Dielectric and Magnetic Materials

Dielectric and Magnetic Materials

• Focuses on the properties and applications of dielectric and magnetic materials.

Dielectric Materials

• Electrically non-conducting (insulating) materials.
• Examples include glass, mica, rubber, ebonite, wood, and paper.
• Insulating materials in which dipoles can be produced by applying an external electric potential.
• All dielectric materials are insulators, but not all insulators are dielectric.

Significant Properties of Dielectric Materials

• Very high resistivity (10^10 to 10^16 Ω-m), resulting in very low electrical conductivity.
• A forbidden energy gap of more than 3 eV.
• Localized electrons engaged in bonding.
• A negative temperature coefficient of resistance.

Types of Dielectric Materials

• Classified into non-polar dielectrics and polar dielectrics based on molecular structure.

Non-Polar Dielectrics

• Atoms or molecules consist of positive and negative charges in equal magnitudes.
• The center of gravity of positive and negative charges coincide.
• The net dipole moment is zero.
• Electrically neutral in the normal state.
• Placed in an external electric field causes both positive and negative charges to move, resulting in polarization and induced dipole moment.
• Polarized only when placed in an electric field.
• Examples: H2, N2, O2, CO2, C6H6.

Polar Dielectrics

• The center of gravity of positive and negative charges do not coincide.
• Molecules have a permanent dipole moment.
• Molecules are oriented randomly, resulting in a net dipole moment of zero in the absence of an electric field.
• Have unsymmetrical structures.
• Placed in an external electric field orients the molecular dipoles in the direction of the field.
• Exhibit both permanent and induced dipole moments.
• Examples: H2O, N2O, NH3, HCl.

Difference between Non-Polar and Polar Dielectrics

• Non-Polar: Centers of positive and negative charges coincide; Polar: Centers do not coincide.
• Non-Polar: Zero net dipole moment in the absence of an external field; Polar: Permanent dipole moment, but net moment is zero due to random orientation.
• Non-Polar: Polarized and acquires induced dipole moment when placed in an external field; Polar: Molecules orient in the direction of the external field and exhibit both permanent and induced dipole moment.
• Non-Polar: Symmetrical structure; Polar: Unsymmetrical structure.

Electric Dipole

• A pair of two equal and opposite charges separated by a distance.

Dipole Moment

• The product of the magnitude of the charge and the distance between the two charges.
• Denoted by μ, where μ = qd (q is the charge, d is the distance).
• Vector quantity with direction from negative to positive charge.
• Unit is debye: 1 debye = 3.33 x 10^-30 coulomb-meter.
• The net dipole moment of a sample is given by μ = Σqi di.

Electric Polarization

• The process of inducing a dipole moment in a dielectric by an applied electric field.
• Occurs in both polar and non-polar dielectrics.
• Non-polar atoms or molecules subjected to an external electric field experience separation of positive and negative charge distributions.
• Polar substances exposed to an external field experience torque, causing them to orient in the direction of the field.

Polarization Vector (P)

• The induced dipole moment per unit volume of a dielectric placed in an electric field.
• P = (induced dipole moment) / (volume) = (q x l) / (A x l) = q/A
• If there are 'N' molecules per unit volume and μ is the average dipole moment per molecule, then P = Nμ = NαE, where α = polarizability.
• Units: coulomb/m².

Polarizability (α)

• The induced dipole moment is proportional to the electric field E, μ ∝ E.
• μ = αE ⇒ α = μ/E
• Constant of proportionality called the polarizability.
• The induced dipole moment per unit electric field.

Permittivity (ε)

• A quantity representing the dielectric property of a medium.
• Determines the ability of a material to get polarized easily.
• The permittivity of free space ε₀ = 8.85 x 10^-12 F/m.

Dielectric Constant (or Relative Permittivity) (εr)

• The ratio between the permittivity of a medium to the permittivity of free space.
• εr = ε / ε₀
• A dimensionless quantity with no unit.

Electric Field Intensity (E)

• Electric field intensity E at any point is mathematically equal to the force experienced by a unit positive charge placed at that point.
• E = F/q
• Unit: N/C or V/m.
• Vector quantity with direction along which a unit positive charge tends to move.

Electric Flux (Φ)

• The number of electric lines of force emanating from a charge.
• Unit: weber.

Electric Flux Density or Electric Displacement Vector (D)

• The number of electric lines of force passing normally through a surface per unit cross-sectional area.
• Proportional to the electric field intensity.
• D = εE = ε₀εrE
• "The surface charge per unit area is called electric flux density".
• Unit: C/m².
• Vector quantity.

Electric Susceptibility (χ)

• When a dielectric is placed in an electric field of strength E, polarization takes place; polarization vector is proportional to electric field strength.
• P ∝ E ⇒ P = ε₀χE
• χ = P / (ε₀E).
• Defined as the ratio between electric polarization to electric field strength.
• Has no units.

Relation between electric vectors D, E, and P

• When a dielectric material is placed between the plates of a charged capacitor, charges are induced on the surface of the dielectric.
• if q' is the induced charge on the dielectric and the electric field (E') due to these charges is in the opposite direction to the electric field (E₀) due to the charges on the capacitor plates, the resultant electric field between the plates is E = E₀ - E'.
• This leads to the relation D = ε₀E + P.

Relation between Dielectric Constant (εr) and Electric Susceptibility (χ)

• The relation is given by εr = 1 + χ

Types of Polarization Processes

• Polarization occurs due to several microscopic mechanisms.
• Four types of processes: Electronic Polarization, Ionic Polarization, Orientational Polarization, and Space-charge Polarization.

Electronic Polarization

• "The displacement of the positively charged nucleus and the (negative) electrons of an atom in opposite directions, on application of an electric field, results in electronic polarization".
• Induced dipole moment is proportional to the field strength: μ ∝ E ⇒ μ = αeE, where αe is the electronic polarizability.
• Increases with increasing volume of atoms in the dielectric material and is independent of temperature.

Ionic Polarization

• "When an electric field is applied on an ionic dielectric, then cations (positive ions) and anions (negative ions) move in opposite directions, hence dipoles will be formed. This phenomena is known as ionic polarization".
• Happens in ionic substances like NaCl and H2O.
• Not influenced by temperature.
• Given by μi ∝ E ⇒ μi = αi E, where αi is the ionic polarizability.

Orientational Polarization (or) Dipolar Polarization

• Certain substances consist of molecules with permanent dipoles even in the absence of an external field.
• Molecular dipoles align in the field direction when placed in an external field.
• The dipole moment induced depends upon the external field intensity.
• Given by μ ∝ E ⇒ μ = αo E, where αo is orientational polarizability.
• Is inversely proportional to absolute temperature of the material.
• α = μ²/3KT

Space-Charge Polarization

• Occurs due to the accumulation of charges at the electrodes or at the interfaces in a multiphase dielectric material where there is a change in resistivity between different phases.
• An unimportant factor in common dielectrics.

Total Polarization and Dependence on Temperature

• The total polarizability of a dielectric material is equal to the sum of the electronic, ionic, orientational, and space-charge polarizabilities: α = αe + αi + αo + αs.

Frequency Dependence of the Polarizability

• On applying an electric field, polarization occurs as a function of time.
• Maximum polarization is attained prolonged application of a static field and relaxation time depends on particular polarization process.
• Space charge polarization - power frequencies (50-60 Hz)

Local (or) Internal Field (or) Lorentz Field

• The total electric field which a dipole experiences in a medium, different from the externally applied field.
• Dipole moment is product of polarizability and electric field intensity
• Lorentz field is greater than the electric field applied by an amount that is directly proportional to polarization density

Clausius - Mosotti Relation

• Gives the relation between dielectric constant and polarizability of atoms in a dielectric material.
• Dipole moment is proportional to the internal field

Complex Dielectric Constant

• Denoted as ε (epsilon), describes how materials interact with electric fields, especially in the context of electromagnetic waves.
• Has both a real (ε') and imaginary (ε") part: ε = ε' - jε"
• ε' (epsilon prime): Real part, represents how much the material can store electric energy; ε" (epsilon double prime): Imaginary part, accounts for "dielectric losses".

Dielectric Loss

• The dissipation of energy through the movement of charges in an alternating electromagnetic field as polarization switches direction.
• "An efficient dielectric supports a varying charge with minimal dissipation of energy in the form of heat ("dielectric loss")

Dielectric Breakdown

• The sudden change in state of a dielectric material subjected to a very high electric field, or when a dielectric material loses its resistivity.
• It permits very large current to flow through it – this phenomenon is called dielectric breakdown

Important Requirements of a Good Dielectric Material

• Electrical, Mechanical, Thermal and Chemical requirements.

Application of Dielectric Materials

• Dielectric materials are mainly used as insulating materials.
• Commonly used in :electrical conductors, heater coils, electric irons, transformers, motor and generator windings.
• Use as energy storage capacitors