Notes 4 Maxwell's Equations
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Electromagnetism As Quantum Physics
Electromagnetism as Quantum Physics Charles T. Sebens California Institute of Technology May 29, 2019 arXiv v.3 The published version of this paper appears in Foundations of Physics, 49(4) (2019), 365-389. https://doi.org/10.1007/s10701-019-00253-3 Abstract One can interpret the Dirac equation either as giving the dynamics for a classical field or a quantum wave function. Here I examine whether Maxwell's equations, which are standardly interpreted as giving the dynamics for the classical electromagnetic field, can alternatively be interpreted as giving the dynamics for the photon's quantum wave function. I explain why this quantum interpretation would only be viable if the electromagnetic field were sufficiently weak, then motivate a particular approach to introducing a wave function for the photon (following Good, 1957). This wave function ultimately turns out to be unsatisfactory because the probabilities derived from it do not always transform properly under Lorentz transformations. The fact that such a quantum interpretation of Maxwell's equations is unsatisfactory suggests that the electromagnetic field is more fundamental than the photon. Contents 1 Introduction2 arXiv:1902.01930v3 [quant-ph] 29 May 2019 2 The Weber Vector5 3 The Electromagnetic Field of a Single Photon7 4 The Photon Wave Function 11 5 Lorentz Transformations 14 6 Conclusion 22 1 1 Introduction Electromagnetism was a theory ahead of its time. It held within it the seeds of special relativity. Einstein discovered the special theory of relativity by studying the laws of electromagnetism, laws which were already relativistic.1 There are hints that electromagnetism may also have held within it the seeds of quantum mechanics, though quantum mechanics was not discovered by cultivating those seeds. -
Electromagnetic Field Theory
Lecture 4 Electromagnetic Field Theory “Our thoughts and feelings have Dr. G. V. Nagesh Kumar Professor and Head, Department of EEE, electromagnetic reality. JNTUA College of Engineering Pulivendula Manifest wisely.” Topics 1. Biot Savart’s Law 2. Ampere’s Law 3. Curl 2 Releation between Electric Field and Magnetic Field On 21 April 1820, Ørsted published his discovery that a compass needle was deflected from magnetic north by a nearby electric current, confirming a direct relationship between electricity and magnetism. 3 Magnetic Field 4 Magnetic Field 5 Direction of Magnetic Field 6 Direction of Magnetic Field 7 Properties of Magnetic Field 8 Magnetic Field Intensity • The quantitative measure of strongness or weakness of the magnetic field is given by magnetic field intensity or magnetic field strength. • It is denoted as H. It is a vector quantity • The magnetic field intensity at any point in the magnetic field is defined as the force experienced by a unit north pole of one Weber strength, when placed at that point. • The magnetic field intensity is measured in • Newtons/Weber (N/Wb) or • Amperes per metre (A/m) or • Ampere-turns / metre (AT/m). 9 Magnetic Field Density 10 Releation between B and H 11 Permeability 12 Biot Savart’s Law 13 Biot Savart’s Law 14 Biot Savart’s Law : Distributed Sources 15 Problem 16 Problem 17 H due to Infinitely Long Conductor 18 H due to Finite Long Conductor 19 H due to Finite Long Conductor 20 H at Centre of Circular Cylinder 21 H at Centre of Circular Cylinder 22 H on the axis of a Circular Loop -
Electro Magnetic Fields Lecture Notes B.Tech
ELECTRO MAGNETIC FIELDS LECTURE NOTES B.TECH (II YEAR – I SEM) (2019-20) Prepared by: M.KUMARA SWAMY., Asst.Prof Department of Electrical & Electronics Engineering MALLA REDDY COLLEGE OF ENGINEERING & TECHNOLOGY (Autonomous Institution – UGC, Govt. of India) Recognized under 2(f) and 12 (B) of UGC ACT 1956 (Affiliated to JNTUH, Hyderabad, Approved by AICTE - Accredited by NBA & NAAC – ‘A’ Grade - ISO 9001:2015 Certified) Maisammaguda, Dhulapally (Post Via. Kompally), Secunderabad – 500100, Telangana State, India ELECTRO MAGNETIC FIELDS Objectives: • To introduce the concepts of electric field, magnetic field. • Applications of electric and magnetic fields in the development of the theory for power transmission lines and electrical machines. UNIT – I Electrostatics: Electrostatic Fields – Coulomb’s Law – Electric Field Intensity (EFI) – EFI due to a line and a surface charge – Work done in moving a point charge in an electrostatic field – Electric Potential – Properties of potential function – Potential gradient – Gauss’s law – Application of Gauss’s Law – Maxwell’s first law, div ( D )=ρv – Laplace’s and Poison’s equations . Electric dipole – Dipole moment – potential and EFI due to an electric dipole. UNIT – II Dielectrics & Capacitance: Behavior of conductors in an electric field – Conductors and Insulators – Electric field inside a dielectric material – polarization – Dielectric – Conductor and Dielectric – Dielectric boundary conditions – Capacitance – Capacitance of parallel plates – spherical co‐axial capacitors. Current density – conduction and Convection current densities – Ohm’s law in point form – Equation of continuity UNIT – III Magneto Statics: Static magnetic fields – Biot‐Savart’s law – Magnetic field intensity (MFI) – MFI due to a straight current carrying filament – MFI due to circular, square and solenoid current Carrying wire – Relation between magnetic flux and magnetic flux density – Maxwell’s second Equation, div(B)=0, Ampere’s Law & Applications: Ampere’s circuital law and its applications viz. -
Physics 112: Classical Electromagnetism, Fall 2013 Birefringence Notes
Physics 112: Classical Electromagnetism, Fall 2013 Birefringence Notes 1 A tensor susceptibility? The electrons bound within, and binding, the atoms of a dielectric crystal are not uniformly dis- tributed, but are restricted in their motion by the potentials which confine them. In response to an applied electric field, they may therefore move a greater or lesser distance, depending upon the strength of their confinement in the field direction. As a result, the induced polarization varies not only with the strength of the applied field, but also with its direction. The susceptibility{ and properties which depend upon it, such as the refractive index{ are therefore anisotropic, and cannot be characterized by a single value. The scalar electric susceptibility, χe, is defined to be the coefficient which relates the value of the ~ ~ local electric field, Eloc, to the local value of the polarization, P : ~ ~ P = χe0Elocal: (1) As we discussed in the last seminar we can `promote' this relation to a tensor relation with χe ! (χe)ij. In this case the dielectric constant is also a tensor and takes the form ij = [δij + (χe)ij] 0: (2) Figure 1: A cartoon showing how the electron is held by anisotropic springs{ causing an electric susceptibility which is different when the electric field is pointing in different directions. How does this happen in practice? In Fig. 1 we can see that in a crystal, for instance, the electrons will in general be held in bonds which are not spherically symmetric{ i.e., they are anisotropic. 1 Therefore, it will be easier to polarize the material in certain directions than it is in others. -
4 Lightdielectrics.Pdf
4. The interaction of light with matter The propagation of light through chemical materials is described by a wave equation similar to the one that describes light travel in a vacuum (free space). Again, using E as the electric field of light, v as the speed of light in a material and z as its direction of propagation. !2 1 ! 2E ! 2E 1 ! 2E # n2 & ! 2E # & . 2 E= 2 2 " 2 = % 2 ( 2 = 2 2 !z c !t !z $ v ' !t $% c '( !t (Read the variation in the electric field with respect distance traveled is proportional to its variation with respect to time.) The refractive index, n, (also represented η) describes how matter affects light propagation: through the electric permittivity, ε, and the magnetic permeability, µ. ! µ n = !0 µ0 These properties describe how well a medium supports (permits the transmission of) electric and magnetic fields, respectively. The terms ε0 and µ0 are reference values: the permittivity and permeability of free space. Consequently, the refractive index for a vacuum is unity. In chemical materials ε is always larger than ε0, reflecting the interaction of the electric field of the incident beam with the electrons of the material. During this interaction, the energy from the electric field is transiently stored in the medium as the electrons in the material are temporarily aligned with the field. This phenomenon is referred to as polarization, P, in the sense that the charges of the medium are temporarily separated. (This must not be confused with the polarization, which refers to the orientation or behavior of the electric field.) This stored energy is re-radiated, but the beam travel is slowed by interaction with the material. -
EM Dis Ch 5 Part 2.Pdf
1 LOGO Chapter 5 Electric Field in Material Space Part 2 iugaza2010.blogspot.com Polarization(P) in Dielectrics The application of E to the dielectric material causes the flux density to be grater than it would be in free space. D oE P P is proportional to the applied electric field E P e oE Where e is the electric susceptibility of the material - Measure of how susceptible (or sensitive) a given dielectric is to electric field. 3 D oE P oE e oE oE(1 e) oE( r) D o rE E o r r1 e o permitivity of free space permitivity of dielectric relative permitivity r 4 Dielectric constant or(relative permittivity) εr Is the ratio of the permittivity of the dielectric to that of free space. o r permitivity of dielectric relative permitivity r o permitivity of free space 5 Dielectric Strength Is the maximum electric field that a dielectric can withstand without breakdown. o r Material Dielectric Strength εr E(V/m) Water(sea) 80 7.5M Paper 7 12M Wood 2.5-8 25M Oil 2.1 12M Air 1 3M 6 A parallel plate capacitor with plate separation of 2mm has 1kV voltage applied to its plate. If the space between the plate is filled with polystyrene(εr=2.55) Find E,P V 1000 E 500 kV / m d 2103 2 P e oE o( r1)E o(1 2.55)(500k) 6.86 C / m 7 In a dielectric material Ex=5 V/m 1 2 and P (3a x a y 4a z )nc/ m 10 Find (a) electric susceptibility e (b) E (c) D 1 (3) 10 (a)P e oE e 2.517 o(5) P 1 (3a x a y 4a z ) (b)E 5a x 1.67a y 6.67a z e o 10 (2.517) o (c)D E o rE o rE o( e1)E 2 139.78a x 46.6a y 186.3a z pC/m 8 In a slab of dielectric -
Displacement Current and Ampère's Circuital Law Ivan S
ELECTRICAL ENGINEERING Displacement current and Ampère's circuital law Ivan S. Bozev, Radoslav B. Borisov The existing literature about displacement current, although it is clearly defined, there are not enough publications clarifying its nature. Usually it is assumed that the electrical current is three types: conduction current, convection current and displacement current. In the first two cases we have directed movement of electrical charges, while in the third case we have time varying electric field. Most often for the displacement current is talking in capacitors. Taking account that charge carriers (electrons and charged particles occupy the negligible space in the surrounding them space, they can be regarded only as exciters of the displacement current that current fills all space and is superposition of the currents of the individual moving charges. For this purpose in the article analyzes the current configuration of lines in space around a moving charge. An analysis of the relationship between the excited magnetic field around the charge and the displacement current is made. It is shown excited magnetic flux density and excited the displacement current are linked by Ampere’s circuital law. ъ а аа я аъ а ъя (Ива . Бв, аав Б. Бв.) В я, я , я , яя . , я : , я я. я я, я я . я . К , я ( я я , я, я я я. З я я я. я я. , я я я я . 1. Introduction configurations of the electric field of moving charge are shown on Fig. 1 and Fig. 2. First figure represents The size of electronic components constantly delayed potentials of the electric field according to shrinks and the discrete nature of the matter is Liénard–Wiechert and this picture is not symmetrical becomming more obvious. -
The Response of a Media
KTH ROYAL INSTITUTE OF TECHNOLOGY ED2210 Lecture 3: The response of a media Lecturer: Thomas Johnson Dielectric media The theory of dispersive media is derived using the formalism originally developed for dielectrics…let’s refresh our memory! • Capacitors are often filled with a dielectric. • Applying an electric field, the dielectric gets polarised • Net field in the dielectric is reduced. Dielectric media + - E - + E - + - + LECTURE 3: THE RESPONSE OF A MEDIA, ED2210 2016-01-26 2 Polarisation Electric field - Polarisation is the response of e.g. - - - • bound electrons, or + - • molecules with a dipole moment - - Emedia - In both cases the particles form dipoles. Electric field Definition: The polarisation, �, is the electric dipole moment per unit volume. Linear media: % � = � �'� where �% is the electric susceptibility LECTURE 3: THE RESPONSE OF A MEDIA, ED2210 2016-01-26 3 Magnetisation Magnetisation is due to induced dipoles, either from Induced current • induced currents B-field • quantum mechanically from the particle spin + Definition: The magnetisation, �, is the magnetic dipole Bmedia moment per unit volume. Linear media: Spin + � = � �/�' B-field Magnetic susceptibility : �+ NOTE: Both polarisation and magnetisation fields Bmedia are due to dipole fields only; not related to higher order moments like the quadropoles, octopoles etc. LECTURE 3: THE RESPONSE OF A MEDIA, ED2210 2016-01-26 4 Field calculations with dielectrics The capacitor problem includes two types of charges: • Surface charge, �0, on metal surface (monopole charges) • Induced dipole charges, �123, within the dielectric media Total electric field strength, �, is generated by �0 + �123, The polarisation, �, is generated by �123 The electric induction, �, is generated by �0, where % �: = �'� + � = � + � �'� = ��'� = �� Here � is the dielectric constant and � is the permittivity. -
Two New Experiments on Measuring the Permanent Electric
Clear evidence of charge conjugation and parity violation in K atoms from atomic permanent electric dipole moment experiments Pei-Lin You1 Xiang-You Huang 2 1. Institute of Quantum Electronics, Guangdong Ocean University, Zhanjiang Guangdong 524025, China. 2. Department of Physics , Peking University, Beijing 100871,China. Quantum mechanics thinks that atoms do not have permanent electric dipole moment (EDM) because of their spherical symmetry. Therefore, there is no polar atom in nature except for polar molecules. The electric susceptibilityχe caused by the orientation of polar substances is inversely proportional to the absolute temperature T while the induced susceptibility of atoms is temperature independent. This difference in temperature dependence offers a means of separating the polar and non-polar substances experimentally. Using special capacitor our experiments discovered that the relationship betweenχe of Potassium atom vapor and T is justχe=B/T, where the slope B≈283(k) as polar molecules, but appears to be disordered using the traditional capacitor. Its capacitance C at different voltage V was measured. The C-V curve shows that the saturation polarization of K vapor has be observed when E≥105V/m and nearly all K atoms (more than 98.9%) are lined up with the field! The ground state neutral K atom is polar atom -9 with a large EDM : dK >2.3×10 e.cm.The results gave clear evidence for CP (charge conjugation and parity) violation in K atoms. If K atom has a large EDM, why the linear Stark effect has not been observed? The article discussed the question thoroughly. Our results are easy to be repeated because the details of the experiment are described in the article. -
Quantum Mechanics Polarization Density
Quantum Mechanics_polarization density In classical electromagnetism, polarization density (or electric polarization, or simplypolarization) is the vector field that expresses the density of permanent or induced electric dipole moments in a dielectric material. When a dielectric is placed in an external Electric field, its molecules gain Electric dipole moment and the dielectric is said to be polarized. The electric dipole moment induced per unit volume of the dielectric material is called the electric polarization of the dielectric.[1][2] Polarization density also describes how a material responds to an applied electric field as well as the way the material changes the electric field, and can be used to calculate the forces that result from those interactions. It can be compared to Magnetization, which is the measure of the corresponding response of a material to a Magnetic field in Magnetism. TheSI unit of measure is coulombs per square metre, and polarization density is represented by a vectorP.[3] Definition The polarization density P is defined as the average Electric dipole moment d per unit volume V of the dielectric material:[4] which can be interpreted as a measure of how strong and how aligned the dipoles are in a region of the material. For the calculation of P due to an applied electric field, the electric susceptibility χ of the dielectric must be known (see below). Polarization density in Maxwell's equations The behavior of electric fields (E and D), magnetic fields (B, H), charge density (ρ) and current density (J) are described by Maxwell's equations in matter. The role of the polarization density P is described below. -
Active Metamaterials with Negative Static Electric Susceptibility
Active metamaterials with negative static electric susceptibility F. Castles1,2*, J. A. J. Fells3, D. Isakov1,4, S. M. Morris3, A. Watt1 and P. S. Grant1* 1 Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, UK. 2 School of Electronic Engineering and Computer Science, Queen Mary University of London, Mile End Road, London E1 4FZ, UK. 3 Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK. 4 Warwick Manufacturing Group, University of Warwick, Coventry CV4 7AL, UK. * email: [email protected]; [email protected] 1 Well-established textbook arguments suggest that static electric susceptibility must be positive in “all bodies”1. However, it has been pointed out that media that are not in thermodynamic equilibrium are not necessarily subject to this restriction; negative static electric susceptibility has been predicted theoretically in systems with inverted populations of atomic and molecular energy levels2,3, though this has never been confirmed experimentally. Here we exploit the design freedom afforded by metamaterials to fabricate active structures that exhibit the first experimental evidence of negative static electric susceptibility. Unlike the systems envisioned previously— which were expected to require reduced temperature and pressure4—negative values are readily achieved at room temperature and pressure. Further, values are readily tuneable throughout the negative range of stability − (0) , resulting in magnitudes that are over one thousand times greater than predicted previously4. This opens the door to new technological capabilities such as stable electrostatic levitation. Although static magnetic susceptibility may take positive or negative values in paramagnetic and diamagnetic materials respectively, a standard theoretical argument by Landau et al. -
Chapter 1 ELECTROMAGNETICS of METALS
Chapter 1 ELECTROMAGNETICS OF METALS While the optical properties of metals are discussed in most textbooks on condensed matter physics, for convenience this chapter summarizes the most important facts and phenomena that form the basis for a study of surface plas- mon polaritons. Starting with a cursory review of Maxwell’s equations, we describe the electromagnetic response both of idealized and real metals over a wide frequency range, and introduce the fundamental excitation of the conduc- tion electron sea in bulk metals: volume plasmons. The chapter closes with a discussion of the electromagnetic energy density in dispersive media. 1.1 Maxwell’s Equations and Electromagnetic Wave Propagation The interaction of metals with electromagnetic fields can be firmly under- stood in a classical framework based on Maxwell’s equations. Even metallic nanostructures down to sizes on the order of a few nanometres can be described without a need to resort to quantum mechanics, since the high density of free carriers results in minute spacings of the electron energy levels compared to thermal excitations of energy kBT at room temperature. The optics of met- als described in this book thus falls within the realms of the classical theory. However, this does not prevent a rich and often unexpected variety of optical phenomena from occurring, due to the strong dependence of the optical prop- erties on frequency. As is well known from everyday experience, for frequencies up to the vis- ible part of the spectrum metals are highly reflective and do not allow elec- tromagnetic waves to propagate through them. Metals are thus traditionally employed as cladding layers for the construction of waveguides and resonators for electromagnetic radiation at microwave and far-infrared frequencies.