Applied Electromagnetics

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 x Q.- 1.2.4 Simple triple product (P. Q)R.- 1.2.5 Scalar triple product P. (Q x R).- 1.2.6 Vector triple product P x (Q x 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 Ampere'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 Ampere'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 Ampere'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 ?/?? < 0 ? 1.- 7 5.2 Good conductor, poor dielectric ?/?? > 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.