⌘K

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 Progress100%

15 of 15 articles

Poisson and Laplace Equations

Del²V = -rho/epsilon and Del²V = 0, uniqueness.

Updated: 19 March 2026

10 min read

#Electromagnetics

Poisson Laplace Equations

Test your command of Poisson and Laplace equations and their applications in electrostatics.

Question 1 of 3

Q1.Poisson's equation in a charge-free region simplifies to Laplace's equation. Which of the following is the correct form of Laplace's equation?

Related Articles

Transmission Line Equations

Telegrapher equations, voltage and current waves.

6 min read

Boundary Conditions Electrostatics

Tangential E and normal D conditions at interface.

11 min read

Wave Equation Derivation

From Maxwell equations, second order wave equation.

7 min read

Electric Potential

V = -integral E dot dL, reference at infinity.

10 min read

Polarization

Dielectric polarization P, electric susceptibility.

5 min read

Energy Stored in Electric Field

Biot-Savart Law