Question

Define the term polarization of a dielectric and write the expression for a linear isotropic dielectric in terms of electric field.

Answer 1

Hint: Dielectric means the insulating material. Dielectric polarization is the term used to describe or explain behaviour of material when an external field is applied on it. Obtain the expression for volume charge density. Express the electric field in terms of the volume charge density.

Complete step by step answer:
Polarization of dielectric is defined as a dipole moment formed in an insulating material due to an externally applied electric field.
In this process, a current interacts with a dielectric (insulating) material, the dielectric material will respond with a shift in charge distribution with positive charges aligned with the electric field and negative charges aligning against it.
In linear isotropic dielectric, polarization of dielectric is parallel to the applied electric field or we can say that polarization is directly dependent on the electric field.
Expression for linear isotropic dielectric in terms of electric field:
Let, $\rho $ be the volume charge density. We can write it with free charges as well as bound charges as follows,
$\rho =\text{ }{{\rho }_{f}}+\text{ }{{\rho }_{b}}\text{ }\to \text{ 1}$
where, ${{\rho }_{f}}$ is volume charge density in case of free charges and ${{\rho }_{b~}}$ is volume charge density in case of bound charges.
equation (1) can be rewritten as function of polarization,
$\rho ={{\rho }_{f}}+\Delta \rho $ …..(2)
Since, electric field is ratio of volume charge density to the permittivity of medium,
$\Delta E=\dfrac{\rho }{{{\varepsilon }_{0}}}$
ε is the permittivity of the medium.
But from equation (2), we can write,
$\Delta E=\dfrac{{{\rho }_{f}}-\Delta \rho }{{{\varepsilon }_{0}}}$
is a required expression for a linear isotropic dielectric in terms of electric field.

Note:
For dielectric polarizations always remember that the total volume density includes both free and bound charge volume density. By taking advantage of the above dielectric polarization response, important circuit elements such as capacitors can be made.