# Electromagnetic Field Theory & Transmission Lines Syllabus

Periods/week : 3 Periods & 1 Tut /week. Ses. : 30 Exam : 70

Examination (Practical): 3hrs. Credits: 4

**Electrostatics**

Introduction, Applications of electrostatic fields, Different types of charge distributions, Coulomb’s law, Applications of coulomb’s law, Limitation of coulomb’s law, Electric field strength due to point charge, Salient features of electric intensity, Electric field due to line charge density, Electric field strength due to an infinite line charge, Field due to surface charge density, Field due to volume charge density, Potential, Potential at a point, Potential difference, Salient features of potential difference, Potential gradient, Salient features of potential gradient, Equipotential surface, Potential due to electric dipole, Electric field due to dipole, Electric flux, Salient features of electric flux, Faradays experiment to define flux, Electric flux density, Salient features of electric flux density, Gauss’s law and applications, Proof of Gauss’s law, Gauss’s law in point form, Divergence of a vector, Applications of Gauss’s law, Limitations of Gauss’s law, Salient features of Gauss’s law, Poisson’s and Laplace’s equations, Applications of Poisson’s and Laplace’s equations, Uniqueness theorem, Boundary conditions on E and D, Proof of boundary conditions, Conductors in electric field, Properties of conductors, Electric current, Current densities, Equation of continuity, Relaxation time, Relation between current density and volume charge density, Dielectric materials in electric field, Properties of dielectric materials, Dipole movement, Polarization, Capacitance of different configurations, Energy stored in an electric field, Energy in a capacitor.

**Steady Magnetic Fields**

Introduction, Applications of magnetic fields, Fundamentals of steady magnetic fields, Faradays law of induction, Magnetic flux density, Ampere’s law of current, Element or Biot-Savart law, Field due to infinitely long current element, Field due to a finite current element, Ampere’s work law or Ampere’s circuit law, Differential form of Ampere’s circuit law, Stock’s theorem, Force on a moving charge due to electric and magnetic charge, Applications of Lorentz force equation, Force on a current element in a magnetic field, Ampere’s force law, Boundary conditions on H and B, Scalar magnetic potentials, Vector magnetic potentials, Force and torque on a loop or coil, Materials in magnetic fields, Magnetization in materials, Inductance, Standard inductance configurations, Energy density in a magnetic field, Energy stored in inductor, Expression for inductance, L in terms of fundamental parameters, Mutual inductance, Comparison between electric and magnetic fields / circuits / parameters.

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**Maxwell’s Equations**

Introduction, Equation of continuity for the varying fields, Maxwell’s equations for time varying fields, Meaning of Maxwell’s equations, Conversion of differential form of Maxwell’s equations to integral form, Maxwell’s equations for static fields, Characteristics of free space, Maxwell’s equations for free space, The Maxwell’s equations for static fields in free space, Proof of Maxwell’s equations, Sinusoidal time varying fields, Maxwell’s equations in phasor form, Influence of medium on the fields, Types of media, Summary of Maxwell’s equations for different cases, Boundary conditions, Proof of boundary conditions on E, D, H and B, Complete boundary conditions in scalar form, Boundary conditions in vector form, Time varying potentials, Retarded potentials, Maxwell’s equations approach to relate potentials, Fields and their sources, Helmoltz theorem, Lorentz gauge condition.

**Electromagnetic Waves**

Introduction, Applications of EM waves, Wave equations in free space, Wave equations for a conducting medium, Uniform plane equation, General solutions of uniform plane wave equations, Relation between E and H in a uniform plane wave, Proof of E and H wave are perpendicular to each other, Wave equations in phasor form, Wave propagation in a lossless medium, Propagation characteristics of EM waves in free space, Propagation characteristics of EM waves in a conducting medium, Summary of propagation, Characteristics of EM waves in conducting medium, Conductors and dielectrics, Wave propagation characteristics in good dielectrics, Summary of the propagation characteristics in good dielectrics, Wave propagation characteristics in good conductors, Summary of characteristics of wave propagation in good conductors, Depth of penetration, Polarization of a wave, Sources of different polarized EM waves, Direct cosines of vector field, Waves on a perfect conductor – Normal incidence, Waves on dielectric –Normal incidence, Oblique incidence of a plane wave on a boundary plane, Oblique incidence of a wave on perfect conductor, Oblique incidence of a plane wave on dielectric, Brewster angle, Total internal reflection, Surface impedance, Poynting vector and flow of power, Complex poynting vector.

**Guided Waves**

Induction, Waves between parallel plates, Derivation of field equations between parallel plates and propagation parameters, Field components for TE waves ( ), Field components of TM waves (), Propagation parameters of TE and TM waves, Guide wavelength, Transverse electromagnetic waves (TEM wave), Velocities of propagation, Attenuation in parallel plane guides, Wave impedances, Waves in rectangular waveguides, Derivation of field equations in rectangular hallow waveguides, Propagation parameters of TE and TM waves in rectangular waveguides, TEM does not exist in waveguides, Excitation methods for different TM and TM modes, Evanescent wave or mode, Wave impedance in waveguide, Power transmitted in a lossless waveguide, Waveguide resonators, Salient features of cavity resonators, Circular waveguides, Salient features of circular waveguides.

**Transmission Lines**

Types of transmission lines, Applications of transmission lines, Equivalent circuit of pair of transmission lines, Primary constants, Transmission line equations, Secondary constants, lossless transmission lines, Distortionless line, Phase and group velocities, Loading of lines, Input impedance of transmission lines, RF lines, Relation between reflection coefficient, Load and characteristic impedance, Relation between reflection coefficient and voltage standing wave ratio (VSWR), Lines of different lengths – lines, Losses in transmission lines, Smith chart and applications, Stubs, Double stubs.

**Textbook**

- Electromagnetic Field Theory and Transmission Lines, G.S.N. Raju, Pearson Education (Singapore) Pvt., Ltd., New Delhi, 2005.

**References:**

- Engineering Electromagnetics, W. H. Hayt Jr., McGraw Hill – New York.
- EM Waves and Radiating Systems, E. C. Jordan, PHI, 1997.
- Electromagnetics with Applications, Kraus and Fleisch, McGraw Hill, 1999.
- Time Harmonic EM Fields, R. F. Harington, McGraw Hill.

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