Engineering Physics-II

Engineering physics refers to the study of the combined disciplines of physics, mathematics and combined with engineering studies in computer, electrical, materials or mechanical engineering.

Unit I: Crystal Structures & X-Ray Diffraction


Space Lattice

The Basis & Crystal Structure

Unit Cells & Lattice Parameters

Primitive Cell; A kind of Unit Cell

Wigner-Seitz Cell

Seven Crystal Systems & Fourteen Bravais Lattices

Solved Numerical Examples

Space Lattices of Cubic System

Coordination Number & Atom Positions in Cubic Unit Cells

Atomic Radius

Packing Factor or Atomic Packing Density

Hexagonal Closed Packed Structure (hcp)

Calculation of c/a Ratio for HCP Structure

Calculation of Atomic Packing Factor (APF) for HCP Structure

Solved Numerical Examples

Some Important Crystal Structure

(i) Structure of Cesium Chloride (C ClS )

(ii) Crystal Structure of Sodium Chloride (NaCl) or Rock Salt

Solved Numerical Examples

(iii) Crystal Structure of Diamond

(iv) Cubic Zinc Sulphide (ZnS) or Zinc Blende

Solved Numerical Example

Unit Cell & Lattice Constant of a Space Lattice

Solved Numerical Example

Lattice Planes in a Crystal

Miller Indices (Position & Orientation of Lattice Planes)

Direction Indices

Important Features of Miller Indices of Crystal Planes

Sketching of Important Planes & their Directions in a Cubic Crystal

Solved Numerical Examples

Relation between Interplanar Distance & Cube Edge (Interplanar Spacing)

Density of Lattice Points in Lattice Plane

Solved Numerical Examples

Reciprocal Lattice

Reciprocal Lattice Vector

Relation Between Direct ( a b c→ → →Properties of Reciprocal Lattice)

Reciprocal Lattice to Simple Cubic (sc) Lattice

Reciprocal Lattice to the Body Centered Cubic (bcc) Lattice

Reciprocal Lattice to the Face Centered Cubic (fcc) Lattice

Solved Numerical Examples

X-Ray Diffraction


Diffraction of X-Rays by Crystal Planes

Laue's Crystal Diffraction of X-Rays

Laue's Method for the Study of Crystal Structure

Bragg's Law

Bragg's Spectrometer & Experimental Determination of Wavelength of X-Rays

Bragg's Law & Study of Crystal Structure

Solved Numerical Examples

Practical Applications of X-Rays


Unit II: Dielectric & Magnetic Properties of Materials

Section A: Dielectric Properties


Dielectric Constant

Measurement of Dielectric Constant

Polarization of Dielectric Materials

Electric Displacement Vector, D

Behaviour of a Dielectric Slab in an Electric Field

Relation between P&K

Dielectric Strength

Types of Polarization (or Types of Polarizability)

Total Polarization or Polarizability

Langevin - Debye Theory of Orientational Polarizability & Total Polarizability of Polar Dielectrics

Measurement of Polarization

Solved Numerical Examples

Clausius-Mossotti Equation

Debye Equation

Internal Fields in Liquids & Solids (One-Dimensional)

Evaluation of Local Field for Cubic Structure

Relation between Dielectric Constant & Refractive Index (Lorentz - Lorentz Formula)

Solved Numerical Examples

Frequency Dependence of the Dielectric Constant or Dielectrics in Alternating Fields

Dielectric Losses

Circuit Analogue of Dielectric Losses & Loss Tangent

Variation of Dielectric Loss with Frequency or Dielectric Loss Spectrum

Solved Numerical Examples

Important Applications of Dielectric Materials

Section B : Magnetic Properties


Magnetisation ( I or M)

Origin of Magnetic Moment

Magnetic Permeability (µ), Relative Permeability ( )µr & Magnetic Susceptibility ( )χ

Solved Numerical Examples

Para- Dia- & Ferromagnetic Materials

Dia-magnetic Materials

Para-magnetic Materials

Ferromagnetic Materials

Langevin's Theory of Dia- Magnetic Material

Langevin's Theory of Para-magnetism

Determination of Susceptibilities of Para- & Dia-magnetic Materials

Solved Numerical Examples

Phenomenon of Hysteresis: Retentivity & Coercivity

Demagnetisation of Ferromagnetic Material

Domain Concept of Hysteresis

Hysteresis Loss & their Determination

Applications of Phenomena of Hysteresis (or Hysteresis Curves for the selection of Materials)

Selection of Magnetic Materials

Permanent Magnets


Cores for Transformers, Armature of Dynamos, Motors & Telephone Diaphragms

Solved Numerical Examples


b Short Question Bank

b Long Question Bank

b Unsolved Numerical Problems

b Answers to unsolved Numerical Problems

Unit III: Electromagnetic Theory


Current (Conduction & convection)

Current Density

Conduction & Convection current Densities

Drift Velocity of charge Carriers in a Conductor

Continuity Equation

A Note on Continuity Equation

Solved Numerical Examples

Displacement Current

Modified Ampere's Law & Displacement Current

Modified Ampere's Law & Displacement Current Density

Solved Numerical Examples

Maxwell's Equations

Physical Significance of Maxwell's Equations

Derivations of Maxwell's Equations in Differential Forms

Maxwell's Equations in Integral Form

Solved Numerical Examples

Electromagnetic Waves

Poynting Theorem & Poynting Vector

Electromagnetic Wave Equations in Free Space

Nature of Electromagnetic Waves

Solution of Plane Electromagnetic Wave (Transverse Nature of E.M. Waves)

Electric & Magnetic Vectors & Mutually Perpendicular to Each Other & also to the Direction of

Propagation of Wave Vector

Propagation of Plane Electromagnetic Wave in Free Space

Solved Numerical Examples

Plane Wave Equation & its Solution in Non-Conducting (or Perfect Dielectric or Lossless) Medium 223

Plane Electromagnetic Wave & its Solution in Conducting Media (Lossy Dielectric or Partially

Conducting Media)

Conductors & Dielectrics

Wave Propagation in a Good Dielectric (That is, Dielectric having Law or Partially Conducting Media or

Lossy Dielectric)

Wave Propagation in Good Conductors or Conducting Media

Characteristic Impedance of Conducting Medium

Solved Numerical Examples

Depth of Penetration-Skin Depth

Solved Numerical Examples


b Short Question Bank

b Long Question Bank

b Unsolved Numerical Problems

b Answers to unsolved Numerical Problems 254

Unit IV: Physics of Some Technologically Important Materials

Section-A : Semiconductors


Band Theory of Solids

Valence Band, Conduction Band & Forbidden Bands

Classifications of Solids into Insulators, Semiconductors & Conductors on the Basis of Band Structure of Solids

Origin of Energy Bands & Forbidden Bands on the Basis of Bragg Reflections

Brillouin Zones

Density of States

Fermi - Dirac Probability Distribution Function

Fermi Level in an Intrinsic Semiconductor

Law of Mass of Action For Intrinsic Semiconductors

Solved Numerical Examples

Fermi Level

Position of Fermi Level in Intrinsic Semiconductors

Position of Fermi Level in Extrinsic Semiconductors

Variation of Fermi Level with Temperature in Extrinsic Semiconductors

Concept of Electrical Conductivity

Solved Numerical Examples

Conductivity of a Conductor

Drift Velocity & Mobility

Conductivity of Semiconductors

Conductivity of Intrinsic Semiconductor

Conductivity of Extrinsic Semiconductor

Solved Numerical Examples

Variation of conductivity with Temperature

Solved Numerical Examples

Section-B: Superconductors



Temperature Dependence of Resistivity in Superconducting Materials

Essential properties of Superconductors (Zero Resistivity)

Characteristics of Superconductors in Superconducting State

London Equations

London Penetration Depth

Coherence Length

Effect of Magnetic Field (Meissner Effect)

Persistent Currents

Critical Currents (or Silsbee's Rule)

Solved Numerical Examples

Type I & Type II Superconductors

Solved Numerical Examples

Thermal Properties of Superconductors

Difference Between Type I & Type II Superconductors

Flux Quantization

Free Carrier (Electrons & Holes) Density (or Concentration) in Intrinsic Semiconductor

Density of Holes or Concentration of Holes in the Valence Band

Existence of Energy Gap in Superconductors

Isotope Effect

Solved Numerical Examples

High Temperature Superconductors

Organic Superconductors

Applications of Superconductors

B.C.S. Theory (Qualitative) of Superconductivity

Josephson Effect

Section-C: Nanomaterials


Nano-Science & Nanotechnology



Techniques for Characterization of Nanoparticles

Methods of Nanoparticles Synthesis


Porous Silicon as Nanomaterial

Aerogels as Nanomaterial

Carbon Nanotubes

Toxic Effects of Nanotubes

Uses of Nanotubes

Fullerence or Buckyballs & Nanotubes

Creation of Buckyballs

Uses of Buckyballs

Synthesis of Carbon Nanotubes

Properties of Nanotubes

Nanotubes as Drug Delivery Vessel

Applications of Nano-Materials