(Approved by AICTE & affiliated to JNTU)

Aushapur (V) , Ghatkesar (M), R.R. Dist - 501301,A.P.,India.

ACADEMIC PLAN

( 2011-12)

ELECTROMAGNETIC WAVES and TRANSMISSION LINES

II Year B.Tech ECE-II Sem

K.BADARI NATH,

Associate Professor,

Dept. Of Electronics and Communication Engineering.

Subject: ELECTROMAGNETIC WAVESAND

TRANSMISSION LINESS.NO CONTENT

(1) - Objectives and Relevance

(2) - Scope

(3) - Prerequisites

(4) - Syllabus

1. JNTU

2. GATE

3. IES

(5) - Suggested Books

(6) - Websites

(7) - Expert Details

(8) - Journals

(9) - Subject (lesson) Plan

(10) - Question Bank

1. JNTU

2. GATE

(11) - Tutorial Question sets

(12) - List of topics for student’s seminars

(1) OBJECTIVES AND RELEVANCE

Main objective of our course is to deep discussion of the Electromagnetic Fields. Radiating of the signal depends of the field strength of the signal. Types of Transmission lines are used to provide various applications for transmitting the signal. Various types of mediums are used for various types of signals. Fields Strength of electromagnetics are used to find various parameters values.

(2) SCOPE

The scope of this subject is to provide the tremendous power and usefulness of the applications of communications and the Transmission can be seen from the wide variety of industrial machinery, military applications. These Fields are used to propagate the Electromagnetic signals in space.

(3) PREREQUISITES

This subject recommends continuous practice of vector calculus and electromagnetic field theory. To understand this subject student should have thorough knowledge about vector calculus, electromagnetic fields, retarding potentials and transmission lines fundamentals. Even mathematical approach and circuit analyzation point of view should be strong.

(4.1) SYLLABUS – JNTU

UNIT-I

OBJECTIVE Discuss Electric Field Intensity and due to different charge distributions Discuss Gauss Law and Applications Discuss Maxwell’s Two Equations for Electrostatics Fields

SYLLABUS

ELECTROSTATICS – I:

Coulomb’s Law, Electric Field Intensity – Fields due to Different Charge Distributions, Electric Flux Density, Gauss Law and Applications, Electric Potential, Relations Between E and V, Maxwell’s Two Equations for Electrostatics Fields, Energy Density, Illustrative Problems.

UNIT – II

OBJECTIVE Discuss Potential Isotropic and Homogeneous Dielectrics Discuss Continuity Equation, Relaxation Time Discuss Poisson’s and Laplace’s Equations Discuss Capacitance and types

SYLLABUS

ELECTROSTATICS – II:

Convection and Conduction Currents, Dielectric Constant, Isotropic and Homogeneous Dielectrics, Continuity Equation, Relaxation Time, Poisson’s and Laplace’s Equations; Capacitance – Parallel Plate, Coaxial, Spherical Capacitors, Illustrative Problems.

UNIT –III

OBJECTIVE

Introduction-Magneto statics

Discuss Biot – Savart’s law, Ampere’s Circuital Law.

Discuss Maxwell’s Two equations for Magnetic Fields

Discuss Forces due to Magnetic Fields, Ampere’s Force Law

SYLLABUS

MAGNETOSTATICS:

Biot – Savart’s law, Ampere’s Circuital Law and Applications, Magnetic Flux Density, Maxwell’s Two equations for Magnetic Fields, Magnetic Scalar and Vector Potentials, Forces due to Magnetic Fields, Ampere’s Force Law, Inductance and Magnetic Energy, Illustrative Problems. UNIT – IV

OBJECTIVE Introduction-Maxwell’s equations Discuss Inconsistency of Ampere’s Law and Displacement Current Density Discuss Maxwell’s Equations indifferent Final Forms Discuss Dielectric – Dielectric and Dielectric – Conductor Interfaces Discuss related problems

SYLLABUS

MAXWELL’S EQUATIONS (Time Varying Fields):

Faraday’s Law and Transformer emf, Inconsistency of Ampere’s Law and Displacement Current Density, Maxwell’s Equations indifferent Final Forms and Word Statements, Conditions at a Boundary Surface: Dielectric – Dielectric and Dielectric – Conductor Interfaces, Illustrative Problems. ).

UNIT – V

OBJECTIVE Introduction to Wave Equations Discuss all Relations between E & H . Discuss Wave Propagation in Lossless and Conducting Media. Discuss Wave Propagation in good Conductors and Good Dielectrics Discuss Polarization and problems

SYLLABUS

EM WAVE CHARACTERISTICS - I:

Wave Equations for Conducting and Perfect Dielectric Media, Uniform Plane Waves, All Relations between E & H, Sinusoidal Variations, Wave Propagation in Lossless and Conducting Media, Conductors & dielectrics – Characterization, Wave Propagation in good Conductors and Good Dielectrics, Polarization, Illustrative Problems

UNIT – VI

OBJECTIVE Introduction-Reflection and Refraction of plane waves Discussion Reflection and refraction of Normal and Oblique Incidences for PC and PD. Discuss Brewster angle, Critical angle and TIR. Discuss Poynting Vector and Poynting Theorem – Applications Discuss Power Loss in a Plane Conductor and Problems

SYLLABUS

EM WAVE CHARACTERISTICS - II:

Reflection and Refraction of Plane Waves – Normal and Oblique Incidences, for both Perfect Conductor and Perfect Dielectrics, Brewster Angle, Critical Angle and Total Internal Reflection, Surface Impedance, Poynting Vector and Poynting Theorem – Applications, Power Loss in a Plane Conductor, Illustrative Problems

UNIT – VII

OBJECTIVE Introduction Transmission lines-types. Discuss Parameters, Transmission Line Equations. Discuss Primary & Secondary Constants, Expression for Characteristics Impedance, Propagation Constant Discuss Infinite Line Concepts, Losslessness/Low Loss Characterization Discuss Distortion – Condition for Distortion less ness and minimum Attenuation Discuss Loading –types and Problems

SYLLABUS

TRANSMISSION LINES - I:

Types, Parameters, Transmission Line Equations, Primary & Secondary Constants, Expression for Characteristics Impedance, Propagation Constant, Phase and Group Velocities, Infinite Line Concepts, Lossless ness/Low Loss Characterization, Distortion – Condition for Distortion less ness and minimum Attenuation, Loading – Types of Loading, Illustrative Problems.

UNIT – VIII

OBJECTIVE Introduction-Input impedance relations Discuss SC and OC lines Discuss RC,VSWR Discuss λ/4, λ/2, λ/8 Lines – Impedance Transformations Discuss Smith Chart – Configuration and Applications Discuss Single and Double Stub Matching-Problems

SYLLABUS

TRANSMISSION LINES - II:

Input Impedance Relations, SC and OC Lines, Reflection Coefficient, VSWR, UHF Lines as Circuit Element: λ/4, λ/2, λ/8 Lines – Impedance Transformations, Significance of Zmin and Zmax Smith Chart – Configuration and Applications, Single and Double Stub Matching, Illustrative Problems.

(4.2) SYLLABUS - GATE

UNIT I Maxwell’s Two Equations for Electrostatics Fields

UNIT II NA

UNIT III

. Maxwell’s two equations for Magnetic Fields

UNIT IV Maxwell’s Equations indifferent Final Forms and Word Statements

UNIT V Wave Equations for Conducting and Perfect Dielectric Media

UNIT VI Reflection and Refraction of Plane Waves-Poyinting vector

.UNIT VII Transmission Line Equations, Primary & Secondary Constants, Expression for Characteristics Impedance, Propagation Constant, Phase and Group Velocities

UNIT VIII Smith Chart – Configuration and Applications

(4.3) SYLLABUS - IES

UNIT I and UNIT II Analysis of electrostatic and magneto static fields; Laplace's and Poisson's equations; Boundary value problems and their solutions; Maxwell’s Two Equations for Electrostatics Fields and Magneto static fields

UNIT III Maxwell’s Two Equations for Magneto static fields

UNIT IV Maxwell’s equations for time varying fields

UNIT V and UNIT VI Application to wave propagation in bounded and unbounded media

UNIT VII and UNIT VIII Transmission lines: basic theory, standing waves, matching applications

(5) SUGGESTED BOOKS

TEXT BOOKS:-

1. Elements of Electromagnetics – Mathew N. O. Sadiku, 4th Edn., 2008. Oxford Univ. Press.

2. Electromagnetic Waves and Radiating Systems – E.C. Jordan and K.G. Balmain, PHI, 2nd ed., 2000.

3. Transmission Lines and Networks – Umesh Sinha, Satya Prakashan, 2001, (Tech. India Publication), New Delhi

REFERENCE BOOKS:-

1. Engineering Electromagnetics – Nathan Ida, 2nd ed., 2005, Springer (India) Pvt. Ltd., new Delhi.

2. Engineering Electromagnetics – William H. hayt Jr. and John A. Buck, 7th ed., 2006, TMH.

3. Networks Line and Fields – John D. ryder, 2nd ed., 1999, PHI.

(6) WEBSITES

Do not confine yourself to the list of websites mentioned here alone. Be cognizant and keep yourself abreast of the others too. The given list is not exhaustive.

1. www.iitk.ac.in

2. www.iitd.ernet.in

3. www.iitb.ac.in

4. www.iitm.ac.in

5. www.iitr.ac.in

6. www.iitg.ernet.in

7. www.mit.edu

9. www.grad.gatech.edu

10. www.gsas.harward.edu

11. www.tpub.com

14. www.electricalsandelectronics.com

15. www.electronics-tutorials.

(7) EXPERT DETAILS

The Expert Details which have been mentioned below are only a few of the eminent ones known Internationally, Nationally and Locally. There are a few others known as well.

INTERNATIONAL1. Mr.N.O.Sadiku.

2. Mr.E.C. Jordan and Mr. Balanis

NATIONAL

1. Mr. Umesh Sinha

2. Mr.Satya Prakashan

3. Dr.Ratnajith Bhattacharjee,IITG

4. Prof.R.K.Shevgoankar,IITB

5. Prof.Harishankar Ramchandran,IITM

REGIONAL

1. Dr.G.S.N.Raju,AU2.

(8) JOURNALS E-learning material NPTEL

INTERNATIONAL

1. IEEE Electronics Letters

2. Journal of the Institution of Electronics and Telecommunication Engineers (IETE)

3. electronics weekly

4. IEEE transactions on Electromagnetic

5. IEEE Transactions on Propagation

6. IEEE Journal of Antennas and Propagation

7. Journal of the Institution of Electronics and Telecommunication Engineers (IETE)

8. Journal of electronics

9. IEEE transactions on very large scale integration (VLSI) systems

NATIONAL

1. e-journal of Radio Propagation

2. Electronics for you

9. SUBJECT (LESSON) PLAN

Units Name of the topic No. of Hrs Required

Total no. of hrs

requiredUNIT-I Electro statistics-I

Introduction

Coulomb’s law ,Electric field intensity

Fields due to different charge distribution

Electric flux density

Gauss law and applications

Electric potential

Relation between E and V

Maxwell’s Two equations for Electrostatic fieldEnergy density

Problems

Assignment

02

01

02

01

01

01

01

01

10

UNIT-II Electro statistics-IIConvection and conduction currents

Dielectric constant , isotropic and homogeneous dielectrics

Continuity equation and Relaxation time

Poisson’s equation

Laplace ‘s equationParallel plate capacitor

Coaxial capacitor and Spherical capacitor

01

01

01

01

01

07

Problems

Assignment

01

01

UNIT-III Magneto staticsBiot-Savart’s law

Ampere’s circuit law and applications

Magnetic flux density ,Maxwell’s two equations for magneto static fields

Magnetic scalar and vector potentials

Forces due to magnetic fields

Ampere’s force law andInductance and magnetic energy

Problems

Assignment

01

01

01

01

01

01

01

07

UNIT-IV

Maxwell’s Equations(Time varying fields)Faraday’s law and transformer emf

Inconsistency of Ampere’s law

Displacement current density

Maxwell’s equation in different final forms and word statements

Conditions at a boundary surface-Dielectric-dielectric

Dielectric-conductor interfaces and problems

Assignment

01

01

01

02

01

01

07

UNIT-V EM Wave Characteristics-IWave equations for conducting and perfect dielectric media

Uniform plane waves-definition

02

01

11

All relations between E &H

Sinusoidal variations

Wave propagation in lossless media

Wave propagation in conducting media

Conductors &dielectrics-characterization

Wave propagation in good conductors and good dielectrics

Polarization

Problems

Assignment

01

01

01

01

01

01

01

01

UNIT-VI

EM Wave Characteristics-IIReflection and refraction of plane waves-normal and oblique incidences

Brewster angle and critical angle

Total Internal Reflection, surface impedance

Pointing vector and pointing theorem-applications

Power loss in a plane conductor

Problems

Assignment

01

01

01

01

01

01

07

UNIT-VII

Transmission lines-I

Types, parameters

Tr. Line equations

Primary and secondary constants

Expression for characteristic impedance

Propagation constant

Phase and group velocities and Infinite line

01

01

01

01

01

09

concepts

Losslessness/Low Loss Characterization

Distortion-condition for distortionlessness and Min.attenuation and Types of loading

Problems

Assignment

01

01

01

01

UNIT-VIII

Transmission Lines II

Input impedance relations

SC and OC lines

Reflection coefficient &VSWR

UHF lines as circuit elements

Smith chart-configuration and applications

Single and Double stub matching

Problems

Assignment

01

01

01

01

01

01

01

07

Total hrs 65

(10) QUESTION BANK

1. JNTU

1. (a) State and Prove Gauss’s law. List the limitations of Gauss’s law.(b) Derive an expression for the electric field strength due to a circular ring ofradius ‘a’ and uniform charge density, C/m, using Gauss’s law. Obtain thevalue of height ‘h’ along z-axis at which the net electric field becomes zero.Assume the ring to be placed in x-y plane.(c) Define Electric potential. 2. (a) State Ampere’s circuital law. Specify the conditions to be met for determiningmagnetic field strength, H, based on Ampere’s circuital law(b) A long straight conductor with radius ’a’ has a magnetic field strength H =(Ir/2_a2) ˆa_ within the conductor (r < a) and H = (I/2_r) ˆa_ outsidethe conductor (r > a) Find the current density J in both the regions (r <a and r > a)(c) Define Magnetic flux density and vector magnetic potential. [4+8+4]3. (a) Explain faraday?s law for time varying fields.(b) Verify that the displacement current in the parallel plate capacitor is the sameas the conduction current in the connecting wires. [8+8]4. (a) Derive wave Equations for source free regions.(b) The electric field in free space is given by E=50 cos (108t + _x)ay V/mi. Find the direction of propagationii. Calculate b and the time it takes to travel a distance of _/2iii. Sketch the wave at t=0, T/4 and T/2 [8+8]5. Write short notes on the following(a) Surface Impedance(b) Brewster angle(c) Total Internal Reflection (b) Explain the impossibility of TEM wave propagation in wave guides.

7. (a) An open-wire transmission line having Z0 = 650,−120 is terminated in Z0 atthe receiving end. If this line is supplied from a source of internal resistance300 , calculate the reflection factor and reflection loss at the sending endterminals.(b) A two wire line has a characteristic impedance of 600 and is to feed a 180 resistor at 200 MHz. A half wave line is to be used as a tube, 1.2cm indiameter .Find centre ?to-centre spacing in air? [8+8]8. (a) Explain the significance and Utility of _/8, _/4, and _/2 Line.(b) A low transmission line of 100 characteristic impedance is connected to aload of 400 . Calculate the reflection coefficient and standing wave ratio.Derive the Relationships used. 9.a) State and explain Coulomb?s law. Obtain an expression in vector form.(b) Two uniform line charges of density 8nC/m are located in a plane with y = 0at x = ±4m. find the E- field at a point P(0m, 4m, 10m) [6+10]10. (a) State Ampere’s circuital law. Specify the conditions to be met for determiningmagnetic field strength, H, based on Ampere’s circuital law(b) A long straight conductor with radius ’a’ has a magnetic field strength H =(Ir/2_a2) ˆa_ within the conductor (r < a) and H = (I/2_r) ˆa_ outsidethe conductor (r > a) Find the current density J in both the regions (r <a and r > a)(c) Define Magnetic flux density and vector magnetic potential. [4+8+4]

11. A square filamentary loop of wire is 25 cm on a side and has a resistance of 125per meter length. The loop lies in z=0 plane with its corners at (0,0,0) (0.25,0,0),(0.25,0.25,0) and (0,0.25,0) at t=0 the loop is moving with velocity vy = 50m/sin the field Bz = 8cos(1.5 × 108t − 0.5x)μT. Develop a function of time whichexpresses the ohmic power being delivered to the loop. [16]12. (a) Explain about uniform plane waves.(b) In a loss less medium for which _ = 60_, μr = 1 and H=-0.1 cos (wt-z)ax+0.5sin (wt-z)ay A/m. calculate 2 r and w. 13.. (a) What is Poynting theorem and Poynting vector . How can you apply this overthe cross-section of co-axial cable.(b) Obtain an expression for the power loss in a plane conductor in terms of thesurface resistance Rs . [8+8]14. (a) Explain about attenuation in parallel-plate wave guides. Also draw attenu-ation versus frequency characteristics of waves guided between parallel con-ducting plates.(b) A parallel plate wave guide made of two perfectly conducting infinite planesspaced 3 cm apart in air operates at a frequency of 10 GHz. Find the maximumtime average power that can be propagated per unit width of the guide forTE1andTM1 modes. [8+8]15. (a) What are the different types of losses in transmission lines?

(b) A co-axial cable has following parameters Z0 = 50 ohms, L= 20KM if thepower input is 1 watt and the attenuation constant is 1.5dB/km, find theoutput power of the cable provided it is terminated by Z0. Also determine theout put current. [8+8]16. (a) Give a neat sketch for a smith chart and explain clearly, step by step howwould you use this chart toi. Calculate the complex reflection coefficientii. Transfer impedance from one point to other along the line.iii. Determine the length and location of a short circuited stub line for im-pedance matching purpose.(b) Discuss the merits and demerits of stub matching techniques.

17. (a) Obtain an expression for electric field intensity at a point, P(x, y, z) due to apoint charge located at Q(x0, y0, z0)(b) Derive an expression for the electric field intensity due to an infinite lengthline charge along the z-axis at an arbitrary point Q (x, y, z).(c) A charge of −0.3μC is located at A (25, -30, 15) Cm and a second charge of0.5 μ C is located at B (-10, 8, 12) Cm. Find the electric field strength, ?E?ati. The originii. Point P (15, 20, 50) Cm 18. (a) Obtain an expression for differential magnetic field strength dH due to differ-ential current element I dl at the origin in the positive Z- direction.(b) Find the magnetic field strength, H at the centre of a square conducting loopof side ‘2a’ in Z=0 plane if the loop is carrying a current , I, in anti clock wisedirection. [6+10]19. Consider the region defined by and |X| , |Y | and |Z| < 1 , let 2 r = 5, μr = 4and_ =0.ifJd = 20cos(1.5 × 108t − bx)ayμA/mv

(a) Find D and E(b) Use the point form of faraday?s law and an integration with respect to timeto find B and H(c) Use rxH = Jd + J to find Jd(d) What is the numerical value of b? [4×4]20. A certain loss less material has μr = 4,2 r = 9. A 10 MHz uniform planewave is propagating in the ay dierection with EX0 = 400V/m and Ey0 = E20 =0atP(0.6, 0.6, 0.6) at t= 60ns

(a) Find E(t)(b) Find H(t) 21. (a) Explain the significances of Poynting theorem and Pointing vector.(b) A plane wave traveling in a medium of "r = 1, μr = 1 has an electric fieldintensity of 100×p_. Determine the energy density in the magnetic field andalso the total energy density.

(c) Circular wave guide

(d) Stub matching 22. (a) Explain the principal of impedance matching with Quarter wave Transformer?(b) A 100 loss less line connects a signal of 100 KHz to a load of 140 . Theload power is 100 m W. calculatei. Voltage Reflection coefficientii. VSWR,iii. Position of VMax, Imax, VminandImin.

23. a) Explain the following termsi) Homogenous and isotropic mediumii) line, surface and volume charge distributions. (8M)b) A point charge of 3nC is on z -axis 2 m away from the origin. Find the resultant V 24. a) Define and explain the Biot-savort’s law. Hence obtain the field due to a straight currentcarrying filamentary conductor of finite length. (8M)3. a) Derive Maxwell’s equations from their basics. (8M)b) Explain the concept of displacement current introduced by Maxwell to account for theproduction of magnetic fields in the empty space. (8M)4. a) List out propagation characteristics of EM waves in free space. (8M)b) In a lossless medium for which μ= 60_, μr =1 and H = -0.1 Cos (t-z)ax+0.5 sin(t-z)ayA/m. Calculate , r and (8M)5. a) Define reflection and transmission coefficients of a plane wave (8M)b) Obtain an expression for reflection coefficient when a wave is incident on a dielectricwith oblique incident parallel polarization (8M)6. What are the field components for TM waves? Derive them and draw the sketches for TM10mode. (16M)7. a) List out the applications of transmission lines.b) Draw an equivalent circuit of a two wire transmission linec) A lossy cable which has R=2.25_/m, L= 1.0 μH/m, C=1pF/m and G=0 operates atf = 0.5GHz. Find out the attenuation constant of the line (4+4+8M)8. Derive Zin for a lossless transmission line when it is terminated by a)ZL b)Open c)Shortcircuit and draw the suitable sketches

1. a) Explain the equation of continuity for time varying fields. (8M)

b) A uniform line of length 2 m with total charge 3nC is situated co-incident to the z-axiswith the center point 2 m from the origin, at a point on the x-axis 2m from the origin. Find V2. a) State Ampere’s circuital law. Specify the conditions to be met for determining magneticfield strength H, based on Amperes circuital law (6M)3. a) Explain Faraday’s law for time varying fields. (8M)b) Verify that the displacement current in the parallel plate capacitor is the same as theconduction current in the connecting wires. (8M)4. A plain wave with E=2.0 V/m and has a frequency of 300MHz is moving in free spaceimpinging on thick copper sheet located perpendicular to the direction of the propagation.Finda) E and H at the plane surface, b) depth of penetration and c) the surface impedance(4+6+6M)5. a) For good dielectrics derive the expression for _, _, V and _.6. a) Explain and sketch the nature of variations of attenuation with frequency in a parallel

plate waveguide for TE, TM and TEM waves. (8M)b) Explain the significance of TEM wave in a parallel plane guide and derive an expressionfor the attenuation factor for TEM wave (8M)7. a) Explain about the propagation constant in transmission lines.b) Explain the conditions which are used for minimum attenuation in transmission lines.c) What is loading? Explain different types of loading in transmission lines.(4+4+8M)8. a) Describe all the characteristics of UHF lines.b) Explain the significance and design of single stub impedance matching. Discuss thefactors on which stub length depends. (8+8M)1. a) Derive Poisson’s and Laplace’s equations starting form Gauss law.b) Obtain the expression for the far field and the potential due to a small electric dipoleoriented along Z- axis. (8+8M)2. a) Derive equation of continuity for static magnetic fields. (6M)b) Derive an expression for magnetic field strength H, due to a current carrying conductor offinite length placed on Y- axis at point P in the X-Z plane and ‘r’ distant form the origin.Hence deduce the expression for H due to semi-finite length of the conductor. (10M)3. a) Derive Maxwell’s equation in integral form and differential form of time varying fields.(8M)b) State the boundary conditions satisfied by electromagnetic fields E and H at the interface ofair and perfect dielectric. (8M)b) Determine the phase velocity of propagation, attenuation constant, phase constant andintrinsic impedance for a forward travelling wave in a large block of copper at 1 MHz(_ =5.8x107, r= 1, μr=1). Determine the distance that the wave must travel to be attenuatedby a factor of 100( 40db) (8+8M)5. a) Define Brewster angle and derive an expression for Brewster angle when a wave isparallelly polarized.b) A plane wave travelling in medium of r=1,μr=1 has an electric field intensity of 200__V/m ,determine the energy density in the magnetic field and also the total energy density(8+8M)6. a) Explain the factors on which cutoff frequency of a parallel plate wave guide depend.b) Obtain the frequency in terms of cutoff frequency fc at which the attenuation constant dueto conductor losses for the TMn mode is minimum for parallel plate wave guide. (8+8M)7. Write a short notes ona) Lossless Transmission linesb) Distortion less line (8+8M)8. a) Explain the principle of impedance matching with quarter wave transformer.b) A 100_ lossless line connects a signal of 100 KHz to a load of 140_ .The load power is100mW. Calculatei) Voltage reflection coefficientii) VSWRiii) Position of Vmax , Imax, Vmin and Imin

1. a) Define and distinguish between the terms electric fields, electric displacement and electricflux density.(8M)b) A line charge L= 400 pC /m lies along the X-axis. The surface of zero potential passesthrough the point P(0,5,12)m. Find the potential at point (2,3,-4)m. (8M)2. a) Find the magnetic field strength , H on the Z-axis at a point P (0,0,4) due to a currentcarrying conductor loop, x2 +y2 = a2 in Z= 0 plane. (8M)b) Define i) Magnetic flux densityii) Vector magnetic potentialiii) Magnetic scalar potential (8M)3. a) State the boundary conditions satisfied by electromagnetic fields E and H at the interfaceof air and perfect dielectric. (8M)

b) In a nonmagnetic medium E=50 Cos(109t-8x)ay+40Sin(109t-8x)azV/m. Find the dielectricconstant r and the corresponding H. (8M)4. a) Derive the expression for attenuation and phase constants of uniform plane wave. (8M)b) If r =9, μ=μ0 for the medium in which a wave with frequency f= 0.3GHz is propagating,determine propagation constant and intrinsic impedance of the medium when i) _ = 0 andii) _ =10 mho/m (8M)5. a) State and explain Poynting theorem.b) A plane wave travelling in free space has an average pointing vector of 5 watts/m2. Findthe average energy density. (8+8M)6. Starting from Maxwell’s equations derive the expressions for the E and H field componentfor TE waves in a parallel plane waveguide. (16M)7. a) Define the input impedance of a transmission lines and derive the expression for it.b) Explain how the input impedance varies with frequency with sketches.(8+8M)8. a) Explain the significance and utility of /8, /4 and /2 lines.Calculate the reflection coefficient and standing wave ratio.

1. (a) State and Prove Gauss’s law. List the limitations of Gauss’s law.(b) Derive an expression for the electric field strength due to a circular ring ofradius ‘a’ and uniform charge density, ρL C/m, using Gauss’s law. Obtain thevalue of height ‘h’ along z-axis at which the net electric field becomes zero.Assume the ring to be placed in x-y plane.(c) Define Electric potential. [6+8+2]2. (a) State Maxwell’s equations for magneto static fields.(b) Show that the magnetic field due to a finite current element along Z axis ata point P, ‘r’ distance away along y- axis is given by H = (I/4πr)(sin α1 −sin α2).ba_ where I is the current through the conductor , α1 and α2 are theangles made by the tips of the conductor element at ?P?. [6+10]3. The electric field intensity in the region 0 < x < 5, 0 < y < π/12, 0 < z < 0.06m infree space is given by E=c sin12y sin az cos2 × 10 t ax v/m. Beginning with the∇xE relationship, use Maxwell’s equations to find a numerical value for a , if it isknown that a is greater than’0’. [16]4. (a) For good dielectrics derive the expressions for α, β, ν and η.(b) Find α, β, ν and η. for Ferrite at 10GHz ∈ r = 9, μr = 4, σ = 10ms/m. [8+8]5. (a) Define surface impedance and explain how it exists.(b) Derive expression for Reflection and Transmission coefficients of an EM wavewhen it is incident normally on a dielectric. [8+8]6. (a) Explain about attenuation in parallel-plate wave guides. Also draw attenu-ation versus frequency characteristics of waves guided between parallel con-ducting plates.(b) A parallel plate wave guide made of two perfectly conducting infinite planesspaced 3 cm apart in air operates at a frequency of 10 GHz. Find the maximumtime average power that can be propagated per unit width of the guide forTE1andTM1 modes. [8+8]7. (a) Explain the different types of transmission lines. What are limitations to themaximum power that they can handle.(b) A coaxial limes with an outer diameter of 8 mm has 50 ohm characteristicimpedance. If the dielectric constant of the insulation is 1.60, calculate theinner diameter.(c) Describe the losses in transmission lines [8+4+4]8. (a) Define the reflection coefficient and derive the expression for i/p impedancein terms of reflection coefficient.(b) Explain how the i/p impedance varies with the frequency with sketches. [8+8]1. (a) State and prove Gauss’s law. Express Gauss’s law in both integral and differ-ential forms.

(b) Discuss the salient features and limitations of Gauss’s law .(c) Derive Poisson’s and Laplace’s equations starting from Gauss’s law. [6+4+6]2. (a) State Maxwell’s equations for magneto static fields.(b) Show that the magnetic field due to a finite current element along Z axis ata point P, ‘r’ distance away along y- axis is given by H = (I/4πr)(sin α1 −sin α2).ba_ where I is the current through the conductor , α1 and α2 are theangles made by the tips of the conductor element at ?P?. [6+10]3. (a) Write down the Maxwell’s equations for Harmonically varying fields.(b) A certain material has σ = 0and 2R= 1ifH = 4sin(106t − 0.01z)ay A/m.make use of Maxwell’s equations to find μr [8+8]4. (a) For a conducting medium derive expressions for αandβ.(b) Determine the phase velouty of propagation, attenuation constant, phase con-stant and intrinsic impedance for a forward travelling wave in a large blockof copper at 1 MHz (σ = 5.8 × 107,2 r = μr = 1) determine the distance thatthe wave must travel to be attenuated by a factor of 100 (40 dB) [8+8]5. For an incident wave under oblique incident from medium of ε1 to medium of ε2with parallel polarization(a) Define and establish the relations for the critical angle θC and Brewster angleθBr for non-magnetic media with neat sketches.(b) Plot θC and θBr versus the ratio of ε1/ε2 [8+8]6. For a parallel plane wave guide of 3 cm separation, determine all the propagationcharacteristics, for a signal at 10 GHz, for(a) TE10 waves(b) TEM waves [16]Explain the terms used.7. (a) Definite following terms and explain their physical significance.i. Attenuation functionii. Characteristic impedanceiii. Phase function, andiv. Phase velocity as applied to a transmission line.(b) At 8 MHz the characteristic impedance of transmission line is (40-j2) and thepropagation constant is (0.01+j0.18 ) per meter. Find the primary constants.[8+8]8. (a) Explain the significance and Utility of λ/8, λ/4, and λ/2 Line.(b) A low transmission line of 100 characteristic impedance is connected to aload of 400 . Calculate the reflection coefficient and standing wave ratio.Derive the Relationships used. [8+8]1. (a) Define conductivity of a material.(b) Apply Gauss’s law to derive the boundary conditions at a conductor-dielectricinterface.(c) In a cylindrical conductor of radius 2mm, the current density varies withdistance from the axis according to J = 103e−400rA/m2. Find the total currentI. [4+6+6]2. (a) State Ampere’s circuital law. Specify the conditions to be met for determiningmagnetic field strength, H, based on Ampere’s circuital law(b) A long straight conductor with radius ‘a’ has a magnetic field strength H =(Ir/2πa2) ˆa_ within the conductor (r < a) and H = (I/2πr) ˆa_ outsidethe conductor (r > a) Find the current density J in both the regions (r <a and r > a)(c) Define Magnetic flux density and vector magnetic potential. [4+8+4]4. (a) A plane sinusoidal electromagnetic wave travelling in space has Emax = 1500μv/mi. Find the accompanying Hmaxii. The average power transmitted(b) The electric field intersity associated with a plane wave travelling in a perfectdielectric medium is given by Ex(z, t) = 10 cos (2π x 107 t - 0.1 πz)v/m[4+4+8]

i. What is the velocity of propagationii. Write down an expression for the magnetic field intesity associated withthe wave if μ = μ05. Write short notes on the following(a) Surface Impedance(b) Brewster angle(c) Total Internal Reflection [5+5+6]6. (a) Account for the presence of TE, TM and TEM waves in parallel plane waveguides and explain their significance.(b) Assuming z-direction of propagation in a parallel plane wave guide, deter-mine the expressions for the transverse field components in terms of partialderivatives of Ez and Hz. [8+8]7. (a) Define the followingi. Infinite lineii. Insertion lossiii. Lossy and loss less linesiv. Phase and group velocities(b) Derive the characteristic impedance of a transmission line in terms of its lineconstants [8+8]8. (a) Explain the significance of VmaxandVmin positions along the transmission line,for a complex load ZR Hence calculate the impedances at these positions.(b) An aerial of (200-j300) is to be matched with 500 lines. The matching isto be done by means of low loss 600 stub line. Find the position and lengthof the stub line used if the operating wave length is 20 meters. [8+8]1. (a) Using Gauss’s law derive expressions for electric field intensity and electricflux density due to an infinite sheet of conductor of charge density ρ C/cm(b) A parallel plate capacitance has 500mm side plates of square shape separatedby 10mm distance. A sulphur slab of 6mm thickness with 2r = 4 is kept onthe lower plate find the capacitance of the set-up. If a voltage of 100 volts isapplied across the capacitor, calculate the voltages at both the regions of thecapacitor between the plates. [8+8]2. (a) Derive equation of continuity for static magnetic fields.(b) Derive an expression for magnetic field strength, H, due to a current carryingconductor of finite length placed along the y- axis, at a point P in x-z planeand ‘r’ distant from the origin. Hence deduce expressions for H due to semi-infinite length of the conductor. [6+10]3. (a) What is the inconsistency of Amperes law?(b) A circular loop conductor of radius 0.1m lies in the z=0plane and has a resis-tance of 5 given B=0.20 sin 103 t az T. Determine the current [8+8]4. (a) Explain wave propagation in a conducting medium.(b) A large copper conductor (σ = 5.8 × 107s/m, εr = μr = 1)support a unifomplane wave at 60 Hz. Determine the ratio of conduction current to displace-ment current compute the attenuation constant. Propagation constant, in-trinsic impedance, wave length and phase velocity of propagation. [8+8]5. (a) Explain the difference between the Intrinsic Impedance and the Surface Im-pedance of a conductor. Show that for a good conductor , the surface im-pedance is equal to the intrinsic impedance.(b) Define and distinguish between the terms perpendicular polarization, parallelpolarization, for the case of reflection by a perfect conductor under obliqueincidence. [8+8] (b) Explain the impossibility of TEM wave propagation in wave guides. [10+6]7. (a) Explain the meaning of the terms characteristic impedance and propagationconstant of a uniform transmission line and obtain the expressions for themin terms of Parameters of line?(b) A telephone wire 20 km long has the following constants per loop km resistance90 , capacitance 0.062 μF, inductance 0.001H and leakage = 1.5 x 10−6

mhos. The line is terminated in its characteristic impedance and a potentialdifference of 2.1 V having a frequency of 1000 Hz is applied at the sendingend. Calculate :i. The characteristic impedanceii. Wavelength.iii. The velocity of propagation [8+8]8. (a) Describe all the characteristics of UHF Lines?(b) Explain the significance and design of single stub impedanceMatching .Discussthe factors on which stub length depends. [6+10]1. (a) State the Coulomb’s law in SI units and indicate the parameters used in theequations with the aid of a diagram. [6](b) Point charges Q1 and Q2 are respectively located at (4, 0, -3) and (2, 0, 1). IfQ2 = 4 nC, find Q1 such that. [10]i. The E at (5, 0, 6) has no Z-component.ii. The force on a test charge at (5, 0, 6) has no X-component.2. An infinitely long straight conducting rod of radius ‘a’ carries a current of I in +b Z direction. Using Ampere’s Circuital Law, find bH in all regions and sketch thevariation of H as a function of radial distance. If I = 3 mA. and a = 2 cm., find bHand β at ( 0, 1cm., 0) and (0, 4cm., 0). [16]3. (a) In free space D = Dm Sin (wt +β z)ax. Determine B and displacement currentdensity. [8](b) Region 1, for which μr1 = 3 is defined by X < 0 and region 2, X < 0 hasμr2 = 5 given H1 = 4 ax + 3ay 6 az (A/m). Determine H2 for X > 0 and theangles that H1 and H2 make with the interface. [8]4. Prove that under the condition of no reflection at an interface, the sum of theBrewster angle and the angle of refraction is π/2 for parallel polarization for thecase of reflection by a perfect conductor under oblique incident, with neat sketches.[16]5. (a) Define and differentiate between the terms: Instantaneous average and com-plex poynting vectors, giving their mathematical expressions. [8](b) An EM wave of 3 W/m2 Power density is incident normally from air on aperfect dielectric boundary. If the resulting VSWR is 2.2, find the reflectedand transmitted powers. [8]6. (a) Explain the factors on which cut off frequency of a parallel plate wave guidedepend. [8](b) Obtain the frequency in terms of cut off frequency fc at which the attenuationconstant due to conductor losses for the TMn mode is minimum for a parallelplate wave-guide. [8]7. (a) Derive a relation between reflection coefficient and characteristic impedance.[8](b) Determine the reflection coefficients when [8]i. ZL = Z0ii. ZL = short circuitiii. ZL = open circuit.iv. Also find out the magnitude of reflection coefficient when ZL is purelyreactive.8. (a) Explain how UHF lines can be treated as circuit elements, giving the necessaryequivalent circuits. [8](b) A loss less line of 100 is terminated by a load which produces SWR = 3. Thefirst Maxima is found to be occurring at 320 cm. If f = 300 MHz, determineload impedance.1. (a) State Gauss’s law. Using divergence theorem and Gauss’s law, relate thedisplacement density D to the volume charge density ρv. [8](b) A sphere of radius “a” is filled with a uniform charge density of ‘ρv’ c/m3.Determine the electric field inside and outside the sphere. [8]2. (a) Define Ampere’s Force Law and establish the associated relations. [6]

(b) A long coaxial cable has an inner conductor carrying a current of 1 mA. along+ b Z direction , its axis coinciding with Z-axis. Its inner conductor diameter is6 mm. If its outer conductor has an inside diameter of 12 mm. and a thicknessof 2 mm., determine bH at (0, 0, 0), (0, 1.5 mm, 0), (0, 4.5 mm, 0) and (0, 1cm, 0). (No derivations) [10]3. (a) In a perfect dielectric medium, the EM wave has maximum value for E of 10V/m with μr = 1 and εr = 4. Find the velocity of the wave, peak poyntingvector, average poynting vector, impedance of the medium and peak value ofthe magnetic field. [6](b) What is the inconsistency in Ampere’s Law? How it is rectified by Maxwell?[5](c) Show that the total displacement current between the condenser plates con-nected to an alternating voltage sources is exactly the same as the value ofcharging current (conduction current). [5]4. (a) Define uniform plane wave. [5](b) Prove that uniform plane wave does not have field components in the directionof the propagation. [6](c) Determine the intrinsic impedance of free space. [5]5. (a) State and Prove Poynting Theorem. [10](b) A Plane wave traveling in a free space has an average poynting vector of 5watts/m2. Find the average energy density. [6]6. Starting from Maxwell’s equations, derive the expressions for the E and H fieldcomponents for TE waves in a parallel plane wave guide. [16]7. (a) List out types of transmission lines and draw their schematic diagrams. [5](b) Draw the directions of electric and magnetic fields in parallel plate and coaxiallines. [5](c) A transmission line in which no distortion is present has the following parame-ters Z0= 50, α= 20mNP/m, υ= 0.6υ0. Determine R, L, G, C and wavelengthat 0.1 GHz. [6]8. (a) Draw the equivalent circuits of a transmission lines when [8]i. length of the transmission line, 1 <λ/4, with shorted loadii. when 1 <λ/4, with open endiii. 1 =λ/4.(b) Find out VSWR if [8]i. Z0 = 100 , RL = 80 ii. when Z0 = 80 , RL = 100(a) Derive the boundary conditions for the tangential and normal components ofElectrostatic fields at the boundary between two perfect dielectrics. [8](b) x-z-plane is a boundary between two dielectrics. Region y < 0 contains dielec-tric material εr1 = 2.5 while region y > 0 has dielectric with εr2= 4.0. IfE = −30ax+50ay+70azv/m, find normal and tangential components of the Efield on both sides of the boundary. [8]

2.GATE questions from all the units:-

1. A uniform plane electromagnetic wave traveling in free space enters into a lossless medium at normal incidence. In the medium its velocity reduces by 50% and in free space sets up a standing wave having a reflection coefficient of - 0.125. Calculate the permeability and the permittivity of the medium.2.

3.

4.

6.

7.

8.

9.

11.The wavelength of a wave with propagation constant (0.1+j0.2)m-1 is(a)0.05m (b) 10 m (c) 20 m (d) 30 m

12. The depth of penetration of wave in a lossy dielectric increases with increasing (a) conductivity (b) permeability (c) wavelength (d) permittivity 13. The vector H in the far field of an antenna satisfies (a) .H 0 and H 0 (b) .H 0 and H 0 (c) .H 0 and H 0 (d) .H 0 and H 0

14.An electric field on a plane is described by its potential 1 2 V 20 r r −−where r is the distance from the source. The field is due to

(a) a monopole (b) a dipole(c) both a monopole and a dipole (d) a quadrupole

15. 2.24. In air, a lossless transmission line of length 50 cm with L = 10 9H/m, C = 40pF/m is operated at 25 MHz. Its electrical path length is

(a) 0.5 meters (b) meters(c)radians (d) 180 degrees16. A TEM wave is incident normally upon a perfect conductor. The E and H fields atthe boundary will be, respectively.(a) minimum and minimum (b) maximum and maximum(c) minimum and maximum (d) maximum and minimum 17. Given 4 10 ˆ j x kt E e y V m −−in free space.(a) Write all the four Maxwell’s equations in free space.(b) Find E.(c) Find H.18. The phase velocity of waves propagating in a hollow metal waveguide is(a) greater than the velocity of light in free space.(b) less than the velocity of light in free space.(c) equal to the velocity of light in free space.(d) equal to the group velocity.19. A medium has breakdown strength of 16 KV/m r.m.s. Its relative permeability is1.0 and relative permittivity is 4.0 A plane electromagnetic wave is transmittedthrough the medium. Calculate the maximum possible power flow density and theassociated magnetic filed.20. The VSWR can have any value between(a) 0 and 1 (b) -1 and +1 (c) 0 and (d) 1 and In an impedance Smith chart, a clockwise movement along a constant resistance circle gives rise to

(a) a decrease in the value of reactance(b) an increase in the value of reactance(c) no change in the reactance value(d) no change in the impedance value22. The unit of H is(a) Ampere (b) Ampere/meter(c) Ampere/meter2 (d) Ampere-meter23. The depth of penetration of electromagnetic wave in a medium havingconductivity at a frequency of 1 MHz is 25 cm. The depth of penetration at afrequency of 4 MHz will be

(a) 6.25 cm (b) 12.50 cm (c) 50.00 cm (d) 100.00 cm24. Medium 1 has the electrical permitivity 1=1.5 0 farad/m and occupies the regionto the left of x = 0 plane. Medium 2 has the electrical permitivity 2 = 2.5 0

farad/m and occupies the region to the right of x = 0 plane. If E1 in medium 1 is

E1 2ux −3uy 1uz volt/m, then E2 in medium 2 is

(a) 2.0 7.5 2.5 x y z u −u u volt/m (b) 2.0 2.0 0.6 x y z u −u u volt/m

(c) 1.2 3.0 1.0 x y z u −u u volt/m (d) 1.2 2.0 0.6 x y z u −u u volt/m25.If the electric field intensity associated with a uniform plane electromagneticwave traveling in a perfect dielectric medium is give by

E z, t 10cos 2107t 0.1zvolt/m, then the velocity of the traveling waveis(a) 3.00 108 m/sec (b) 2.00 108 m/sec(c) 6.28 107 m/sec (d) 2.00 107 m/sec26. The phase velocity of an electromagnetic wave propagating in a hallow metallicrectangular waveguide in the TE10 mode is(a) equal to its group velocity(b) less than the velocity of light in free space(c) equal to the velocity of light in free space(d) greater than the velocity of light in free space27. A plane electromagnetic wave propagating in free space in incident normally on alarge slab of loss-less, non-magnetic, dielectric material with >0. Maxima andminima are observed when the electric field is measured in front of the slab. Themaximum electric field is found to be 5 times the minimum field. The intrinsicimpedance of the medium should be

(a) 120 (b) 60 (c) 600 (d) 24

A lossless transmission line is terminated in a load which reflects a part of theincident power. The measured VSWR is 2. the percentage of the power that isreflected back is(a) 57.73 (b) 33.33 (c) 0.11 (d) 11.11

11. Tutorial Question sets

Unit-I

1.Point charges Qx = 5 jtC and Q2 = - 4 /xC are placed at (3, 2, 1) and (-4, 0, 6), respectively. Determine the force on Qx.2. Five identical 15-/*C point charges are located at the center and corners of a squaredefined by - 1 < x, y < 1, z = 0.(a) Find the force on the 10-/*C point charge at (0, 0, 2).(b) Calculate the electric field intensity at (0, 0, 2).3. Point charges Qx and Q2 are, respectively, located at (4,0, -3) and (2,0, 1). IfQ2 = 4 nC, find Qx such that(a) The E at (5, 0, 6) has no z-component(b) The force on a test charge at (5, 0, 6) has no jc-component.4. Charges + Q and + 3Q are separated by a distance 2 m. A third charge is located such thatthe electrostatic system is in equilibrium. Find the location and the value of the thirdcharge in terms of Q.5. Determine the total charge

(a) On line 0 < x < 5 m if pL = \2x2 mC/m(b) On the cylinder p = 3, 0 < z < 4 m if ps = pz2 nC/m2

6.A point charge 100 pC is located at ( 4 , 1 ,— 3) while the x-axis carries charge 2 nC/m. If

the plane z = 3 also carries charge 5 nC/m2, find E at (1, 1, 1).7. Linex = 3, z = — 1 carries charge 20 nC/m while plane x = —2 carries charge 4 nC/m2.Find the force on a point charge - 5 mC located at the origin.

8.State Gauss's law. Deduce Coulomb's law from Gauss's law thereby affirming thatGauss's law is an alternative statement of Coulomb's law and that Coulomb's law is implicitin Maxwell's equation V • D = pv

9.Determine the work necessary to transfer charges Q\ = \ mC and Q2 = —2 mC frominfinity to points ( — 2, 6, 1) and (3, —4, 0), respectively.

10. A point charge Q is placed at the origin. Calculate the energy stored in region r > a.

11. Find the energy stored in the hemispherical region r < 2 m , 0 < 6 < it, whereE = 2r sin 8 cos <j> ar + r cos 6 cos <f> ae — r sin <j> a^ V/mexists.

Unit-II

1. A conducting sphere of radius 10 cm is centered at the origin and embedded in a dielectricmaterial with e = 2.5eo. If the sphere carries a surface charge of 4 nC/m2, find E at( — 3 cm, 4 cm, 12 cm).2. At the center of a hollow dielectric sphere (e = eoer) is placed a point charge Q. If thesphere has inner radius a and outer radius b, calculate D, E, and P.

3.Two homogeneous dielectric regions 1 (p < 4 cm) and 2 (p > 4 cm) have dielectricconstants 3.5 and 1.5, respectively. If D2 = 12ap - 6a0 + 9az nC/m2, calculate: (a) Eiand D,, (b) P2 and ppv2, (c) the energy density for each region.

4. The region between x = 0 and x = d is free space and has pv = po(x — d)ld. IfV(x = 0) = 0 and V(x = d) = Vo, find: (a) V and E, (b) the surface charge densities atx = 0 and x = d.

5.A parallel-plate capacitor has plate area 200 cm2 and plate separation 3 mm. The chargedensity is 1 /xC/m2 with air as dielectric. Find(a) The capacitance of the capacitor(b) The voltage between the plates(c) The force with which the plates attract each other

6.Two conducting plates are placed at z = — 2 cm and z = 2 cm and are, respectively,maintained at potentials 0 and 200 V. Assuming that the plates are separated by apolypropylene (e = 2.25eo). Calculate: (a) the potential at the middle of the plates,(b) the surface charge densities at the plates.

7.Two point charges of 50 nC and - 2 0 nC are located at ( - 3 , 2, 4) and (1, 0, 5) above theconducting ground plane z = 2. Calculate (a) the surface charge density at (7, —2, 2),(b) D at (3, 4, 8), and (c) D at (1, 1, 1).

Unit-III

1. (a) State Biot-Savart's law(b) The y- and z-axes, respectively, carry filamentary currents 10 A along ay and 20 Aalong -az. Find H at ( - 3 , 4, 5).

2. A 3-cm-long solenoid carries a current of 400 mA. If the solenoid is to produce a magneticflux density of 5 mWb/m , how many turns of wire are needed?3. A solenoid of radius 4 mm and length 2 cm has 150 turns/m and carries current 500 mA.Find: (a) [H at the center, (b) |H | at the ends of the solenoid.

4.(a) State Ampere's circuit law.(b) A hollow conducting cylinder has inner radius a and outer radius b and carries current Ialong the positive z-direction. Find H everywhere.

5.For a current distribution in free space,A = {2x2y + yz)ax + {xy2 - xz3)ay - (6xyz ~ 2jc2.y2 )az Wb/m(a) Calculate B.(b) Find the magnetic flux through a loop described by x = 1, 0 < y, z < 2.(c) Show that V • A = 0 and V • B = 0.

Unit-IV

1. A medium is characterized by a = 0, n = 2/*,, and s = 5eo. If H = 2cos {(jit — 3y) a_, A/m, calculate us and E.

2. conducting circular loop of radius 20 cm lies in the z = 0 plane in a magnetic fieldB = 10 cos 377? az mWb/m2. Calculate the induced voltage in the loop.

3. A 30-cm by 40-cm rectangular loop rotates at 130 rad/s in a magnetic field 0.06 Wb/m2

normal to the axis of rotation. If the loop has 50 turns, determine the induced voltage inthe loop.

4. Show that in a source-free region (J = 0, pv = 0), Maxwell's equations can be reducedto two. Identify the two all-embracing equations.

Unit-V and Unit-VI

1. 10.1 An EM wave propagating in a certain medium is described byE = 25 sin (2TT X 106f ™ 6x) a, V/m(a) Determine the direction of wave propagation.(b) Compute the period T, the wavelength X, and the velocity u.(c) Sketch the wave at t = 0, 778, 774, 772.

2. 10.4 A lossy material has /x = 5fio, e = 2eo. If at 5 MHz, the phase constant is 10 rad/m, calculate(a) The loss tangent(b) The conductivity of the material(c) The complex permittivity(d) The attenuation constant(e) The intrinsic impedance

3. A nonmagnetic medium has an intrinsic impedance 240 /30° 0. Find its(a) Loss tangent(b) Dielectric constant(c) Complex permittivity(d) Attenuation constant at 1 MHz

4. The amplitude of a wave traveling through a lossy nonmagnetic medium reduces by18% every meter. If the wave operates at 10 MHz and the electric field leads the magneticfield by 24°, calculate: (a) the propagation constant, (b) the wavelength, (c) the skindepth, (d) the conductivity of the medium.

5. A 5-GHz uniform plane wave Efa = 10 e~jl3z ax V/m in free space is incident normallyon a large plane, lossless dielectric slab (z > 0) having s = 4e0, /u. = /x0. Findthe reflected wave ErJ and the transmitted wave Ets.

6. The plane wave E = 50 sin (o)t — 5x) ay V/m in a lossless medium (n = 4/*o,e = so) encounters a lossy medium (fi = no, e = 4eo, <r = 0.1 mhos/m) normal tothe x-axis at x = 0. Find(a) F, T, and s(b) ErandHr

(c) ErandH,(d) The time-average Poynting vectors in both regions

7. If the plane wave of Practice Exercise 10.10 is incident on a dielectric mediumhaving a = 0, e — 4eo, /x = /to and occupying z ^ 0 , calculate

(a) The angles of incidence, reflection, and transmission(b) The reflection and transmission coefficients(c) The total E field in free space(d) The total E field in the dielectric(e) The Brewster angle.

8. Calculate the skin depth and the velocity of propagation for a uniform plane wave at frequency6 MHz traveling in polyvinylchloride {p.r — 1, er = 4, tan 8V = 1 X 10~2).

9. A uniform plane wave in a lossy medium has a phase constant of 1.6 rad/m at 107 Hz andits magnitude is reduced by 60% for every 2 m traveled. Find the skin depth and speed ofthe wave.

10. Show that in a good conductor, the skin depth 8 is always much shorter than the wavelength.

11. A polarized wave is incident from air to polystyrene with fx = no, e = 2.6e at Brewsterangle. Determine the transmission angle.

Unit-VII and Unit-VIII

1. A telephone line has the following parameters:R = 40 fi/m, G = 400 /iS/m, L = 0.2 /xH/m, C = 0.5 nF/m(a) If the line operates at 10 MHz, calculate the characteristic impedance Zo and velocity

u. (b) After how many meters will the voltage drop by 30 dB in the line?

2. A distortionless line operating at 120 MHz has R = 20 fi/m, L = 0.3 /xH/m, andC = 63 pF/m. (a) Determine 7, u, and Zo. (b) How far will a voltage wave travel beforeit is reduced to 20% of its initial magnitude? (c) How far will it travel to suffer a 45°

phase shift?

3. A coaxial line 5.6 m long has distributed parameters R = 6.5 fi/m, L = 3.4/xH/m,G = 8.4 mS/m, and C = 21.5 pF/m. If the line operates at 2 MHz, calculate the characteristic impedance and the end-to-end propagation time delay4. A lossless transmission line operating at 4.5 GHz has L = 2.4 /xH/m and Zo = 85 ohmCalculate the phase constant j3 and the phase velocity u.

5. A 50-fi coaxial cable feeds a 75 + J20-Q dipole antenna. Find T and s6. A quarter-wave lossless 100-fi line is terminated by a load ZL = 210 Q. If the voltage atthe receiving end is 80 V, what is the voltage at the sending end?7. A 60-fi lossless line is connected to a source with Vg = 10/CT l/ms and Zg = 50 -7'40 fi and terminated with a load j40 0. If the line is 100 m long and /3 = 0.25 rad/m,calculate Zin and V at(a) The sending end(b) The receiving end(c) 4 m from the load(d) 3 m from the source8. A 60-fi air line operating at 20 MHz is 10 m long. If the input impedance is 90 + jl50 fi.calculate ZL, T, and s.9. The observed standing-wave ratio on a 100-ft lossless line is 8. If the first maximumvoltage occurs at 0.3A from the load, calculate the load impedance and the voltage reflectioncoefficient at the load.10. A 50-fl line is terminated to a load with an unknown impedance. The standing wave ratios = 2.4 on the line and a voltage maximum occurs A/8 from the load, (a) Determine theload impedance, (b) How far is the first minimum voltage from the load?11. It is desired to match a 50-fi line to a load impedance of 60 — j50 fi. Design a 50-fi stubthat will achieve the match. Find the length of the line and how far it is from the load.11. A 60-fi lossless line is connected to a 40-0 pulse generator. The line is 6 m long and isterminated by a load of 100 0. If a rectangular pulse of width 5/x and magnitude 20 V issent down the line, find V(0, t) and /(€, t) for 0 < t < 10 jus. Take u = 3 X 108 m/s.12. A 50-fi microstrip line has a phase shift of 45° at 8 GHz. If the substrate thickness ish = 8 mm with er = 4.6, find: (a) the width of the conducting strip, (b) the length of themicrostrip line.

12. List of topics for student’s seminars

1. Basics of Vectors2. Types of capacitors3. Electricity and magnetism4. Dielectric materials5. Polarization and TIR6. Reflection, Refraction and other basics of Optics

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