**ENGG. ELECTROMAGNETIC FIELD THEORY**

**Contents **

**Chapter-1 vector analysis **

Introduction

Scalars and vectors

Scalar field

Vector field

Representation of a vector

Unit vector

Vector algebra

Scaling of vector

Addition of vectors

Subtraction of vectors

Identical vectors

The coordinate systems

Cartesian coordinate system

Cartesian coordinate system

Representing a point in rectangular coordinate system

Base vectors

Position and distance vectors

Differential elements in Cartesian coordinate system

Cylindrical coordinate system

Base vectors

Differential elements in cylindrical coordinate system

Relationship between Cartesian and cylindrical systems

Spherical coordinate system

Base vectors

Differential elements in spherical coordinate system

Relationship between Cartesian and spherical systems

Vector multiplication

Scalar or dot product of vectors

Properties of dot product

Applications of dot product

Vector or cross product of vectors

Properties of cross product

Applications of cross product

Products of three vectors

Scalar triple product

Characteristics of scalar triple product

Vector triple product

Characteristics of vector triple product

Transformation of vectors

Transformation of vectors from Cartesian to cylindrical

Transformation of vectors from cylindrical to Cartesian

Transformation of vectors from Cartesian to spherical

Transformation of vectors from spherical to Cartesian

Distances in all coordinate systems

Types of integral related to electromagnetic theory

Line integral

Surface integral

Volume integral

Divergence

Divergence theorem

Gradient of a scalar

Properties of gradient of a scalar

Curl of a vector

Stoke’s theorem

Examples with solutions

Review questions

University questions

**Chapter-2 Electric field intensity **

Introduction

Coulomb’s law

Statement of coulomb’s law

Constant of proportionality

Vector form of coulomb’s law

Principle of superposition

Steps to solve problems on coulomb’s law

Electric field intensity

Units of E

Method of obtaining E in Cartesian system

Electric field due to discrete charges

Important observations

Types of charge distributions

Point charge

Line charge

Method of finding Q from p

Surface charge

Method of finding Q from p

Volume charge

Method of finding Q from p

Electric field intensity due to various charge distributions

E due to line charge

E due to surface charge

E due to volume charge

Electric field due to infinite line charge

Electric field due to charged circular ring

Electric field due to infinite sheet of charge

Examples with solutions

Review questions

University questions

**Chapter-3 Electric flux density and gauss’s law **

Introduction

Electric flux

Properties of flux lines

Electric flux density

Vector form of electric flux density

D due to a point charge Q

Relationship between D and E

Electric flux density for various charge distributions

Line charge

Surface charge

Volume charge

Gauss’s law

Mathematical representation of gauss’s law

Special Gaussian surfaces

Applications of gauss’s law

Point charge

Use of gauss’s law to obtain D and E

Infinite line charge

Coaxial cable

Infinite sheet of charge

Spherical shell of charge

Variation of E against r

Uniformly charged sphere

Variation of E against r

Gauss’s law applied to differential volume element

Divergence

Physical meaning of divergence

The vector operator

Divergence in different coordinate systems

Properties of divergence of vector field

Maxwell’s first equation

Divergence theorem

Examples with solutions

Review questions

University questions

**Chapter-4 Energy and potential **

Introduction

Work done

The line integral

Important comments about work done

Potential difference

Unit of potential difference

Potential due to point charge

Concept of absolute potential

Potential due to pint charge not at origin

Potential due to several point charges

Potential calculation when references is other than infinity

Potential due to a line charge

Potential due to surface charge

Potential due to volume charge

Potential difference due to infinite line charge

Equipotential surfaces

Conservative field

Potential gradient

Relation between E and V

The vector operator

Properties of gradient of a scalar

Energy density in the electrostatic fields

Energy stored interms of D and E

An electric dipole

Expression of E due to an electric dipole

Dipole moment

Examples with solutions

Review questions

University questions

**Chapter-5 Conductors, dielectrics and capacitance**

Introduction

Current and current density

Relation between I and J

Relation between J and P

Continuity equation

Steady current

Conductors

Point form of ohm’s law

Resistance of a conductor

Properties of conductor

Relaxation time

Dielectric materials

Polarization

Mathematical expression for polarization

Properties of dielectric materials

Boundary conditions

Boundary conditions between conductor and free space

E at the boundary

Dn at the boundary

Boundary conditions between conductor dielectric

Boundary conditions between two perfect dielectrics

Reflection of D at the boundary

Concept of capacitance

Capacitors in series

Capacitors in parallel

Parallel plate capacitor

Capacitance of a co-axial cable

Spherical capacitor

Capacitance of single isolated sphere

Isolated sphere coated with dielectric

Composite parallel plate capacitor

Dielectric boundary normal to the plates

Energy stored in a capacitor

Energy density

Method of images

The image theory

Method of images

The image theory

Method of images for point charges

Examples with solutions

Review questions

University questions

**Chapter-6 poisson’s and Laplace’s equation **

Introduction

Poisson’s and laplace’s equations

Operation in different co-ordinate systems

Uniqueness theorem

Procedure for solving laplace’s equation

Calculating capacitance using laplace’s equation

Examples with solutions

Review questions

**Chpater-7 magnetostatics **

Introduction

Magnetic field and its properties

Magnetic field due to current carrying conductor

Magnetic field intensity

Magnetic flux density

Relation between B and H

Biot-savart law

Biot-savart law interms of distributed sources

H due to infinitely long straight conductor

H due to straight conductor of finite length

Sign convention for

H at the center of a circular conductor

H on the axis of a circular loop

Ampere’s circuital law

Proof of ampere’s circuital law

Steps to apply ampere’s circuital law

Applications of ampere’s circuital law

H due to infinitely long straight conductor

H due to a co-axial cable

H due infinite sheet of current

Curl

Curl in various co-ordinate systems

Properties of curt

Physical significance of a curl

Stoke’s theorem

Proof of stoke’s theorem

Magnetic flux and flux density

Maxwell’s equations for static electromagnetic fields

Application of flux density and flux to co-axial cable

Magnetic scalar and vector potentials

Scalar magnetic potential

Laplace’s equation for scalar magnetic potential

Vector magnetic potential

Poisson’s equation for magnetic field

A due to differential current element

Examples with solutions

Review questions

University questions

**Chapter-8 Magnetic forces, materials and inductance **

Introduction

Force on a moving point charge

Force on a differential current element

Force between differential current elements

Magnetic torque and magnetic dipole moment

Magnetic moment of a planar coil

Magnetic dipole moment

Nature of magnetic materials

Origin of magnetic dipole moment in the material

Classification of magnetic materials

Magnetization and permeability

Magnetic boundary conditions

Boundary conditions for normal components

Boundary conditions for tangential component

Magnetic circuits

Inductance and mutual inductance

Inductance of a solenoid

Inductance of a toroid

Inductance of a co-axial cable

Mutual inductance

Magnetic energy

Forces on magnetic materials

Examples with solutions

Important results

Review questions

University questions

**Chapter-9 Time varying fields and Maxwell’s equations **

Introduction

Faraday’s law

Displacement current

General field relations for time varying electric and magnetic fields

Maxwell’s equations for good conductor

Maxwell’s equations for harmonically varying fields

Boundary conditions for time varying fields

Retarded potentials

Phasor representation of a vector

Poynting vector and pointing theorem

Average power density

Integral and point forms of pointing theorem

Examples with solutions

Important results

Review questions

University questions

**Chapter-10 uniform plane waves **

Introduction

Uniform plane wave in free space

Wave equations in phasor form

Uniform plane wave in perfect dielectric

Uniform plane waves in lossy dielectric

Uniform plane wave in practical dielectric

Uniform plane waves in good conductor

Reflection of uniform plane waves

Normal incidence at plane dielectric boundary

Normal incidence at plane conducting boundary

Standing wave ratio

Oblique incidence

Direction cosines

Oblique incidence at a plane conducting boundary

Horizontal polarization

Vertical polarization

Oblique incidence at a plane dielectric boundary

Total reflection

Horizontal polarization

Vertical polarization

Polarization of uniform plane waves

Linear polarization

Elliptical polarization

Circular polarization

Conditions for the polarization of a sinusoidal wave

Examples with solutions

Important results

Review questions

University questions

**Chapter-11 transmission lines **

Introduction

Types of transmissions lines

Transmission line parameters

The infinite line

Important properties of the infinite line

Short line

Determination of Z for finite line terminated in Z

Currents and voltages along an infinite line

Attenuation and phase constant

Propagation constant interms of Z and Z

T section equivalent interms of Z and y

Section equivalent interms of Z and Y

Wavelength and velocity

Relationship between primary and secondary constants

Determination of Z interms of primary constants

Determination of Y interms of primary constants

Practical formulae for underground cables

General solution of a transmission line

Physical significance of general solution

Application of general solution to the particular cases

Finite line terminated in Z

Finite line open circuited at distant End

Finite line short circuited at distant End

Determination of b and primary constants

Input and transfer impedance

Conditions for minimum attenuation

Variable L

Variable C

R and G for minimum attenuation

Waveform distortion

Distortion due to Z varying with frequency

Frequency distortion

Phase distortion

Dissipation less line

Telephone cable

Loading of lines

Continuous loading

Advantages

Disadvantages

Lumped loading

Campbell’s equation

Advantages

Disadvantages

Practical formulae for Z and y for loaded underground cable

Reflection phenomenon

Disadvantages of reflection

Reflection coefficient

Input impedance interms of Z and K

Reflection loss and reflection factor

Return loss

Insertion loss

Expression for insertion loss

The line at radio frequencies

Parameters of the line at high frequency

Parameters of the coaxial line at high frequencies

Line constants for zero dissipation line

Voltages and currents on dissipation less line

Standing waves

Standing wave ratio

Relation between standing wave ratio and magnitude of reflection coefficient

Relation between standing wave ratio and reflection coefficient

Input impedance of the dissipation less line

Input impedance of open and short circuited lines

Input impedance of short circuited line

Input impedance of open circuited line

Reflection losses on the unmatched line

The Eighth-wave line

The Quarter-wave line

The half-wave line

Single stub matching on a line

Smith chart

Applications of the smith chart

Measurement of input impedance

Measurement of SWR

Measurement of reflection coefficient

Location of voltage maximum and voltage minimum

Double stub impedance matching on a line

Voltage and current on the line of small dissipation

Open and short circuit impedances of the line with small dissipation

Quarter wave line and half wave line of small dissipation

Tapped quarter wave line-impedance transformer

Examples with solutions

Important results

Review questions

University questions

**Chapter-12 Guided waves **

Introduction

Waves between parallel planes

Transverse electric wave or H wave

Transverse magnetic wave or E wave

Characteristics of TE and TM waves

Transverse electromagnetic waves

Properties of TEM waves

Velocities of propagation

Attenuation in parallel plane guides

Wave impedances

Electric field and current flow within the conductor

Important results

Review questions

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