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Course overview
This course covers electromagnetic theory from vector calculus foundations through to wave propagation in unbounded and bounded media. The progression is: coordinate systems and vector operators, electrostatics with Gauss's law and potential, magnetostatics with Ampere's law, time-varying fields and Maxwell's equations, and finally plane wave propagation and transmission lines. Students who complete the course can apply Gauss's law and Ampere's law to symmetric configurations, compute electric and magnetic potentials, derive and apply the wave equation, and analyze transmission line behavior using the telegrapher equations.
Details
Target audience: Third-year B.Tech ECE students taking Electromagnetic Theory or Fields and Waves, and GATE aspirants covering the Electromagnetics section.
Duration: 13 to 16 hours across 5 modules
Prerequisites
- Vector algebra and dot and cross products
- Calculus: partial derivatives and multiple integrals
- Basic physics: Coulomb's law and magnetic force concepts
Learning outcomes
- Express vector fields in Cartesian, cylindrical, and spherical coordinates and compute gradient, divergence, and curl
- Apply Gauss's law to find electric fields for charge distributions with planar, cylindrical, or spherical symmetry
- Use Ampere's law to compute magnetic fields for infinite wires, solenoids, and toroids
- State Maxwell's four equations in both integral and differential form and explain the physical meaning of each
- Derive the wave equation from Maxwell's equations and compute phase velocity, attenuation, and skin depth for a given medium
- Analyze transmission lines using the telegrapher equations and calculate reflection coefficient and VSWR
Modules
- Cartesian, cylindrical, and spherical coordinate systems
- Gradient, divergence, and curl operators
- Divergence theorem and Stokes' theorem
- Line integrals and surface integrals
- Helmholtz theorem and vector field decomposition
- Coulomb's law and electric field due to charge distributions
- Gauss's law in integral and differential form
- Electric potential and relationship to field
- Laplace and Poisson equations
- Boundary conditions at dielectric interfaces
- Biot-Savart law and magnetic field calculations
- Ampere's law and applications to symmetric configurations
- Magnetic vector potential
- Magnetic boundary conditions at material interfaces
- Inductance calculation for coils and toroids
- Faraday's law and displacement current
- Maxwell's equations in differential and integral form
- Poynting theorem and energy flow
- Wave equation derivation from Maxwell's equations
- Time-harmonic fields and phasor representation
- Uniform plane wave propagation in lossless and lossy media
- Reflection and transmission at normal incidence
- Skin depth and surface impedance
- Transmission line equations and characteristic impedance
- Standing wave ratio and impedance matching