to the two ferromagnetic sub-networks with different amplitudes (NiFe2O4 ). 2.3 - The anti-ferromagnetism The anti-ferromagnetic susceptibility is The micromagnetism The microscopic magnetism is inseparable from quantum mechanics, because a purely classical system in thermodynamic equilibrium cannot have magnetic moment. 1 - The diamagnetism The magnetization as a function of H is Magnetization and magnetic susceptibility The expression of the diamagnetic susceptibility is To explain these two phenomena of magnetism a physical Magnetization is defined, it is connected to the magnetic field by the following equation [3] [ χ ] is the susceptibility tensor. χ > 0 for paramagnetic materials and χ < 0 for diamagnetic material. If χ = 0 the material is not magnetic. Conclusion An efficient method for the description of isotropic magnetic materials is studied in this article. It defines the different magnetic behaviorism which can appear in materials. The beginning of the article describes the experience of Feynman which identifies the diamagnetic with negative susceptibility and the paramagnetic with positive susceptibility. The next step shows the method which let’s to find the three equations of magnetism from the Maxwell equations. The study of these three equations distinguishes the macromagnetism, which describes the electromagnet, and the micromagnetism, which describes the magnetic properties of the material submissive to the effect of the electromagnet. 2 - The paramagnetic The paramagnetic susceptibility is The three equations of magnetism Based on the assumptions of magnetism, which implies that and therefore the displacement vector of the electric field is References equal to zero . Knowing that , the three equations of magnetism are [4] [1]-Feynman/Leighton/Sands; Le cours de physique de Feynman, Electromagnétisme 1. Inter Editions, Paris 1979. [2]-Feynman/Leighton/Sands; Le cours de physique de Feynman, Electromagnétisme 2. Inter Editions, Paris 1979. [3]-R. Khatiwada and al, Materials with low DC magnetic susceptibility for sensitive magnetic measurements; 1Department of Physics, Indiana University, Bloomington, IN, 47405 and IU Center for Exploration of Energy and Matter, Bloomington, IN, 47408, USA: July 1, 2015. [4]-Florian Bruckner and al, Macroscopic Simulation of Isotropic Permanent Magnets; Christian Doppler Laboratory of Advanced Magnetic Sensing and Materials, Institute of Solid State Physics, Vienna University of Technology, Austria: July 3, 2015. [5]–M.J. Bales, P. Fierlinger, and R. Golub, Nonextensive statistics in spin precession, Physikdepartment, Technische Universit¨at M¨unchen, D-85748 Garching, Germany and Physics Department, North Carolina State University, Raleigh, NC 27695-8202, USA (February 3, 2016) 2.1 - The ferromagnetism The ferromagnetism susceptibility is The first equation is the general la w for the induction magnetic field. The second equation is the magnetic field expression, which is inducing by the density of conduction current. The third equation takes into account the magnetization existing in side the material. The macromagnetism The theory of the macroscopic magnetism is based on the application of the three magnetism equations. The experimental conditions impose the direction and sense of orientation of the magnetic field. Let Oz to be the axis of orientation, then the total magnetic field H(x, y, z) is Fig . 1 An improved algorithm of pyramidal testing