 # GATE Electronics & Communication Vol-10- Electromagnetics

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 Edition 8th Authors R K Kanodia & Ashish Murolia Publisher NODIA Pages 751 Binding Paper Back Language English

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SALIENT FEATURES

• Brief Theory

• Problem Solving Methodology

• Fundamental Concepts & Formulae Review

• Vast Question book with Full Solutions

• Multiple Choice Questions, Memory Based Questions and Numerical Types Questions

• Full width coverage of GATE Syllabus

• Well explained and error free solutions

CHAPTER 1 VECTOR ANALYSIS

1.1 INTRODUCTION

1.2 VECTOR QUANTITY

1.2.1 Representation of a Vector

1.2.2 Unit Vector

1.3 BASIC VECTOR OPERATIONS

1.3.1 Scaling of a Vector

1.3.3 Position Vector

1.3.4 Distance Vector

1.4 MULTIPLICATION OF VECTORS

1.4.1 Scalar Product

1.4.2 Vector or Cross Product

1.4.3 Triple Product

1.4.4 Application of Vector Multiplication

1.5 COORDINATE SYSTEMS

1.5.1 Rectangular Coordinate System

1.5.2 Cylindrical Coordinate System

1.5.3 Spherical Coordinate System

1.6 RELATIONSHIP BETWEEN DIFFERENT COORDINATE SYSTEMS

1.6.1 Coordinate Conversion

1.6.2 Relationship between Unit Vectors of Different Coordinate Systems

1.6.3 Transformation of a Vector

1.7 DIFFERENTIAL ELEMENTS IN COORDINATE SYSTEMS

1.7.1 Differential Elements in Rectangular Coordinate System

1.7.2 Differential Elements in Cylindrical Coordinate System

1.7.3 Differential Elements in Spherical Coordinate System

1.8 INTEGRAL CALCULUS

1.9 DIFFERENTIAL CALCULUS

1.9.2 Divergence of a Vector

1.9.3 Curl of a Vector

1.9.4 Laplacian Operator

1.10 INTEGRAL THEOREMS

1.10.1 Divergence theorem

1.10.2 Stokeâ€™s Theorem

1.10.3 Helmholtzâ€™s Theorem

EXERCISE 1.1

EXERCISE 1.2

EXERCISE 1.3

EXERCISE 1.4

SOLUTIONS 1.1

SOLUTIONS 1.2

SOLUTIONS 1.3

SOLUTIONS 1.4

CHAPTER 2 ELECTROSTATIC FIELDS

2.1 INTRODUCTION

2.2 ELECTRIC CHARGE

2.2.1 Point Charge

2.2.2 Line Charge

2.2.3 Surface Charge

2.2.4 Volume Charge

2.3 COULOMBâ€™S LAW

2.3.1 Vector Form of Coulombâ€™s Law

2.3.2 Principle of Superposition

2.4 ELECTRIC FIELD INTENSITY

2.4.1 Electric Field Intensity due to a Point Charge

2.4.2 Electric Field Intensity due to a Line Charge Distribution

2.4.3 Electric Field Intensity due to Surface Charge Distribution

2.5 ELECTRIC FLUX DENSITY

2.6 GAUSSâ€™S LAW

2.6.1 Gaussian Surface

2.7 ELECTRIC POTENTIAL

2.7.1 Potential Difference

2.7.3 Equipotential Surfaces

2.8 ENERGY STORED IN ELECTROSTATIC FIELD

2.8.1 Energy Stored in a Region with Discrete Charges

2.8.2 Energy Stored in a Region with Continuous Charge Distribution

2.8.3 Electrostatic Energy in terms of Electric Field Intensity

2.9 ELECTRIC DIPOLE

2.9.1 Electric Dipole Moment

2.9.2 Electric Potential due to a Dipole

2.9.3 Electric Field Intensity due to a Dipole

EXERCISE 2.1

EXERCISE 2.2

EXERCISE 2.3

EXERCISE 2.4

SOLUTIONS 2.1

SOLUTIONS 2.2

SOLUTIONS 2.3

SOLUTIONS 2.4

CHAPTER 3 ELECTRIC FIELD IN MATTER

3.1 INTRODUCTION

3.2 ELECTRIC CURRENT DENSITY

3.3 CONTINUITY EQUATION

3.4 ELECTRIC FIELD IN A DIELECTRIC MATERIAL

3.4.1 Electric Susceptibility

3.4.2 Dielectric Constant

3.4.3 Relation between Dielectric Constant and Electric Susceptibility

3.5 ELECTRIC BOUNDARY CONDITIONS

3.5.1 Dielectricâ€“Dielectric Boundary Conditions

3.5.2 Conductor-Dielectric Boundary Conditions

3.5.3 Conductor-Free Space Boundary Conditions

3.6 CAPACITOR

3.6.1 Capacitance

3.6.2 Energy Stored in a Capacitor

3.7 POISSONâ€™S AND LAPLACEâ€™S EQUATION

3.7.1 Uniqueness Theorem

EXERCISE 3.1

EXERCISE 3.2

EXERCISE 3.3

EXERCISE 3.4

SOLUTIONS 3.1

SOLUTIONS 3.2

SOLUTIONS 3.3

SOLUTIONS 3.4

CHAPTER 4 MAGNETOSTATIC FIELDS

4.1 INTRODUCTION

4.2 MAGNETIC FIELD CONCEPT

4.2.1 Magnetic Flux

4.2.2 Magnetic Flux Density

4.2.3 Magnetic Field Intensity

4.2.4 Relation between Magnetic Field Intensity (H) and Magnetic Flux Density (B)

4.3 BIOT-SAVARTâ€™S LAW

4.3.1 Direction of Magnetic Field Intensity

4.3.2 Conventional Representation of (H ) or Current (I )

4.4 AMPEREâ€™S CIRCUITAL LAW

4.5 MAGNETIC FIELD INTENSITY DUE TO VARIOUS CURRENT DISTRIBUTIONS

4.5.1 Magnetic Field Intensity due to a Straight Line Current

4.5.2 Magnetic Field Intensity due to an Infinite Line Current

4.5.3 Magnetic Field Intensity due to a Square Current Carrying Loop

4.5.4 Magnetic Field Intensity due to a Solenoid

4.5.5 Magnetic Field Intensity due to an Infinite Sheet of Current

4.6 MAGNETIC POTENTIAL

4.6.1 Magnetic Scalar Potential

4.6.2 Magnetic Vector Potential

EXERCISE 4.1

EXERCISE 4.2

EXERCISE 4.3

EXERCISE 4.4

SOLUTIONS 4.1

SOLUTIONS 4.2

SOLUTIONS 4.3

SOLUTIONS 4.4

CHAPTER 5 MAGNETIC FIELDS IN MATTER

5.1 INTRODUCTION

5.2 MAGNETIC FORCES

5.2.1 Force on a Moving Point Charge in Magnetic Field

5.2.2 Force on a Differential Current Element in Magnetic Field

5.2.3 Force on a Straight Current Carrying Conductor in Magnetic Field

5.2.4 Magnetic Force Between Two Current Elements

5.2.5 Magnetic Force Between Two Current Carrying Wires

5.3 MAGNETIC DIPOLE

5.4 MAGNETIC TORQUE

5.4.1 Torque in Terms of Magnetic Dipole Moment

5.5 MAGNETIZATION IN MATERIALS

5.5.1 Magnetic Susceptibility

5.5.2 Relation between Magnetic Field Intensity and Magnetic Flux Density

5.5.3 Classification of Magnetic Materials

5.6 MAGNETOSTATIC BOUNDARY CONDITIONS

5.6.1 Boundary condition for the normal components

5.6.2 Boundary Condition for the Tangential Components

5.6.3 Law of Refraction for Magnetic Field

5.7 MAGNETIC ENERGY

5.7.1 Energy Stored in a Coil

5.7.2 Energy Density in a Magnetic Field

5.8 MAGNETIC CIRCUIT

EXERCISE 5.1

EXERCISE 5.2

EXERCISE 5.3

EXERCISE 5.4

SOLUTIONS 5.1

SOLUTIONS 5.2

SOLUTIONS 5.3

SOLUTIONS 5.4

CHAPTER 6 TIME VARYING FIELDS AND MAXWELL EQUATIONS

6.1 INTRODUCTION

6.2 FARADAYâ€™S LAW OF ELECTROMAGNETIC INDUCTION

6.2.1 Integral Form of Faradayâ€™s Law

6.2.2 Differential Form of Faradayâ€™s Law

6.3 LENZâ€™S LAW

6.4 MOTIONAL AND TRANSFORMER EMFS

6.4.1 Stationary Loop in a Time Varying Magnetic Field

6.4.2 Moving Loop in Static Magnetic Field

6.4.3 Moving Loop in Time Varying Magnetic Field

6.5 INDUCTANCE

6.5.1 Self Inductance

6.5.2 Mutual Inductance

6.6 MAXWELLâ€™S EQUATIONS

6.6.1 Maxwellâ€™s Equations for Time Varying Fields

6.6.2 Maxwellâ€™s Equations for Static Fields

6.6.3 Maxwellâ€™s Equations in Phasor Form

6.7 MAXWELLâ€™S EQUATIONS IN FREE SPACE

6.7.1 Maxwellâ€™s Equations for Time Varying Fields in Free Space

6.7.2 Maxwellâ€™s Equations for Static Fields in Free Space

6.7.3 Maxwellâ€™s Equations for Time Harmonic Fields in Free Space

EXERCISE 6.1

EXERCISE 6.2

EXERCISE 6.3

EXERCISE 6.4

SOLUTIONS 6.1

SOLUTIONS 6.2

SOLUTIONS 6.3

SOLUTIONS 6.4

CHAPTER 7 ELECTROMAGNETIC WAVES

7.1 INTRODUCTION

7.2 ELECTROMAGNETIC WAVES

7.2.1 General Wave Equation for Electromagnetic Waves

7.2.2 Wave Equation for Perfect Dielectric Medium

7.2.4 Wave Equation for Time-Harmonic Fields

7.3 UNIFORM PLANE WAVES

7.4 WAVE PROPAGATION IN LOSSY DIELECTRICS

7.4.1 Propagation Constant in Lossy Dielectrics

7.4.2 Solution of Uniform Plane Wave Equations in Lossy Dielectrics

7.4.3 Velocity of Wave Propagation in Lossy Dielectrics

7.4.4 Wavelength of Propagating Wave

7.4.5 Intrinsic Impedance

7.4.6 Loss Tangent

7.5 WAVE PROPAGATION IN LOSSLESS DIELECTRICS

7.5.1 Attenuation Constant

7.5.2 Phase Constant

7.5.3 Propagation Constant

7.5.4 Velocity of Wave Propagation

7.5.5 Intrinsic Impedance

7.5.6 Field Components of Uniform Plane Wave in Lossless Dielectric

7.6 WAVE PROPAGATION IN PERFECT CONDUCTORS

7.6.1 Attenuation Constant

7.6.2 Phase Constant

7.6.3 Propagation Constant

7.6.4 Velocity of Wave Propagation

7.6.5 Intrinsic Impedance

7.6.6 Skin Effect

7.7 WAVE PROPAGATION IN FREE SPACE

7.7.1 Attenuation Constant

7.7.2 Phase Constant

7.7.3 Propagation Constant

7.7.4 Velocity of Wave Propagation

7.7.5 Intrinsic Impedance

7.7.6 Field Components of Uniform Plane Wave in Free Space

7.8 POWER CONSIDERATION IN ELECTROMAGNETIC WAVES

7.8.1 Poyntingâ€™s Theorem

7.8.2 Average Power Flow in Uniform Plane Waves

7.9 WAVE POLARIZATION

7.9.1 Linear Polarization

7.9.2 Elliptical Polarization

7.9.3 Circular Polarization

7.10 REFLECTION & REFRACTION OF UNIFORM PLANE WAVES

7.11 NORMAL INCIDENCE OF UNIFORM PLANE WAVE AT THE INTERFACE BETWEEN TWO DIELECTRICS

7.11.1 Reflection and Transmission Coefficients

7.11.2 Standing Wave Ratio

7.12 NORMAL INCIDENCE OF UNIFORM PLANE WAVE ON A PERFECT CONDUCTOR

7.12.1 Reflection and Transmission Coefficients

7.12.2 Standing Wave Ratio

7.13 OBLIQUE INCIDENCE OF UNIFORM PLANE WAVE AT THE INTERFACE BETWEEN TWO DIELECTRICS

7.13.1 Parallel Polarization

7.13.2 Perpendicular Polarization

7.14 OBLIQUE INCIDENCE OF UNIFORM PLANE WAVE ON A PERFECT CONDUCTOR

7.14.1 Parallel Polarisation

7.14.2 Perpendicular Polarisation

EXERCISE 7.1

EXERCISE 7.2

EXERCISE 7.3

EXERCISE 7.4

SOLUTIONS 7.1

SOLUTIONS 7.2

SOLUTIONS 7.3

SOLUTIONS 7.4

CHAPTER 8 TRANSMISSION LINES

8.1 INTRODUCTION

8.2 TRANSMISSION LINE PARAMETERS

8.2.1 Primary Constants

8.2.2 Secondary Constants

8.3 TRANSMISSION LINE EQUATIONS

8.3.1 Input Impedance of Transmission Line

8.3.2 Reflection Coefficient

8.4 LOSSLESS TRANSMISSION LINE

8.4.1 Primary Constants of a Lossless Line

8.4.2 Secondary Constants of a Lossless Line

8.4.3 Velocity of Wave Propagation in a Lossless Line

8.4.4 Input Impedance of a Lossless Line

8.5 DISTORTIONLESS TRANSMISSION LINE

8.5.1 Primary Constants of a Distortionless Line

8.5.2 Secondary Constants of a Distortionless Line

8.5.3 Velocity of Wave Propagation in a distortionless Line

8.6 STANDING WAVES IN TRANSMISSION LINE

8.7 SMITH CHART

8.7.1 Constant Resistance Circles

8.7.2 Constant Reactance Circles

8.7.3 Application of Smith Chart

8.8 TRANSIENTS ON TRANSMISSION LINE

8.8.1 Instantaneous Voltage and Current on Transmission Line

8.8.2 Bounce Diagram

EXERCISE 8.1

EXERCISE 8.2

EXERCISE 8.3

EXERCISE 8.4

SOLUTIONS 8.1

SOLUTIONS 8.2

SOLUTIONS 8.3

SOLUTIONS 8.4

CHAPTER 9 WAVEGUIDES

9.1 INTRODUCTION

9.2 MODES OF WAVE PROPAGATION

9.3 PARALLEL PLATE WAVEGUIDE

9.3.1 TE Mode

9.3.2 TM Mode

9.3.3 TEM Mode

9.4 RECTANGULAR WAVEGUIDE

9.4.1 TM Modes

9.4.2 TE Modes

9.4.3 Wave Propagation in Rectangular Waveguide

9.5 CIRCULAR WAVEGUIDE

9.5.1 TM Modes

9.5.2 TE Modes

9.6 WAVEGUIDE RESONATOR

9.6.1 TM Mode

9.6.2 TE Mode

9.6.3 Quality Factor

EXERCISE 9.1

EXERCISE 9.2

EXERCISE 9.3

EXERCISE 9.4

SOLUTIONS 9.1

SOLUTIONS 9.2

SOLUTIONS 9.3

SOLUTIONS 9.4

CHAPTER 10 ANTENNA AND RADIATING SYSTEMS

10.1 INTRODUCTION

10.2 ANTENNA BASICS

10.2.1 Types of Antenna

10.2.2 Basic Antenna Elements

10.2.3 Antenna Parameters

10.3.2 Retarded Potentials

10.4 RADIATION FROM A HERTZIAN DIPOLE

10.4.1 Field Components at Near Zone

10.4.2 Field Components at Far Zone

10.4.3 Power Flow from Hertzian Dipole

10.4.4 Radiation Resistance of Hertzian Dipole

10.5 DIFFERENT CURRENT DISTRIBUTIONS IN LINEAR ANTENNAS

10.5.1 Constant Current along its Length

10.5.2 Triangular Current Distribution

10.5.3 Sinusoidal Current Distribution

10.6 RADIATION FROM SHORT DIPOLE (d < Î»/ 4)

10.7 RADIATION FROM SHORT MONOPOLE (d < Î»/ 8)

10.8 RADIATION FROM HALF WAVE DIPOLE ANTENNA

10.8.1 Power Flow from Half Wave Dipole Antenna

10.8.2 Radiation Resistance of Half Wave Dipole Antenna

10.9 RADIATION FROM QUARTER WAVE MONOPOLE ANTENNA

10.9.1 Power Flow from Quarter Wave Monopole Antenna

10.9.2 Radiation Resistance of Quarter Wave Monopole Antenna

10.10 ANTENNA ARRAY

10.10.1 Two-elements Arrays

10.10.2 Uniform Linear Arrays

10.11 FRIIS EQUATION

EXERCISE 10.1

EXERCISE 10.2

EXERCISE 10.3

EXERCISE 10.4

SOLUTIONS 10.1

SOLUTIONS 10.2

SOLUTIONS 10.3

SOLUTIONS 10.4

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