Part 1 : Nanoparticles Module 1 : Introduction
Lecture 1 : Maxwell's equations and Time-harmonic fields
 
The set of four equations
\begin{displaymath} \begin{array}{lcrcl} {\rm Coulomb's\,law} &\,:\,& \vec{\na... ...rac{\partial {\vec{B}}}{\partial t}&\,=\,& 0,\\ \end{array} \end{displaymath}
are called Maxwell's equations. The quantity $\frac{\partial {\vec{D}}}{\partial t}$ has the dimension of ${\vec{j}}_{\rm free}$, and Maxwell called it Displacemnt current. These equations form the basis of all classical electromagnetic phenomena.
The electric displacement field ${\vec{D}}$ and the magnetic field ${\vec{H}}$ are defined by
\begin{displaymath}{\vec{D}}= \epsilon_o {\vec{E}}+{\vec{P}},\quad\quad\quad{\rm and}\quad {\vec{H}}=\frac{1}{\mu_o}{\vec{B}}-{\vec{M}},\end{displaymath}
where ${\vec{P}}\equiv$ electric polarization = average electric dipole moment per unit volume, ${\vec{M}}\equiv$ magnetization = average magnetic dipole moment per unit volume, $\epsilon_o \equiv$ the free space permittivity and $\mu_o\equiv$ the free space permeability. Note that ${\vec{P}}$-${\vec{D}}$ relationship implicitly assumes that ${\vec{P}}$ is entirely due to dipole moments, and the contributions from quadrupole and higher moments are negligible.