# Subject: Field Theory (2140909) - Fetr

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Subject: Field Theory (2140909)B.E. – Second year [Fourth Semester]Branch – Electrical EngineeringTerm: 16/2 (Jan-17 to May-17)Faculty: Prof. L.S.PATELProf. T.M. PANCHAL1.2.3.4.5.6.7.Prof. S. P. SHAHProf. K.C.SHAHContents:Course OutcomesCourse Contents[Syllabus]List of Reference BooksList of ExperimentsMajor Equipments required for ExperimentsList of Open source software and learning websites required forexperimentsActive Learning Assignments and Tutorial.Instructions For Assignment/Tutorial: This set of Assignment-Tutorial consist the collection of questions of past GTUQuestion papers. Attend those questions which are bold marked and/or frequently asked inGTU exam. Students should make a separate Chapter wise Files[write on File Pages] tosolve these Questions. Students must solve these given set of Assignments by themselves only. Assessment of given assignment should be done regularly after completion ofeach chapter by Students from the respective faculty members.

 Course Outcomes:1. Vector Algebra and Different Co-ordinate System2. Laws governing to Electric Field Intensity and their application3. Laws governing to Electric Flux density and their application4. Potential and Energy of the charge in an Electrostatic Fields5. Nature and Boundary Condition of Dielectric Materials6. Poisson’s and Laplace’s Equations’ Application7. Laws governing to Steady Magnetic Fields and their application8. Types of Inductance, Nature of Magnetic materials and Magnetic Forces on CurrentElements9. Lossless Propagation of Transmission Line and its Equation Solution10. Electromagnetic Interference and Compatibility

 Course htageVector AnalysisScalars and Vectors, Vector Algebra, The rectangularcoordinate system, Vector components and unit vectors, Thevector field, The dot product, The cross product, Circularcylindrical co-ordinates, Spherical co-ordinate system.39Coulomb’s law and Electric Field IntensityThe experimental law of Coulomb, Electric field intensity,Field due to a continuous volume charge distribution, Field ofa line charge, Field of a sheet charge.49Electric Flux Density, Gauss’ law and DivergenceElectric flux density, Gauss’ law, Application of Gauss’ law:some symmetrical charge distributions, Application ofGauss’ law to differential volume element, Divergence,Maxwell’s first equation, The divergence theorem.Energy and PotentialEnergy expended in moving a point charge in electric field,The line integral, Definition of potential and potentialdifference, The potential field of a point charge, Thepotential field of a system of charges, Potential gradient, Thedipole, Energy density in the electrostatic field.Current and ConductorsCurrent and current density, Continuity of current, Metallicconductors, Conductor properties and boundary conditions,Semiconductors.Dielectrics and capacitanceThe nature of dielectric materials, Boundary conditionsfor perfect dielectric materials, Capacitance, Severalcapacitance examples, Capacitance of a two wire line.Poisson’s and Laplace’s EquationDerivation of Poisson’s and Lapalce’s equations, Uniquenesstheorem, Example of the solution of Laplace’s equationExample of solution of Poisson’s equation.The Steady Magnetic FieldBiotSavart law, Ampere’s circuital law, Curl, Stoke’s theorem,Magnetic flux and magnetic flux density, The scalar and vectormagnetic potentials, Derivation of steady magnetic field laws.4949373738410

9101112Magnetic Forces, Materials and InductanceForce on a moving charge, Force on a differential currentelement, Force between differential current elements, Forceand torque on a closed circuit, The nature of magneticmaterials, Magnetization and permeability, Magneticboundary conditions, The magnetic circuit, Potential energyand forces on magnetic materials, Inductance and mutualinductance.Time Varying Fields and Maxwell’s equationFaraday’s Law, Displacement current, Maxwell’s equation inpoint form, Maxwell’s equation in integral form.Transmission LinesPhysical description of transmission line propagation, Thetransmission line equation, Lossless propagation, Losslesspropagation of sinusoidal voltages, Complex analysis ofsinusoidal voltages, Transmission line equations and theirsolutions in phasor form.Effects of Electromagnetic FieldsElectromagnetic Interference and Compatibility (EMI/EMC),EMI Sources, Effects of EMI, Methods to eliminate EMI, EMCStandards, Advantages of EMC standards, Biological effects ofEMI/EMR (Electromagnetic Interference, Electromagneticradiation).49374838 Text Books:1. William Hart Hayt and John A. Buck. Engineering Electromagnetics, McGraw-HillEducation, 2006.2. Field Theory by Uday A. Bakshi and Ajay V.Bakshi, Technical Publications.3. Matthew N. O. Sadiku, Principles of Electromagnetics, fourth edition, Oxford university press,2007.4. Fundamentals of Engineering Electromagnetics by Sunil Bhooshan, Oxford University Press.5. Nathan Ida, “Engineering Electromagnetics” Second edition, Springer, Indian Edition, 2005.Reference Book:1. Problems & Solutions of Engineering Electromagnetics by CBS Problems & SolutionsSeries.2. Electromagnetic Field Theory and Transmission Lines by G.S.N. Raju, Pearson Education.3. Fundamentals of Electromagnetics by A.V. Mahatme, University Science Press.4. Elements of Electromagnetics by Matthew N.O. Sadiku, Oxford University Press.5. Electromagnetics with Applications by Kraus and Fleisch, Tata McGraw Hill Publications.

 List of Experiments:SR.NO.LIST OF PRACTICALSINTRODUCTION TO THE MATLAB 2010 SOFTWARE.1.EXECUTE A PROGRAM TO COMPUTES SCALER , VECTORS,CO-ORDINATE2.SYSTEMS AND FIELDSWRITE A PROGRAM COMPUTES COORINATES FOR VARIOUS COORDINATESYSTEMS:1. CARTESIAN TO POLAR2. CARTESIAN TO SPHERICAL3. POLAR TO CARTESIAN4. SPHERICAL TO CARTESIANWRITE A PROGRAMME TO FIND FORCE BETWEEN TWO CHARGES IN3.4.ELECTRIC FIELD.EXECUTE A PROGRAM COMPUTES THE POTENTIAL DIFFERENCE BETWEEN5.TWO POINTS DUE TO A POINT CHARGE.EXECUTE A PROGRAM COMPUTES THE CAPACITANCE OF CO-AXIAL CABLEOF THE CONDUCTOR.EXECUTE A PROGRAM COMPUTES A MAGNETIC FIELD ON THE AXIS OF AROTATING CHARGED DISC.6.7.8.TUTORIAL NO 19.TUTORIAL NO 210.TUTORIAL NO 3 Major Equipments required for Experiments : Computers: Intel core i5 CPU 500 GB Hard disk 4 GB DDR-3 RAM 18.5” LCD Monitor Keyboard, MouseList of Open source software and learning websites requiredfor experiments :1. Numericals based on solving Engg. Electromagnetics problems using MATLABfor tutorials are available in CD accompanied with the book of “Fundamentals ofEngineering Electromagnetics by Sunil Bhooshan”2. Matlab Experiments manual for Electromagnetics by Dr. M.H. Bakr

 Learning Assignments / Tutorial :ChapterNo.1TopicTeachingHrs.Vector AnalysisScalars and Vectors, Vector Algebra, The rectangularcoordinate system, Vector components and unit vectors,The vector field, The dot product, The cross product,Circular cylindrical co-ordinates, Spherical co-ordinatesystem.ModuleWeightage39 ATTEMPT THREE THEORY AND SIX EXAMPLES:SR.NO.1.2.3.4.5.6.7.8.9.QUESTIONSExplain dot product and cross product of two vectors. AlsoDEC-11explain unit vectors of Cartesian, cylindrical and spherical coJAN-13ordinate systems.Explain cylindrical coordinate system, differential elements andtransformation method from cylindrical to Cartesian coordinate JUNE-13system.Explain the physical significance of the term: (i) Divergence of aMAY-13vector field and (ii) curl of a vector field.Give the basic concepts of transformation of one coordinate systemMAY-13to another.Explain spherical coordinate system. Explain conversion fromDec-14cylindrical to spherical system.Explain cylindrical coordinate system in brief. Also write theequations of differential length, differential surfaces andMAY-15Differential volume elements.Explain Cartesian co-ordinate system along with the equationsof differential length, differential surfaces and differentialvolume elements.Give the importance of unit vectors. And discuss the concepts ofdifferential surface vector.Draw the figure for the orthogonal system which has its secondcoordinate is angle made by cone and z- axis. Transform the coordinates of this system in to Cartesian co-ordinate11.Explain spherical coordinate system in brief. Also write the equationsof differential length, differential surfaces and differential volumeelements.Write down equation for , and for spherical coordinate system.12.Cylindrical coordinate 'z' is related to the Cartesian coordinate JUN-1603JUN-1602JUN-1602

.a) tan 1(y/x) (b) z (c) xy/z (d) cot zCurl of the gradient of scalar magnetic potential is(a) zero (b) 1 (c) -1 (d) undefinedWrite the equation for point form of Ohm’s lawNOV-1602NOV-1602NOV-160216.In a spherical co-ordinate system θ constant is a plane (True orFalse)Explain how dot product and cross product of vectors is carried outNOV-160317.Explain cylindrical co-ordinate system of vectors in .Let each of the vectors A 5ax –ay 3az, B -2ax 2ay 4az andC 3ay-4az extend outward from the origin of a Cartesiancoordinate system to points A, B and C respectively. Find a unitMAY-11vector directed from point A toward: (a) to the origin; (b) pointB; (c) appoint equidistance from B and C on the line BC; (d)Findthe length of the perimeter of the triangle ABC.Given points A( x 2, y 3, z -1) and B(ρ 4, Φ -50, z 2), find aunit vector in cylindrical coordinates at point B directed towards MAY-11point A.Given the point A( x 2 ,y 3 ,z -1) and B( r 4 , θ 250 ,Φ 1200 )Find(a) The spherical co-ordinates of ADEC-11(b) The Cartesian co-ordinates of B(c ) The distance from A to B.Obtain the spherical co-ordinates of 10 āx at the point P(x - 3, y 2,MAY-12z 4).Find Ē at the origin if the following charge distributions arepresent in free space: 1) point charge 12 nC at P (2,0,6), 2)MAY-12uniform line charge density 3 nC/m at x - 2, y 3, 3) uniformsurface charge density 0.2 nC/m2 at x 2.Transform the vector 4ax 2ay 4az into spherical coordinates JUNEat a point P (x 2, y 3, z 4).13Transform the following vectors to spherical coordinates at thepoints given: (a) 10ax at P (x -3, y 2, z 4); (b) 10ay at Q (rho 5, DEC-13Ø 300, z 4); (c) 10az at R(r 4, 1100, Ø 1200).The two vectors are F 10 ax - 6 ay 5 az and G 0.1 ax 0.2ay 0.3 az(i) Find the vector component of F that is parallel to G (ii) Find Dec-14the vector component of F that is perpendicular to G (iii) Findthe vector component of G that is perpendicular to F.If G 5 r sin2 θ cos2 Φ are valuate both sides of DivergenceDEC-14theorem for the region r 2.Find spherical coordinates of 10 axat the point P (-3, 2, 4).DEC-1407070707070707070707

MAY-1507DEC-1507Given points A (x 2 , y 3, z -1) and B ( 4, -500,z 2). Find a unitvector in Cylindrical coordinate(a)At point B directed towards point A(b) At point A directed towards point BJUN-1607A triangle is defined by the three points A (2,-5, 1), B (-3, 2, 4), and C (0,3, 1) Find: (a) X ; (b) The area of the triangle; (c) A unit vectorperpendicular to the in which the triangle 4.15.16.17.ThegivenpointsareA(x 2,y 3,z 1)andB(r 4,θ 25ᵒ,ϕ nco-ordinatesofBand(iii)from A to B.DistanceThe cross product of the same vector to itself is .(a) 0 (b) 1 (c) (d) 100The divergence of is(a) scalar (b) vector (c)curl of F(d) none of thisPoints A(r 100, θ 900, Φ 0) and B (r 100, θ 900, Φ 50) arelocated on the surface of a 100m radius sphere (i) What is theirseparation using a path on the spherical surface? (ii) What isseparation using a straight line path? Give the answer upto fourdecimal places after the decimal point.

ChapterNo.2TopicCoulomb’s law and Electric Field IntensityThe experimental law of Coulomb, Electric field intensity,Field due to a continuous volume charge distribution, Fieldof a line charge, Field of a sheet charge.TeachingHrs.ModuleWeightage49 ATTEMPT THREE THEORY AND FOUR ONYEARDefine electric field intensity. Obtain an expression for the electric field MAY-11intensity at a point which is at a distance of R from a point charge Q.JAN-13Write short note: Electrostatic boundary conditions between perfectMAY-11dielectrics.Describe coulomb’s law also explain concept of electric potentialDEC-11difference.Derive expression of electric field intensity due to a uniform line JAN-13charge over z-axis having a charge density of P C/m.ORDEC-13Define Electric field intensity. Derive the necessary equation for Dec-14electric filed Intensity due to line charge.Develop an Expression for electric field intensity at a general point P due to aMAY-14semi –infinite straight line charge with charge density ρl C/m.Derive the expression for total electric field intensity due to infiniteJUNE-13surface charge distribution in free space.Derive the equation of total electric field intensity in vector form due toMAY-15infinite uniform sheet charge distribution in free space.Derive the expressionof (Electricfieldintensity) at any point P due toDEC-15infinite uniform line charge distribution in free space.State coulomb’s law of electric for various type of charge distribution.JUN-16NOV-16Write down Streamlines equation of electric field intensity for (r, θ, Φ)JUN-16and (ρ, Φ, z)1) The proportionality constant in Coulomb’s law has a unit ofNOV-16(a) Farad (b) Farad/metre (c) Newton/metre (d) metre/FaradIf a pair of ( )ve and (-ve) charges of 1C are separated by a distance of 1 μm,the magnitude of dipole moment isNOV-16(a) 1C- μm (b) 1C/ μm (c) zero (d) 2C- μmDerive the expression for electric field intensity due to line chargeNOV-16EXAMPLESFind the total charge inside a volume having volume charge density as1. 10z2e-0.1xsinπy c/m3. The volume is defined between -2 x 2, 0 y 1and 3 z 4.An electric potential is given by,2.V 60sinθ / r2 volt. Find V and E atP(3, 600, 250).3. A charge of -0.3 μC is located at A(25,-30,15) (in cm), and a second 107DEC-1307

of 0.5 μC is at B(-10,8,12) cm. Find Electric field intensity E at (a) theorigin; (b) P(15,20,50) cm.Potential is given by V 2(x 1)2 (y 2)2 (z 3)2 V in free space. At point P (2,-1,4)4. calculate : (i) The potential at point P, (ii) electric field intensity E at point P,(iii)volume charge density at P.Find E at P(1,5,2) in free space if a point charge of 6 μC is located at5. Q(0,0,1),a uniform line charge of 180 nC/m lies along the x axis and auniform sheet of charge equal to 25 nC/m2 lies in the plane z - 507NOV-1607NOV-1604NOV-16038.9.10.11.12.An infinite uniform line charge having line charge density of ρL 200nC/m placed on the z-axis. Find the total electric field intensity at (6, 8,3) m.A circular ring with radius of 5 m lies on z 0 plane with its center atorigin. If ρL 10 nC/m, find value of a point charge Q placed at originwhich will produce the same value of(Electric field intensity) atpoint (0, 0, 5) m.A point charge Q1 2μC is located at P1(3,7,-4) and Q2 -5μC is at P2 (2,4,1) At a point (12,15,18) find (i) E (ii) E (iii) aEWhat net flux crosses the closed surface which contains charge distributionin the form of a plane disc of radius 4m in z 0 plane with ρs sin2Φ/2ρIf E 2xax – 4yay V/m find the work done in moving a point charge of 2Cfrom (2,0,0) to (0,0,0) to (0,2,0)

ChapterNo.3TopicElectric Flux Density, Gauss’ law and DivergenceElectric flux density, Gauss’ law, Application of Gauss’law:some symmetricalchargedistributions,Applicationof Gauss’lawtodifferential Thedivergence theorem.TeachingHrs.ModuleWeightage49 ATTEMPT THREE THEORY AND ONE EXAMPLE:SRNO.QUESTIONYEARMARKS1.State and prove the Gauss’s law. Also state the conditions to be satisfiedby the special Gaussian surfaces.MAY-11072.State and explain gauss’s law. Obtain electric field intensity of linecharge using gauss’s lawORExplain the Gauss’s law applied to infinite line charge and derivethe expression for D due to infinite line charge.DEC-11MAY-12JAN-13JUNE-13NOV-16073.State and explain gauss’s law. Obtain electric field intensity of linecharge using gauss’s lawMAY-15074.Derive Maxwell’s first equation as applied to the electrostatics,using Gauss’s law. Also state the Divergence theorem.5.State and Explain Gauss Law. Explain Divergence Theorem.JAN-13MAY-14MAY-11Dec-146.Derive the Maxwell’s first equation applied to Electrostatic by usingequations of divergence and Gauss’s law for electric flux 1.12.13.Define divergence and its physical significance.Derive Maxwell’s first equation applied to electrostatic using Gauss’slaw.State and explain the gauss’s lawMaxwell's equations shelter on law(s).JUN-16(a) Faraday's (b) Gauss's (c) Ampere's (d) All of theseIn the case of a linear material medium, equation can be derivedeasily from Gauss' law.JUN-16(a) Poisson (b) Laplace (c) Both (a) and (b) (d) None of theseAnother boundary condition using Maxwell's equations is given as.JUN-16(a) Htan '1' Htan '2' 0 (b) Htan '1' Htan '2' 0 (c) Htan '1' Htan '2' Js (d) Htan '1' Htan '2' JsAt the Brewster angle, polarization .(a) Cannot be reflected (b) Is reflected at 30 JUN-16(c) Is reflected at 90 (d) None of these070702020202

14.15.16.Point form of Gauss’ law is(a) D ρs (b) D ρv (c) D ρv/𝜖0 (d) D QUnit of electric flux is(a) Coulomb (b) Weber (c) Tesla (d) Weber/mWrite Maxwell’s equations in integral form and point 07EXAMPLES1.2.3.The finite sheet 0 x 1, 0 y 1 on the z 0 plane has a chargedensity ρs xy (x2 y2 25)3/2 nC/m2. Find:1) The total charge on the sheet, 2) The electric field at (0, 0, 5)3) The force experienced by a – 1 mC charge located at (0, 0, 5).State Gauss’s Law. Find divergence D at the origin ifA co-axial conducting cylinder has charge density of ρs on the outersurface of the inner cylinder. Use Gauss’ law to find ‘D’ in all the regions.Assume that inner cylinder has radius of ‘a’ metres and outer cylinderhas radius of ‘b’ metres

ChapterNo.TopicTeachingHrs.ModuleWeightage49Energy and PotentialEnergy expended in moving a point charge in electricfield, The line integral, Definition of potential andpotential difference, The potential field of a point charge,The potential field of a system of charges, Potentialgradient, The dipole, Energy density in the electrostaticfield.4 ATTEMPT THREE THEORY AND FIVE 1.2.QUESTIONYEARExplain an electric dipole. Also derive expression of E due to an MAY-11electric dipole.JAN-13Define divergence and its physical significance.JUNE-13Explain potential and potential gradient. Derive relationship betweenJUNE-13potential and electric field intensity.Derive necessary equation for potential gradient from the electric filedDEC-13intensity by means of a line integral.Explain concept of potential gradient and prove that E - hipbetweenpotentialandelectrMAY-15ic fieldintensity.Derive equation of potential differencewith in the electric fieldMAY-15produced by a point charge .Derive expression of electric field intensity due to an electric dipole.DEC-15Derive relationship between potential and electric field intensity.DEC-15Express for electric field intensity at any point to a line charge with uniformJUN-16charge density C/m on the infinitely long Z-axis.Define the potential gradient. Derive relationship between potential andJUN-16electric field intensityDerive equation of energy stored in magnetic fields.JUN-16Emf is closed

1. Numericals based on solving Engg. Electromagnetics problems using MATLAB for tutorials are available in CD accompanied with the book of “Fundamentals of Engineering Electromagnetics by Sunil Bhooshan” 2. Matlab Experiments manual for Electromagnetics by Dr. M.H. Bakr SR. NO. LIST OF PRACTICALS 1. INTR

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