Question

8. (a) Define polarization of dielectric and dielectric susceptibility of a material. Find the relation between them.

(b) Determine the electric susceptibility ($\chi_e$) at 0° for a gas whose dielectric constant ($k$) at 0° is 1.000041

(c) Distinguish between hard magnet and soft magnet on the basis of hysteresis loop.

Answer 1

(a) Refer to the detailed explanation above. (b) The electric susceptibility ($\chi_e$) is 0.000041. (c) Refer to the detailed table and explanation above.

Answer 2

The solution addresses each part of the question separately.

Solution:

(a) Definition of Polarization of Dielectric and Dielectric Susceptibility, and Relation between them:

• Polarization ($\vec{P}$): When a dielectric material is subjected to an external electric field, the constituent atoms or molecules develop induced electric dipole moments due to the displacement of charges. The polarization vector $\vec{P}$ is defined as the net electric dipole moment per unit volume of the dielectric material. Its SI unit is Coulomb per square meter (C/m²).

• Dielectric Susceptibility ($\chi_e$): For linear, isotropic dielectrics, the induced polarization $\vec{P}$ is directly proportional to the net electric field $\vec{E}$ inside the dielectric. Dielectric susceptibility ($\chi_e$) is a dimensionless constant of proportionality that quantifies how easily a dielectric material can be polarized by an external electric field.

• Relation between Polarization ($\vec{P}$) and Dielectric Susceptibility ($\chi_e$): The polarization $\vec{P}$ in a linear dielectric is given by: $\vec{P} = \chi_e \epsilon_0 \vec{E}$ where $\epsilon_0$ is the permittivity of free space and $\vec{E}$ is the net electric field inside the dielectric.

  Furthermore, the electric displacement vector $\vec{D}$ is defined as: $\vec{D} = \epsilon_0 \vec{E} + \vec{P}$ Substituting the expression for $\vec{P}$: $\vec{D} = \epsilon_0 \vec{E} + \chi_e \epsilon_0 \vec{E}$ $\vec{D} = \epsilon_0 \vec{E} (1 + \chi_e)$ We also know that for a dielectric medium, $\vec{D} = \epsilon \vec{E}$, where $\epsilon$ is the permittivity of the medium. Comparing the two expressions for $\vec{D}$: $\epsilon \vec{E} = \epsilon_0 \vec{E} (1 + \chi_e)$ $\epsilon = \epsilon_0 (1 + \chi_e)$ The dielectric constant (or relative permittivity) $k$ is defined as $k = \frac{\epsilon}{\epsilon_0}$. Therefore, the relation between the dielectric constant and dielectric susceptibility is: $k = 1 + \chi_e$ This relation also links $\chi_e$ to a measurable quantity ($k$).

(b) Determination of Electric Susceptibility ($\chi_e$):

Given: Dielectric constant ($k$) = 1.000041 We use the relation derived above: $\chi_e = k - 1$ Substituting the given value of $k$: $\chi_e = 1.000041 - 1$ $\chi_e = 0.000041$

(c) Distinction between Hard Magnet and Soft Magnet on the basis of Hysteresis Loop:

The distinction between hard and soft magnets is primarily based on the characteristics of their B-H hysteresis loop.

Feature	Hard Magnet (Permanent Magnet)	Soft Magnet (Electromagnet)
Hysteresis Loop	Characterized by a large area, indicating significant energy loss per cycle. The loop is wide and tall.	Characterized by a small area, indicating minimal energy loss per cycle. The loop is narrow and short.
Retentivity ($B_r$)	High. They retain a strong magnetic field even after the external magnetizing field is removed.	Low. They lose most of their magnetism quickly once the external field is removed.
Coercivity ($H_c$)	High. A large reverse magnetizing field is required to demagnetize them.	Low. They can be easily demagnetized by a weak reverse magnetizing field.
Applications	Used for making permanent magnets (e.g., Alnico, steel), magnetic recording media.	Used for making temporary magnets like electromagnets, transformer cores, and relay switches, where frequent magnetization and demagnetization are required.

Visual Representation (Hysteresis Loop comparison):