Dielectric Polarization, Semiconductors, and Superconductivity

Posted on Apr 2, 2026 in Physics

Explain the concept of polarisation in dielectrics. Illustrate and discuss the different types with
diagrams and formulas.The Concept of Polarisation

In a dielectric material, polarization is defined as the process of creating or inducing electric dipoles using an external electric field.

When an external electric field is applied, it interacts with the dielectric in two primary ways:

1 Distortion

The field distorts the internal charge distribution, producing an induced dipole moment in each molecule.

2 Alignment

In polar molecules, the field exerts a torque on randomly oriented permanent dipoles, causing them to align.

Polarization Vector ($\vec{P}$): It is defined as the induced dipole moment per unit volume of the dielectric.

P = N(meu) (where N is the number of molecules per unit volume, and $\mu$ is the induced dipole moment). The standard unit for Polarization is C/M2

Types of Polarization

According to your module, four main types of polarization contribute to the total molecular polarizability.

1. Electronic Polarisation;

Mechanism

When an external electric field ($E$) is applied, the electron cloud of an atom is displaced in the opposite direction to the positive nucleus. This relative shift creates an induced dipole moment.

Formula

p e = N .Alpha . E(where $\alphae$ is the electronic polarizability).

2. Ionic Polarisation ($P_i$)

Mechanism

This occurs in ionic materials (like NaCl, KBr, KCl). The applied electric field causes positive and negative ions to displace in opposite directions relative to each other, changing the typical distance between them.

Formula

P i = N .Alphai .E (where alpha_i is the ionic polarizability).

Diagram

Concept: At E=0, ions are positioned evenly in their crystal lattice. At E not equal to 0the alternating positive and negative ions are pulled in opposite directions, stretching the lattice.

3. Orientational Polarization ($P_o$) Mechanism

Found in polar materials with permanent dipole moments (like $H_2O$ and $HCl$). Normally, these dipoles are oriented randomly. Under an external field, they experience a torque and try to align parallel to the direction of the electric field.

Formula

P o = N. Alpao.E (where $\alpha_o$ is the orientational polarizability).

4. Space-Charge Polarization ($P_s$) :- Mechanism

When a dielectric is placed between two electrodes, the applied field causes charges to migrate and accumulate near the electrodes (positive charges near the negative electrode, and vice versa).

Formula

Ps=N.Alphas.E (where $\alpha_s$ is the space-charge polarizability).

Note

This is usually negligible because it primarily occurs only at the physical interfaces or near the electrodes.

Diagram Concept:

At E=0, charges are uniformly distributed. At $E \neq 0, positive and negative charges pool at opposite boundaries of the material.

Total Polarization

The sum of these individual contributions generally gives the Total Polarisation (P) of a dielectric material:

P = P_e + P_i + P_o

P = E \cdot N(\alpha_e + \alpha_i + \alpha_o)

1. Electric Polarization (P)

Electric polarization is defined as the electric dipole moment per unit volume of a dielectric material. P=Total dipole momentVolumeP = \frac{\text{Total dipole moment}}{\text{Volume}}P=VolumeTotal dipole moment​

2. Electric Susceptibility (χₑ)

Electric susceptibility is the measure of how easily a dielectric material gets polarized in the presence of an electric field.

3. Electric Dipole Moment (p)

The electric dipole moment is defined as the product of the magnitude of charge and the separation distance between the charges.

4. Magnetisation (M) Magnetisation is defined as the magnetic dipole moment per unit volume of a material

5. Magnetic Susceptibility (χₘ)

Magnetic susceptibility is the measure of how easily a material can be magnetized in the presence of a magnetic field.

M=χmHM = \chi_m HM=χm​H 6. Permeability (μ)
Permeability is the ability of a material to support the formation of a magnetic field within it.

B=μHB = \mu HB=μH 7. Magnetic Induction / Magnetic Flux Density (B)
Magnetic induction (or flux density) is the amount of magnetic flux passing per unit area perpendicular to the field.

8. Magnetic Field Intensity / Magnetic Field Strength (H)

Magnetic field intensity is the external magnetic field applied to a material, which produces magnetization in it.

1. Magnetostriction Method: It is used to produce ultrasonic waves

Magnetostriction Effect:

When an alternating magnetic field is applied parallel to a ferromagnetic rod, like iron, nickel,l et,c. It
experiences contraction and expansion at the same frequency as the applied magnetic field. This Effect is known as “Magnetostriction Effect”. – Materials that are used to produce ultrasonic waves are known as magnetostrictive materials.

Construction

–

There is a short nickel rod which is clamped at the centre. This rod is permanently magnetised in the beginning by passing a direct current through the coil, which is wrapped around the rod.

–

Coils, L1 and L2 coils, wound on both ends of the rod. The coil L1 is connected tothe collectorr output of the transistor, and the coil L2 is connected to the base of the transistor as shown in fig. To the coil L,1 a variable capacitor C1 is connected in parallel, el and this forms the
tank or resonant circuit.

Working

– when the battery is switched on, the resonant circuit L1C1 sets up an alternating current of frequency. – As a result, the rod gets magnetised by the plate current. Any change in the plate current brings about a change in the magnetisation and consequently a change in the length of the rod. This gives rise to a change in flux in coil L2, thereby inducing an emf in coil L2. This varying emf thereby mmaintainsthe oscillations. By varying capacitor C1, the frequency of oscillation of the tank circuit gets varied. If the frequency of the tank circuit matches the natural frequency of the material, then due to the resonance, the rod vibrates aand producesultrasonic waves at the ends of the rod. – The vibrational frequency of the material of length l, density ρ and elastic constant E of the rod is When the frequency of the circuit becomes equal to the frequency of the rod, resonance occurs, and the sound waves of maximum amplitude are generated.

Merits

– very simple oscillator, and production cost is low. – At low Ultrasonic frequency, large o/p power is possible – frequency ranging from 100 Hz to 3000KHz can be produced

Demerits

– can not generateultrasonic wavese of frequency above 300kHzHz. – The Frequency of oscillations depends greatly on temperature. – There will be losses of energy due to hysteresis and eddy current.

2. Piezo-electric Method:

Piezoelectric effect:

When pressure is applied to one pair of opposite faces of crystals like Quartz, tourmaline, rochelle salt, etc., cut with their faces perpendicular to their optic axis, equal and opposite charges appear across their other faces, as shown in fig. This is known as the piezoelectric effect.

Inverse piezoelectric effect:

If an alternating voltage is applied to one pair of opposite faces of the crystal, alternatively, mechanical contractions and expansions are produced in the crystal,l and the crystal starts vibrating. This effect is known athe s inverse piezoelectric effect or the electrostriction effect. – When the frequency of the applied alternating voltage is equal to the vibrating frequency of the crystal, then the crystal will produce ultrasonic waves.

The experimental arrangement is shown in fig. Quartz crystal Q is placed between two metal plates A and B, connected to the coil L3. The coils L1, L2 and L3ares connected to the triode valve. Coil L1 is connected in parallel with variable capacitor C1, forming the tank circuit. The high-tension battery is
connected between the free end of L2 and the cathode of the triode.

Working

– When a high tension battery is switched on, the oscillator produces a high frequency alternating voltage given by – The frequency of oscillation can be controlled by the variable capacitor C1. – Due to the transformer action, an emf is induced in the secondary coil L3. These EMFs are impressed on the plates A and B, which will excite the quartz crystal into vibrations. By adjusting the variable capacitor C1, frequency can be achieved in resonant conditions andthe crystal will produce ultrasonic waves. The frequency of vibrations is where E is Young’s modulus, ρ is the density of the material, and l is the length.

Merits

– More efficient – frequency can be achieved up to 5 x 108 Hz – o/p of this oscillator is very high. – not affected by temperature and humidity

Demerits

– cost is high, and crystal’s cutting and shaping are very complex.

TYPES OF SEMICONDUCTOR

n-type 

Semiconductors

The n-type semiconductors are the ones in which the electron conduction (negative) exceeds the hole conduction (positive). In such semiconductors, the donor impurity predominates. This can be understood if we introduce a small amount of phosphorous (P) or arsenic (As), i.E., an element of fifth group of the periodic table, as an impurity into a crystal of silicon (Si) or germanium (Ge). This addition of P or As means replacing an atom of Si or Ge at a lattice site by an atom of the impurity. Atoms of fifth group elements have five valence electrons whereas Si or Ge has four valence electrons. So four electrons of P or As form covalent bonds with the electrons of the atoms of Si or Ge. However, the fifth electron remains only very weakly bound to the P or As atom by electrostatic forces and this cannot be accommodated in the already filled original valence band. So, it occupies a discrete energy level which is just below the conduction band (with only a few tenths of an eV). Hence these extra electrons jump easily into the conduction band and contribute to the electric conductivity in addition to the electron hole pairs produced by thermal excitation of the pure semiconductor. This way the number of electrons sits more than holes to serve as charge carriers.

P-type Semiconductors

The p-type semiconductors are the one in which the hole conduction (positive) exceeds the electron conduction (negative). In such semiconductors, the acceptor impurity predominates. This can be understood if we introduce a small amount of Al, Ga or In, i.E., an element of third group of the periodic table, as a impurity into a crystal of silicon (Si) or germanium (Ge). Atoms of third group elements have three valence electrons whereas Si or Ge has four valence electrons. So three electrons of Al or Ga form covalent bonds with the electrons of the atoms of Si or Ge. However, the fourth available electron of the semiconductor lacks an electron with which it can form a bond. This is equivalent to as if a vacancy or hole has been created at the site of the impurity atom. Hence, the impurity atoms introduce vacant discrete energy levels very near the top of completely filled valence band of Si orGe. So these extra holes move from an impurity atom. These holes behave as positive charge carriers and are available in excess. Since the crystals of this type have an excess of positive charge carriers, They are called positive semiconductors or p-type semiconductors.

Critical Phenomena in Superconductors

The superconducting state of a material is not permanent; it only exists within certain limits of temperature, magnetic field, and current density.

1. Critical Temperature ($T_c$)

Definition:

The specific temperature below which a material becomes a superconductor and above which it behaves as a normal conductor is called the Critical Temperature or Transition Temperature (T_c).

Characteristics:

At this temperature, the electrical resistance of the material abruptly drops to zero.

2. Critical Magnetic Field (H_c)

Definition:

The minimum value of the external magnetic field that destroys the superconducting property of a material at a given temperature and restores its normal state is called the Critical Magnetic Field (H_c)

Characteristics:

$H_c$ is not a single value; it depends on the temperature of the material.

3. Critical Current Density (J_c)

Definition:

The maximum current per unit cross-sectional area that can flow through a superconductor without restoring its normal resistive state is called the Critical Current Density (J_c).

Characteristics:

If the current exceeds this critical limit, the magnetic field produced by the current itself will exceed the critical magnetic field (H_c) and destroy the superconductivity.
This self-generated field effect is known as Silsbee’s Rule.

Relations Between Critical Parameters

All three parameters—$T_c$, $H_c$, and $J_c$—are inter-related and define the Critical Surface for a material.

A. Relation Between Critical Magnetic Field and Temperature

The relationship between the critical magnetic field and the temperature of the superconductor is a fundamental 

The critical magnetic field is maximum at absolute zero (0 K) and decreases to zero at the critical temperature (T_c). This dependence is mathematically given by the parabolic relation:

B. The Critical Surface and Inter-dependence

The true boundaries of the superconducting state are best represented by a three-dimensional plot where the axes are the three critical parameters: Temperature ($T$), Magnetic Field ($H$), and Current Density ($J$).