普通物理 General Physics 32 - Maxwell's Equations, Models of Magnetism 郭艷光Yen-Kuang Kuo 國立彰化師大物理系暨光電科技研究所 電子郵件: ykuo@cc.ncue.edu.tw 網頁: http://ykuo.ncue.edu.tw

普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 Outline 32-1 What Is Physics? 32-2 Gauss’ Law for Magnetic Fields 32-3 Induced Magnetic Fields 32-4 Displacement Current 32-5 Maxwell’s Equations 32-6 Magnets 32-7 Magnetism and Electrons 32-8 Magnetic Materials 32-9 Diamagnetism 32-10 Paramagnetism 32-11 Ferromagnetism 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 32-1 What Is Physics? This chapter reveals some of the breadth of physics because it ranges from the basic science of electric and magnetic fields to the applied science and engineering of magnetic materials. We conclude our basic discussion of electric and magnetic fields, finding that most of the physics principles can be summarized in only four equations, known as Maxwell’s equations. 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

32-2 Gauss’ Law for Magnetic Fields The simplest magnetic structure that can exist is a magnetic dipole. Magnetic monopoles do not exists as far as we know. Instead new pole faces appear on the newly cut faces of the pieces and the net result is that we end up with three smaller magnets, each of which is a magnetic dipole. 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

32-2 Gauss’ Law for Magnetic Fields Magnetic Flux For each element we calculate the magnetic flux through it: 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

32-2 Gauss’ Law for Magnetic Fields SI magnetic flux unit: T‧m² known as the “Weber” (Wb) For any closed surface: ФB=0. 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 6

32-3 Induced Magnetic Fields Maxwell’s law of induction : 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 Example 32-1 A parallel-plate capacitor with circular plates of radius R is being charged. (a) Derive an expression for the magnetic field at radius r for the case r ≤ R. (b) Evaluate the field magnitude B for r = R/5 = 11.0 mm and dE/dt = 1.50 × 1012 V/m · s. (c) Derive an expression for the induced magnetic field for the case r ≥ R. 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 Example 32-1 Solutions: 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 Example 32-1 Solutions: 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 Example 32-1 Solutions: 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

32-4 Displacement Current 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

32-4 Displacement Current 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

32-4 Displacement Current B O 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

32-4 Displacement Current 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 Example 32-2 The circular parallel-plate capacitor is being charged with a current i. (a) Between the plates, what is the magnitude of ,in terms of μ0 and i, at a radius r = R/5 from their center? (b) In terms of the maximum induced magnetic field, what is the magnitude of the magnetic field induced at r = R/5, inside the capacitor? 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 Example 32-2 Solutions: 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 32-5 Maxwell’s Equations Gauss’s law for E: Gauss’s law for B: Faraday’s law: Ampere’s law: 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 32-6 Magnets The magnetism of earth: The dipole axis does not coincide exactly with the rotation axis but the two axed form an angle of 11.5˚. The direction of the earth’s magnetic field at any location is described by two angles: 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 19

普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 32-6 Magnets N S Fig. b : Side view horizontal Compass needle N S Fig. a : Top view Geographic North Compass needle Field declination θ is defined as the angle between the geographic north and the horizontal component of the earth’s magnetic field. Field inclination ψ is defined as the angle between the horizontal and the earth’s magnetic field. 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 20

32-7 Magnetism and Electrons Orbital magnetic dipole moment. 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

32-7 Magnetism and Electrons Spin magnetic dipole moment: In addition to the orbital angular momentum, an electron has what is known as “intrinsic” or “spin” angular momentum. 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 22

32-7 Magnetism and Electrons Spin quantization: The quantized values of the spin angular momentum are: The constant is known as “Planck’s constant”. It is the yardstick by which we can tell whether a system is described by classical or by quantum mechanics. 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

32-7 Magnetism and Electrons 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

32-7 Magnetism and Electrons The term ms can take the values +1/2 or -1/2. The constant is known as the electron “Bohr magneton” (symbol μB). 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 32-8 Magnetic Materials Materials can be classified on the basis of their magnetic properties into three categories: Diamagnetic, paramagnetic, and ferromagnetic. SI unit for M: 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 32-9 Diamagnetism . C e Two electrons move on identical orbits radius r with angular speed ω0 When the magnetic field the magnetic moments for each orbit are antiparallel and thus the net magnetic moment . 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 32-9 Diamagnetism The negative sign indicates that are antiparallel. 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 32-9 Diamagnetism . C e Top electron: 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 32-9 Diamagnetism Bottom electron: 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 32-10 Paramagnetism When the ratio B/T is below 0.5 the magnetization M of a paramagnetic material follows Curie’s law: 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 32-10 Paramagnetism The atoms of paramagnetic materials have a net magnetic dipole moment in the absence of an external magnetic field. This moment is the vector sum of the electron magnetic moments. For very high magnetic fields and/or low temperatures, all magnetic moments are parallel to B field and the magnetization. 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 32

普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 Example 32-3 A paramagnetic gas at room temperature (T = 300 K) is placed in an external uniform magnetic field of magnitude B = 1.5 T; the atoms of the gas have magnetic dipole moment μ = 1.0μB. Calculate the mean translational kinetic energy K of an atom of the gas and the energy difference ∆UB between parallel alignment and antiparallel alignment of the atom’s magnetic dipole moment with the external field. 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 Example 32-3 Solutions: 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 32-11 Ferromagnetism Hysteresis Magnetic domains 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 32-11 Ferromagnetism Ferromagnetism is exhibited by Iron, Nickel, Cobalt, Gadolinium, Dysprosium and their alloys. 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 36

普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 Example 32-4 (a) A compass needle made of pure iron (density 7900 kg/m3) has a length L of 3.0 cm, a width of 1.0 mm, and a thickness of 0.50 mm. The magnitude of the magnetic dipole moment of an iron atom is μFe = 2.1 × 1023 J/T. If the magnetization of the needle is equivalent to the alignment of 10% of the atoms in the needle, what is the magnitude of the needle’s magnetic dipole moment ? 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 Example 32-3 (b) If the compass needle is jarred slightly from its (horizontal) north–south equilibrium position, it oscillates about that position. If the period of oscillation is 2.2 s, what is the horizontal component of the local magnetic field? 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 Example 32-4 (a) Solutions: 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 Example 32-3 (b) Solutions: 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授

普通物理講義-32/國立彰化師範大學物理系/郭艷光教授 End of chapter 32! 2018/11/16 普通物理講義-32/國立彰化師範大學物理系/郭艷光教授