Electromagnetism II Cristina Lazzeroni c.lazzeroni@bham.ac.uk Lecture 5
Maxwell s equations for free space They apply simultaneously at any given point in free space. How do they change in presence of material?
Lecture 4: Atomic/molecular dipoles Macroscopic polarization P Equivalent charge/current Re-expression of M1 in dielectrics: electric displacement D LIH: Relative permittivity Electric susceptibility
Lecture 5: Magnetism (I) Atomic / molecular magnetic dipoles Macroscopic magnetization M Types of magnetism and their microscopic origin: diamagnetism paramagnetism ferromagnetism
Why useful? Transformers Motors Generators Iron cores Magnetic recording tapes Computer disks All depend directly on magnetic properties of materials
Magnetism Magnetism is linked to the behaviour of electrons in materials: moving charges, orbital motion and intrinsic spin. Net magnetic moment of atom is obtained by combining orbital and spin moments of all the electrons, taking into account their direction. Why isn t everything magnetic? In a sense, everything is magnetic! But material only exhibit familiar magnetic effects when: - atoms contain unpaired electrons and - large scale alignment of the dipole moments occur
Orbital motion
Spin :
Magnetic and electric dipoles :
Paramagnetism : Atoms of a paramagnetic material have permanent magnetic dipoles. These dipoles are randomly oriented - magnetic fields average to zero. In external field B 0, dipoles tends to align with B 0. Result in an additional magnetic field B m N atoms, maximum dipole moment = µn Thermal collisions randomize dipole orientation and reduce total dipole moment.
Paramagnetism : Relative permeability = ratio between field in material and applied field. If material doesn t respond to B 0, k m =1 Magnetic moment per unit volume M (magnetization):
LIH material Linear : M is proportional to B Isotropic : M is in the same direction as B Homogeneous : same throughout the material Magnetic susceptibility Magnetic susceptibility: small, dimensionless number; value depends on temperature, pressure. Paramagnetic: B > B 0, k m > 1, χ B > 0 Example: for Oxygen (atmospheric pressure, 20 o C)
Paramagnetism : very temperature dependent
Diamagnetism : k m <1 Glass k m = 1-1.5 x10-5 Water χ B / 10-6 = - 9.0 Superconductors are an exception χ B = -1
Ferromagnetism : Materials with atoms having unpaired electron spins. Electron spins become coupled to form a domain (~10 10 atoms, scale of 10-7 m) Large electromagnetic moment When domains are randomly arranged, material as a whole is un-magnetised
Ferromagnetism : Domains which are magnetized in the direction of an applied external field grow at the expenses of those which are not aligned to the magnetic field k m becomes very large: ~10 3-10 5
Ferromagnetism : Magnetization curve: M versus B 0
Ferromagnetism : Hysteresis loop: B M versus B 0
Ferromagnetism :
Ferromagnetism : Magnetization is different when the external field is increasing from when it is decreasing: hysteresis Cause: reorientations of domain directions are not totally reversible Use: magnetic storage of information
Review : Materials can be grouped into para-, dia-, and ferro-magnetic Diamagnetics: atoms don t have intrinsic magnetic dipole moment. A dipole moment may be induced by an external field, its direction being opposite to that of the field (Lenz s law). χ B is negative and usually small. Paramagnetics: atoms have a magnetic dipole moment due to unpaired electrons. Intrinsic magnetic dipole moments tend to line up with external magnetic field thus enhancing (slightly) the field. This tendency is interfered by thermal agitation which randomizes the alignment. χ B is positive and small and very temperature dependent.
Review : Ferromagnetics: quantum interaction between neighbouring atoms locks atomic dipoles in rigid parallelism despite disordering tendency of thermal agitation (magnetic domains). Due to alignment of spin magnetic moments of electrons (quantum effect). M is no longer proportional to B. Hence χ B not well defined, but generally positive and large. Hysteresis: ferromagnetic magnetization curves do not retrace themselves. Some alignment of dipoles remain even when the external field if removed. Familiar permanent magnets.
Summary : Effect χ B k m Origin
Recommended readings: Grant+Phillips: 4.3, 5.1, 5.2 Next Lecture: Magnetism (II) Maxwell s equations for magnetic materials