Description
Electromagnetic theory has been a basic subject taught for more than a century to physics students but not to the electrical-engineering student. Before the Second World War the engineer was weil grounded in circuit theory but was notoriously weak in field theory; by and large he might have heard of Maxwell’s equations but he certainly did not use them. Since the Second World War, many fac. tors have greatly changed the engineer’s outlook; particularly the astonishing advances in electronics, in communications (particularly microwaves) and more recently in solid-state devices. Consequently, a basic course in electromagnetics and applications has been inc1uded in most first-degree courses in electrical and electronic engineering since about 1950. The many earlier excellent texts available were unsuitable for engineering courses in electromagnetics for two reasons. First, they had been written from the point of view of the physicist, being more concerned with basic principles than with applications. Second, the introduction of SI (rationalised MKS) units meant that these earlier texts needed to be revised. Consequently the new texts in this subject have been in the main written by and for electrical engineers: as examples see the books by Skilling, Cullwick, Carter, Hayt, and Lorrain and Corson. These excellent texts have been found too advanced and too lengthy for the short time allocated to electromagnetism at Nottingham, that is about fifteen lecture hours in the first year and about twenty in the second year. 1 Vector Analysis.- 1.1 Vector addition and subtraction.- 1.2 Multiplication with vectors.- 1.2.1 Simple product mP.- 1.2.2 Scalar double product P. Q.- 1.2.3 Vector double product P Q.- 1.2.4 Simple triple product (P. Q)R.- 1.2.5 Scalar triple product P. (Q R).- 1.2.6 Vector triple product P (Q R).- 1.3 Vector differentiation.- 1.3.1 Single vector.- 1.3.2 Vector sum.- 1.3.3 Dot product.- 1.3.4 Cross product.- 1.4 Fields.- 1.4.1 Scalar field S.- 1.4.2 Vector field F.- 1.5 Gradient, divergence and curl.- 1.5.1 The gradient of a scalar.- 1.5.2 The divergence of a vector.- 1.5.3 The curl of a vector.- 1.6 Double operations with del.- 1.6.1 The laplacian.- 1.7 Vector field classification.- 1.7.1 div F = 0, curl F = 0.- 1.7.2 div F ? 0, curl F = 0.- 1.7.3 div F ? 0, curl F ? 0.- 1.7.4 div F ? 0, curl F ? 0.- 1.8 Coordinate systems.- 1.9 Data sheet.- Problems.- 2 The Electric Field.- 2.1 Coulomb’s law.- 2.2 Electric field strength E.- 2.2.1 Field due to several charges Q1, Q2, Q3, etc..- 2.2.2 Field due to a line charge ?L coulombs per metre.- 2.2.3 Field due to a surface charge ?S coulombs per square metre.- 2.2.4 Field due to a volume charge ?V coulombs per cubic metre.- 2.3 Electric flux ? and electric flux density D.- 2.4 Gauss’s theorem.- 2.5 Maxwell’s first equation.- 2.6 Energy and potential.- 2.6.1 Potential difference.- 2.6.2 Potential in field of a single point charge Q.- 2.6.3 Potential due to other charge distributions.- 2.7 Conservative field.- 2 7.1 Maxwell’s second equation.- 2.8 Potential gradient.- 2.9 The potential energy of a system of point charges.- 2.10 Energy density in an electric field.- Problems.- 3 The Electric Field and Materials.- 3.1 Current.- 3.2 The continuity equation.- 3.3 Metallic conductors.- 3.4 Boundary conditions in ideal conductors.- 3.4.1 A boundary-problem example.- 3.5 Dielectrics.- 3.5.1 The electric dipole.- 3.5.2 The electric dipole in a uniform field E.- 3.5.3 Dielectric polarisation.- 3.5.4 Boundary conditions for dielectrics.- 3.5.5 Dielectric-conductor boundary; relaxation time.- 3.6 Capacitors and capacitance.- 3.6.1 Parallel-plate capacitor.- 3.6.2 Cylindrical capacitor.- 3.6.3 Pair of parallel cylinders.- Problems.- 4 The Magnetic Field.- 4.1 Laws of magnetic force.- 4.1.1 Oersted’s and Ampre’s experiments.- 4.1.2 Biot and Savart law.- 4.1.3 Surface and volume elements.- 4.1.4 Field of straight conductor.- 4.1.5 Ampre’s circuital law.- 4.1.6 Magnetic field near a current sheet.- 4.2 Maxwell’s third equation: curl H.- 4.3 Maxwell’s curl equations.- 4.4 Stokes’ theorem.- 4.4.1 Deduction of Ampre’s circuital law.- 4.4.2 div curl F = 0.- 4.4.3 Continuity equation.- 4.4.4 Example on curl F.- 4.5 Maxwell’s fourth equation: div B.- 4.6 Maxwell’s equations for steady (d.c.) fields.- 4.7 Magnetic potential.- 4.7.1 Scalar magnetic potential U.- 4.7.2 Infinite straight wire carrying steady current I.- 4.7.3 Field on axis of a circular loop of current I.- 4.8 Vector magnetic potential A.- 4.8.1 Laplacian of A; ?2A.- 4.8.2 Magnetic flux linking a circuit.- 4.9 Inductance in terms of magnetic potential.- 4.9.1 Long cylindrical conductor.- 4.9.2 Inductance of a pair of long parallel cylinders.- 4.9.3 Inductance of a pair of cylinders (alternative approach).- Problems.- 5 Magnetic Forces and Magnetic Media.- 5.1 Forces due to magnetic fields.- 5.1.1 Differential current element.- 5.1.2 Forces on a closed current-loop.- 5.1.3 Torque on a current-carrying coil.- 5.2 Forces in circuits due to own fields.- 5.2.1 Force between two parallel conductors.- 5.2.2 Force on the blade of a circuit breaker.- 5.2.3 Hoop force in a flexible circular conductor.- 5.3 Magnetic media.- 5.3.1 The atomic theory of magnetism.- 5.4 Boundary conditions for magnetic media.- 5.5 Energy storage in the magnetic field.- 5.5.1 Energy density and magnetic vector potential.- 5.6 Mechanical force on magnetic material.- 5.7 Magnetic circuit.- Problems.- 6 Fields Varying in Time.- 6.1 Faraday’s law.- 6.1.1 Faraday’s law and vector potential.- 6.2 Displacement current; Maxwell’s hypothesis.- 6.2.1 Displacement current in a flat plate capacitor.- 6.2.2 Displacement current in a concentric capacitor.- 6.3 Maxwell’s equations, final forms.- 6.4 Boundary conditions.- 6.5 Field functions.- Problems.- 7 Electromagnetic Waves.- 7.1 Wave motion.- 7.2 Free-space wave equations.- 7.2.1 Possible form of solution of the wave equation.- 7.2.2 Sinusoidal waveforms.- 7.2.3 Uniform plane wave.- 7.2.4 Plane wave with two components.- 7.3 Plane waves in homogeneous loss-free media.- 7.4 Poynting’s vector .- 7.4.1 Stored energy-density components.- 7 4.2 The Poynting vector in a power cable.- 7 4.3 Complex Poynting vector and the phasor notation.- 7.5 Plane waves in a medium having loss.- 7 5.1 Good dielectric, bad conductor ?/?? 10.- 7 5.3 Dissipation factor D.- 7.5.4 Skin effect.- 7.5.5 Flat-plate transmission line.- 7.5.6 Propagation in sea water.- 7.6 Radiation pressure.- Problems.- 8 Field Problems-Non-exact Solutions.- 8.1 Two-dimensional fields: basic principles.- 8.1.1 The condition of orthogonality.- 8.1.2 Example involving w = exp (x + jy).- 8.1.3 Construction of conjugate functions.- 8.2 Current flow in a thin conducting-sheet.- 8.3 Free-hand mapping.- 8.3.1 Example-cylinder and earthed plate.- 8.4 Field correlation with analogues.- 8.4.1 Conduction field (Teledeltos).- 8.4.2 Thermalfield.- 8.4.3 Electric field.- 8.5 Numerical methods.- 8.5.1 Finite-difference solution.- 8.5.2 Iteration process.- 8.5.3 Iteration example.- 8.5.4 Relaxation process.- 8.5.5 Relaxation example-suddenly enlarged section.- 8.5.6 Direct methods of solution.- Problems.- 9 Field Problems-Analytical Solutions.- 9.1 Kelvin’s method of images.- 9.1.1 Point charge and conducting plane.- 9.1.2 Point charge and sphere.- 9.1.3 Line charge and conducting cylinder.- 9.1.4 Line or point charge and two intersecting planes.- 9.1.5 Line current and magnetic plane.- 9.1.6 Example-conductor between two magnetic plates.- 9.2 Conformal transformation.- 9.2.1 Trial transformations.- 9.2.2 w = u + j? = z-1.- 9.2.3 w = z2/3.- 9.3 Separation of variables.- 9.3.1 Cartesian coordinates-Fourier series.- 9.3.2 Cylindrical coordinates-circular harmonics.- 9.3.3 Spherical coordinates-Legendre polynomials.- Problems.- 10 Some Low-frequency Applications.- 10.1 General observations about Maxwell’s equations.- 10.2 Maxwell’s equations applied to a transformer.- 10.2.1 The eddy-current problem in the transformer.- 10.3 Diffusion equation.- 10.4 Field produced by an element of changing flux.- 10.5 The electromagnetic pump.- 10.5.1 The conduction pump.- 10.5.2 Example on the design of a conduction pump.- 10.5.3 Some observations on the conduction pump.- 10.6 Drift and diffusion in semiconductors.- 10.7 The abrupt p-n junction.- 10.7.1 The voltage barrier.- 10.7.2 The depletion region.- 10.7.3 The junction capacitance.- Problems.- 11 High-frequency Effects.- 11.1 Phase and group velocity.- 11.2 The refractive index.- 11.3 Transmission and reflection of waves.- 11.3.1 Waves incident upon a perfect conductor.- 11.3.2 Waves incident at an angle to a perfect conductor.- 11.3.3 Reflection and refraction of uniform plane waves at a dielectric interface.- 11.3.4 Fresnel’s equations and the Brewster angle.- 11.3.5 Propagation through thin films.- 11.4 Fibre Optics.- 11.4.1 Critical angle of incidence and the evanescent wave.- 11.4.2 Propagation and losses.- 11.4.3 Dispension.- 11.4.4 Transmission losses.- 11.4.5 Example of fibre op tic loss calculations.- 11.5 Electromagnetic waves on a transmission line.- 11.6 Transverse electric waves.- 11.6.1 Formation of TE waves.- 11.6.2 TEmo waves.- Problems.- Appendix 1: The Three Main Coordinate Systems.- A1.1 Component transform matrices.- A1.2 Variable transforms.- A1.2.1 Change components and datum vectors.- A 1.2.2 Change variables x, y, z to ?, ?, z.- Appendix 2: Useful Data.- A2.1 Fundamental physical constants.- A2.2 Vector identities.- A2.3 Vector operations.- A2.3.1 Divergence.- A2.3.2 Gradient.- A2.3.3 Curl.- A2.3.4 Laplacian.- Appendix 3: Solid Angle.- A3.1 Examples of solid angles.- Appendix 4: Gaussian Elimination Program.- Solutions to Selected Problems.- References.
