Text_Template

Module 2 : Electrostatics

Lecture 11 : Conductors and Dielectric

	Constitutive Relation
	Electric displacement vector $\vec D$ helps us to calculate fields in the presence of a dielectric. This is possible only if a relationship between $\vec E$ and $\vec D$ is known.
	For a weak to moderate field strength, the electric polarization $\vec P$ is found to be directly proportional to the external electric field $\vec E$ . We define Electric Susceptibility $\chi$ through
	$\begin{displaymath}\vec P = \epsilon_0\chi\vec E\end{displaymath}$
	so that
	$\begin{eqnarray} \vec D &=& \epsilon_0\vec E + \vec P\\ &=& \epsilon_o(1+\chi)\vec E = \epsilon_0\epsilon_r\vec E = \epsilon\vec E \end{eqnarray}$
	where $\kappa\equiv \epsilon_r = 1+\chi$ is called the relative permittivity or the dielectric constant and $\epsilon$ is the permittivity of the medium. Using differential form of Gauss's law for $\vec D$ , we get
	$\begin{displaymath}\vec\nabla\cdot\vec E = \frac{1}{\epsilon}\vec\nabla\cdot\vec D = \frac{\rho_f}{\epsilon}\end{displaymath}$
	Thus the electric field produced in the medium has the same form as that in free space, except that the field strength is reduced by a factor equal to the dielectric constant $\kappa$ .