Engineering reference for Indian students

Circuits & fields

Electromagnetic Theory

5 self-contained study topics — notes, diagrams, formulas, and worked examples for exams and GATE.

Topics

Electrostatic Fields
Electrostatics describes the field of stationary charges through Coulomb’s law and Gauss’s law; symmetry lets Gauss’s law give the field of line, sheet and spherical charge distributions almost by inspection.
$Potential V = -\int E \cdot dl; equipotential ⊥ field lines$
Magnetostatic Fields
Magnetostatics finds the field of steady currents; Ampere’s law ∮H·dl = I_enc gives the field of symmetric geometries (long wire, solenoid, toroid), and the Lorentz force gives the force on moving charges and conductors.
$Magnetic flux \Phi = \int B \cdot dA; no magnetic monopoles$
Maxwell Equations
Maxwell’s four equations unify electricity and magnetism; the displacement-current term ∂D/∂t that Maxwell added predicts electromagnetic waves travelling at v = 1/√(με).
$Poynting vector S = E \times H$
Electromagnetic Waves
A uniform plane wave carries E and H perpendicular to each other and to the direction of travel, related by the intrinsic impedance η = √(μ/ε); in conductors the field decays over one skin depth δ.
$Reflection coefficient Γ = \frac{(\eta_{2} - \eta_{1})}{(\eta_{2} + \eta_{1})}$
Transmission Lines
A transmission line supports forward and reflected waves; its characteristic impedance Z₀ = √(L/C) and the load mismatch determine the reflection coefficient, VSWR and the input impedance seen at any distance.
$Quarter-wave transformer: Z_{in} = \frac{Z_{0}^{2}}{Z_{L}} when l = \frac{\lambda}{4}$