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Contents

Electromagnetic Theory

Vector Analysis

Cartesian Coordinate System Cylindrical Coordinate System Spherical Coordinate System Vector Addition and Subtraction Dot Product Cross Product Scalar Triple Product Gradient Divergence Curl Laplacian Operator Divergence Theorem Stokes Theorem Helmholtz Theorem

Electrostatics

Coulomb Law Electric Field Intensity Electric Field of Line Charge Electric Field of Surface Charge Electric Flux Density Gauss Law Gauss Law Applications Electric Potential Potential and Field Relationship Electric Dipole Polarization Boundary Conditions Electrostatics Capacitance Energy Stored in Electric Field Poisson and Laplace Equations

Magnetostatics

Biot-Savart Law Magnetic Field of Infinite Wire Magnetic Field of Circular Loop Ampere Circuital Law Ampere Law Applications Magnetic Flux Density Magnetic Force on Current Lorentz Force Magnetic Materials Boundary Conditions Magnetostatics Inductance Inductance Calculations Magnetic Energy

Maxwell Equations

Faraday Law of Induction Lenz Law Displacement Current Maxwell Equations Integral Form Maxwell Equations Differential Form Maxwell Equations in Phasor Form Boundary Conditions General

Wave Propagation

Wave Equation Derivation Uniform Plane Wave Phase Velocity and Wavelength Intrinsic Impedance Poynting Vector and Power Flow Wave Propagation in Lossy Media Skin Effect Linear Polarization Circular Polarization Elliptical Polarization Reflection at Normal Incidence Reflection at Oblique Incidence Total Internal Reflection

Transmission Lines

Transmission Line Parameters Transmission Line Equations Characteristic Impedance Reflection Coefficient VSWR Input Impedance of TL Lossless Transmission Line Quarter Wave Transformer Smith Chart Basics Smith Chart Applications Single Stub Matching Double Stub Matching

Antennas

Antenna Fundamentals Radiation Pattern Antenna Parameters Hertzian Dipole Half Wave Dipole Quarter Wave Monopole Antenna Arrays Friis Transmission Equation Yagi-Uda Antenna Parabolic Reflector Antenna

Other Topics

Other Subjects

Analog Electronics Digital Electronics Signals & Systems Control Systems Digital Communication Analog Communication Network Analysis Microprocessors VLSI Design Verilog HDL Power Electronics Embedded Systems DSP Electronic Devices

Section Progress8%

1 of 13 articles

Wave Equation Derivation

From Maxwell equations, second order wave equation.

Updated: 19 March 2026

7 min read

#Electromagnetics

Wave Equation Mechanics

Derive and understand the electromagnetic wave equations.

Question 1 of 3

Q1.Which vector identity is strictly required to derive the second-order wave equation from Maxwell's first-order curl equations?

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Wave Propagation in Lossy Media

Attenuation constant alpha, skin depth.

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Linear Polarization

E-field in single plane, horizontal and vertical.

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Reflection at Oblique Incidence

Snell law, Fresnel equations, Brewster angle.

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Circular Polarization

Equal amplitude, 90 degree phase, RHCP and LHCP.

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Total Internal Reflection

Critical angle, evanescent wave, fiber optics.

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Boundary Conditions General

Uniform Plane Wave