Page 1 Electromagnetism - Lecture 10 Magnetic Materials Magnetization Vector M Magnetic Field Vectors B and H Magnetic Susceptibility & Relative Permeability Diamagnetism Paramagnetism Eects of Magnetic Materials 1 Page 2 Electromagnetism - Lecture 10 Magnetic Materials Magnetization Vector M Magnetic Field Vectors B and H Magnetic Susceptibility & Relative Permeability Diamagnetism Paramagnetism Eects of Magnetic Materials 1 Introduction to Magnetic Materials There are three main types of magnetic materials with dierent magnetic susceptibilities, M : Diamagnetic - magnetization is opposite to external B M is small and negative. Paramagnetic - magnetization is parallel to external B M is small and positive. Ferromagnetic - magnetization is very large and non-linear. M is large and variable. Can form permanent magnets in absence of external B ) In this lecture Diamagnetism & Paramagnetism Ferromagnetism will be discussed in Lecture 12 2 Page 3 Electromagnetism - Lecture 10 Magnetic Materials Magnetization Vector M Magnetic Field Vectors B and H Magnetic Susceptibility & Relative Permeability Diamagnetism Paramagnetism Eects of Magnetic Materials 1 Introduction to Magnetic Materials There are three main types of magnetic materials with dierent magnetic susceptibilities, M : Diamagnetic - magnetization is opposite to external B M is small and negative. Paramagnetic - magnetization is parallel to external B M is small and positive. Ferromagnetic - magnetization is very large and non-linear. M is large and variable. Can form permanent magnets in absence of external B ) In this lecture Diamagnetism & Paramagnetism Ferromagnetism will be discussed in Lecture 12 2 Magnetization Vector The magnetic dipole moment of an atom can be expressed as an integral over the electron orbits in the Bohr model: m = Z atom IA^ z The current and magnetic moment of the i-th electron are: I = ev i 2r i m i = IA^ z = e 2m e L i The magnetic dipole density is the magnetization vector M: M = dm d = N A e 2m e < L i > atom This orbital angular momentum average is also valid in quantum mechanics 3 Page 4 Electromagnetism - Lecture 10 Magnetic Materials Magnetization Vector M Magnetic Field Vectors B and H Magnetic Susceptibility & Relative Permeability Diamagnetism Paramagnetism Eects of Magnetic Materials 1 Introduction to Magnetic Materials There are three main types of magnetic materials with dierent magnetic susceptibilities, M : Diamagnetic - magnetization is opposite to external B M is small and negative. Paramagnetic - magnetization is parallel to external B M is small and positive. Ferromagnetic - magnetization is very large and non-linear. M is large and variable. Can form permanent magnets in absence of external B ) In this lecture Diamagnetism & Paramagnetism Ferromagnetism will be discussed in Lecture 12 2 Magnetization Vector The magnetic dipole moment of an atom can be expressed as an integral over the electron orbits in the Bohr model: m = Z atom IA^ z The current and magnetic moment of the i-th electron are: I = ev i 2r i m i = IA^ z = e 2m e L i The magnetic dipole density is the magnetization vector M: M = dm d = N A e 2m e < L i > atom This orbital angular momentum average is also valid in quantum mechanics 3 Notes: Diagrams: 4 Page 5 Electromagnetism - Lecture 10 Magnetic Materials Magnetization Vector M Magnetic Field Vectors B and H Magnetic Susceptibility & Relative Permeability Diamagnetism Paramagnetism Eects of Magnetic Materials 1 Introduction to Magnetic Materials There are three main types of magnetic materials with dierent magnetic susceptibilities, M : Diamagnetic - magnetization is opposite to external B M is small and negative. Paramagnetic - magnetization is parallel to external B M is small and positive. Ferromagnetic - magnetization is very large and non-linear. M is large and variable. Can form permanent magnets in absence of external B ) In this lecture Diamagnetism & Paramagnetism Ferromagnetism will be discussed in Lecture 12 2 Magnetization Vector The magnetic dipole moment of an atom can be expressed as an integral over the electron orbits in the Bohr model: m = Z atom IA^ z The current and magnetic moment of the i-th electron are: I = ev i 2r i m i = IA^ z = e 2m e L i The magnetic dipole density is the magnetization vector M: M = dm d = N A e 2m e < L i > atom This orbital angular momentum average is also valid in quantum mechanics 3 Notes: Diagrams: 4 Magnetization Currents The magnetization vector M has units of A/m The magnetization can be thought of as being produced by a magnetization current density J M : I L M:dl = Z A J M :dS J M =r M For a rod uniformly magnetized along its length the magnetization can be represented by a surface magnetization current owing round the rod: J S = M ^ n The distributions J M and J S represent the eect of the atomic magnetization with equivalent macroscopic current distributions 5Read More

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