Difference between revisions of "Lecture 1."

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Basic Principle of Electromagnetic Theory

Electromagnetic theory forms the foundation of different physical fields and phenomenon. It is used to explain many wave phenomena like propagation, reflection, refraction, diffraction and scattering. In the following, we shall review the fundamental aspects of the electromagnetic theory.

Maxwell's Equations

The physics of electromagnetic field is described mathematically by the Maxwell's equations. These equations can be written in differential as well as integral forms. For time-varying electromagnetic fields, the Maxwell's equations are as follows.

Differential Form

[math]\nabla\times\vec{E}(\vec{r},t)=-\frac{\partial \vec{B}(\vec{r},t)}{\partial t}[/math]	Faraday's Law;
[math]\nabla\times\vec{H}(\vec{r},t)=\vec{J}(\vec{r},t)+\frac{\partial D(\vec{r},t)}{\partial t}[/math]	Ampere's Law
[math]\nabla\cdot\vec{D}(\vec{r},t)=\rho(\vec{r},t)[/math]	Gauss's Law, electric
[math]\nabla\cdot\vec{B}(\vec{r},t)=0[/math]	Gauss's Law, magnetic

where:

[math]\vec{E}(\vec{r},t)[/math] is electric field intensity in [V/m];

[math]\vec{H}(\vec{r},t)[/math] is magnetic field intensity in [A/m];

[math]\vec{D}(\vec{r},t)[/math] is electric flux density in [C/m[math]^2[/math]];

[math]\vec{B}(\vec{r},t)[/math] is magnetic flux density in [Wb/m[math]^2[/math]];

[math]\vec{J}(\vec{r},t)[/math] is electric current density in [A/m[math]^2[/math]];

[math]\rho(\vec{r},t)[/math] is electric charge density in [C/m[math]^3[/math]].

Constitutive Relations

Interface and Boundary Conditions

Electromagnetics Models - Static Fields

Static Magnetic Field

Electrostatic Field

References