Name: Electric Energy Density
Uploaded: 2019-07-19
Duration: 4 min 11 s
Description: There is an energy associated with the electrostatic field. The expression of this electric field energy density is derived using the energy stored in a para...

Question

Explain why the polarization of a dielectric reduces the electric field inside the dielectric. Hence define dielectric constant.

Accepted Answer

Considered a rectangular dielectric slab placed in a uniform electric field $E_{0}$ acting parallel to two of its faces as shown in fig. its molecular dipoles align themselves in the direction of $E$ . This results in uniform polarization of the dielectric, i.e., every small volume of the slab has a dipole moment in the direction of $E_{0}$ . The positive charges of the dipoles of first vertical column cancel the negative charges of the dipoles of second column and so on. Thus, the volume charge density in the interior of the slab is zero. However, there is a net uncancelled negative charge on the left face and uncancelled positive charge on the right face of the slab. The uncancelled charges are the induced surface charges due to the external field $E$ . Since the slab as a whole remains electrically neutral, the magnitude of the positive induced surface charge is equal to that of the negative induced surface charge. Thus, the polarized dielectric is equivalent to two charged surfaces with induced surface charge densities $\pm σ_{p}$

In case of a homogeneous and isotropic dielectric, the induced surface charges set up electric, field ${\vec{E}}_{p}$ (field due to polarization) inside the dielectric in a direction opposite to that of the external field ${\vec{E}}_{0}$ , thus tending to reduce the original field in the dielectric. The resultant field $\vec{E}$ in the dielectric will be equal to ${\vec{E}}_{0} - {\vec{E}}_{p}$ and directed in the direction of ${\vec{E}}_{0}$ .

The ratio of the original field ${\vec{E}}_{0}$ and the reduced field ${\vec{E}}_{0} - {\vec{E}}_{p}$ in the dielectric is called dielectric constant $(k)$ .

Thus

$k = \frac{{\vec{E}}_{0}}{\vec{E}} = \frac{{\vec{E}}_{0}}{{\vec{E}}_{0} - {\vec{E}}_{p}}$

Explain why the polarization of a dielectric reduces the electric field inside the dielectric. Hence define dielectric constant.

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