## Solutions for Elements Of Electromagnetics

# Browse All Chapters of This Textbook

Chapter MA - Math AssessmentChapter 1 - Vector AlgebraChapter 1.6 - Position And Distance VectorsChapter 1.8 - Components Of A VectorChapter 2 - Coordinate Systems And TransformationChapter 2.4 - Spherical Coordinates (r, Θ, ɸ)Chapter 2.5 - Constant-coordinate SurfacesChapter 3 - Vector CalculusChapter 3.2 - Differential Length, Area, And VolumeChapter 3.3 - Line, Surface, And Volume Integrals

Chapter 3.5 - Gradient Of A ScalarChapter 3.6 - Divergence Of A Vector And Divergence TheoremChapter 3.7 - Curl Of A Vector And Stokes's TheoremChapter 3.8 - Laplacian Of A ScalarChapter 3.9 - Classification Of Vector FieldsChapter 4 - Electrostatic FieldsChapter 4.2 - Coulomb's Law And Field IntensityChapter 4.3 - Electric Fields Due To Continuous Charge DistributionsChapter 4.4 - Electric Flux DensityChapter 4.6 - Applications Of Gauss's LawChapter 4.7 - Electric PotentialChapter 4.8 - Relationship Between E And V-maxwell's EquationChapter 4.9 - An Electric Dipole And Flux LinesChapter 4.10 - Energy Density In Electrostatic FieldsChapter 5 - Electric Fields In Material SpaceChapter 5.4 - ConductorsChapter 5.7 - Linear, Isotropic, And Homogeneous DielectricsChapter 5.9 - Boundary ConditionsChapter 6 - Electrostatic Boundary-value ProblemsChapter 6.4 - General Procedures For Solving Poisson's Or Laplace's EquationChapter 6.5 - Resistance And CapacitanceChapter 6.6 - Method Of ImagesChapter 7 - Magnetostatic FieldsChapter 7.2 - Biot-savart's LawChapter 7.4 - Applications Of Ampère's LawChapter 7.7 - Magnetic Scalar And Vector PotentialsChapter 8 - Magnetic Forces, Materials, And DevicesChapter 8.2 - Forces Due To Magnetic FieldsChapter 8.4 - A Magnetic DipoleChapter 8.6 - Classification Of MaterialsChapter 8.7 - Magnetic Boundary ConditionsChapter 8.9 - Magnetic EnergyChapter 8.11 - Force On Magnetic MaterialsChapter 9 - Maxwell's EquationsChapter 9.3 - Transformer And Motional Electromotive ForcesChapter 9.4 - Displacement CurrentChapter 9.7 - Time-harmonic FieldsChapter 10 - Electromagnetic Wave PropagationChapter 10.2 - Waves In GeneralChapter 10.3 - Wave Propagation In Lossy DielectricsChapter 10.6 - Plane Waves In Good ConductorsChapter 10.7 - Wave PolarizationChapter 10.8 - Power And The Poynting VectorChapter 10.9 - Reflection Of A Plane Wave At Normal IncidenceChapter 10.10 - Reflection Of A Plane Wave At Oblique IncidenceChapter 10.11 - Application Note-microwavesChapter 11 - Transmission LinesChapter 11.3 - Transmission Line EquationsChapter 11.4 - Input Impedance, Standing Wave Ratio, And PowerChapter 11.7 - Transients On Transmission LinesChapter 11.8 - Application Note-microstrip Lines And Characterization Of Data CablesChapter 12 - WaveguidesChapter 12.4 - Transverse Electric ModesChapter 12.5 - Wave Propagation In The GuideChapter 12.7 - Waveguide Current And Mode ExcitationChapter 12.8 - Waveguide ResonatorsChapter 12.9 - Application Note-optical FiberChapter 13 - AntennasChapter 13.5 - Small-loop AntennaChapter 13.6 - Antenna CharacteristicsChapter 13.7 - Antenna ArraysChapter 13.8 - Effective Area And The Friis EquationChapter 13.9 - The Radar EquationChapter 14 - Numerical MethodsChapter 14.2 - Field PlottingChapter 14.3 - The Finite Difference MethodChapter 14.6 - Application Note-microstrip LinesChapter C - Matlab

### Book Details

Using a vectors-first approach,

Streamlined to facilitate student understanding,

*Elements of Electromagnetics*, Seventh Edition, covers electrostatics, magnetostatics, fields, waves, and applications like transmission lines, waveguides, and antennas. The text also provides a balanced presentation of time-varying and static fields, preparing students for employment in today's industrial and manufacturing sectors.Streamlined to facilitate student understanding,

*Elements of Electromagnetics*features worked examples in every chapter that explain how to use the theory presented in the text to solve different kinds of problems. It also covers numerical methods, including MATLAB and vector analysis, to help students analyze situations that they are likely to encounter in industry practice.# Sample Solutions for this Textbook

We offer sample solutions for Elements Of Electromagnetics homework problems. See examples below:

The angle between the two vectors A and B is θ. Suppose the inequality |A+B|<|A−B| exists. This...Suppose the unit vector is an=x′ax+y′ay+z′az. Perform dot product with ax on both sides of...Definition used: The vector differential operator is basically called the del operator (∇), which in...The vector is given as E=(4xy+z)ax+2x2ay+xaz and the points are A(3,7,1) to B(8,9,2) that forms the...Scalar: A quantity which is completely described by the magnitude alone is called as scalar...Given: P=2ax−ay−2azQ=4ax+3ay+2azR=−ax+ay+2az Calculation: Determine the vector term of (P+Q−R)....Calculation: Consider the following two vectors. A=(Ax,Ay, Az) (1) B=(Bx,By, Bz) (2) Calculate the...Given: P(xP,yP,zP)=(−1,4,8)Q(xQ,yQ,zQ)=(2,−1,3)R(xR,yR,zR)=(−1,2,3) Calculation: Write an expression...Given: P=Pxax+Pyay (I) Q=Qxax+Qyay (II) Calculation: Consider the two vectors P and Q. P=Pxax+Pyay...

Calculation: In spherical coordinates system, the variables θ and ϕ range as follows: 0≤θ≤π (or)...Given: F=xaxx2+y2+z2+yayx2+y2+z2+4azx2+y2+z2 . (I). Calculation: Write the expression for the vector...Given: A=ρsinϕap+ρcos aϕ+ρcosaz Calculation: Write the given vector A. A=ρsinϕap+ρcosϕ aϕ−2zaz Here,...Calculation: Write the matrix form of expression to find to the Cartesian coordinates from...The rectangular representation of the cuboid is as shown in below figure. Figure-(1) The dl length...Given: The scalar field (V(x,y,z)) is 10xyz−2x2z. The specified point (P) is (−1,4,3). Calculation:...Given: The two scalar functions U and V. Calculation: The gradient of the function (UV) is ∇(UV)....Given: The vector field is A. The scalar field is V. Calculation: Consider the vector field (A),...Given: The vector (T) is 2zyax+xy2ay+x2yzaz. The position vector (r) is xax+yay+zaz. Calculation:...Given: The vector field (A) is x2yax+y2zay−2xzaz. Calculation: Calculate the curl of vector field...Given: The vector (F) is x2yax−yay. The boundaries for L are as shown in the figure-(1). Figure-(1)...Given: The vector field F is 2ρzaρ+3zsinϕaϕ−4ρcosϕaz. The open surface is defined by the parameters,...Given: The slant height of the cone (l) is 2 m. The cone angle (θ) is 30°. The vector field (Q) is...Like charges repel each other and both the given charges are positive so, option (a) is correct. The...Given: The first charge (Q1) is Q. The second charge (Q2) is −Q. Location of the Q1 charge (r1) is...Given: Surface charge density (ρx) at x=2 is 10 μC/m2. Surface charge density (ρy) at y=−3 is −20...Given: The electric flux density D is 2ρ(z+1)cosϕ aρ−ρ(z+1)sinϕ aϕ+ρ2cosϕ az μC/m2. Calculation:...Given: The atomic radius is a. The volume charge density (ρv) is ρo(1−r2a2). Calculation: Calculate...Given: The electric field intensity (E) is 20rsinθar+10rcosθaθ V/m. The first point (A) is...Given: The potential distribution (V) is (2x2+4y2) V. Calculation: Calculate the electric field...Given: The electric flux density (D) is (2ρsinϕaρ−cosϕ2ρaϕ) C/m2. The limit of the radial axis (ρ)...Discussion: Convection current is different from conduction current and does not include conductors...Calculation: The potential field is, V=10x2yz−5z2 V Consider the general expression for electric...Calculation: Given, the electric interface is defined by 4x+3y=10 m and the electric flux density is...Calculation: Consider the general formula for polarization. P1=χeεoE1 P1=(εr1−1)εoE1 {∵χe=εr1−1} (1)...Calculation: Consider the general expression for dielectric interface. D1n=D2n (1) Consider the...Calculation: Refer to Figure given in the textbook. Given, the relative permittivity of glass is...Calculation: Consider that the Laplace and Poisson’s equations are related as follows. ∇⋅D=∇⋅εE=ρv...Calculation: Consider the given potential expression in option (a). V=2x+5 (1) Write the expression...Calculation: Write the expression for the electric field. E=−∇V=−(∂V∂xax+∂V∂yay+∂V∂zaz) Vm...Calculation: Calculate the electric field....Calculation: Consider the given potential expression. V1=3xyz+y−z2 (1) Write the expression for ∇V2....Calculation: Refer to FIGURE 6.31 in the textbook. Write the expression for the voltage V....Calculation: Consider the following expressions. V(x=0)=0 V V(x=d)=Vo V And ε=εo(1+xd) From the...Calculation: Write the expression for the electric field. E=E++E−=ρL2πεo(aρ1|aρ1|2−aρ2|aρ2|2)...Description: Charge movement with the constant velocity produces a static magnetic or magnetostatic...Calculation: Refer to given Figure in the textbook. Write the expression to calculate the magnetic...Calculation: Given field is, A=ycosaxax+(y+e−x)az Generally, the vector is a magnetostatic field if...Calculation: Given field is, D=y2zax+2(x+1)yzax−(x+1)z2az Generally, the vector is a magnetostatic...Calculation: Given the magnetic vector potential, A=(2x2y+yz)ax+(xy2−xz3)ay−(6xyz−2x2y2)az Wb/m...Calculation: The Del operator in a cylindrical coordinates is expressed as, ∇=∂∂ρaρ+1ρ∂∂ϕaϕ+∂∂zaz...Calculation: The variable R is the distance vector from the line element at the source point...Calculation: Write the general expression for electric force. Fe=QE (1) Here, Q is the electric...Calculation: Refer to the mentioned Figure given in the textbook. Consider the general expression to...Calculation: Write the general expression to calculate the force. F=IL×B or...Calculation: Write the general expression to calculate the force. F=∮LIdl×B (1) Here, Idl is the...Calculation: Given that, B2=10aρ+15aϕ−20az m Wb/m2 Consider, B2=(Bρ, Bϕ, Bz) in m Wb/m2. Consider...Calculation: Given that, f(x, y, z)=x−y+2z−5 Consider the expression for the normal unit vector....Calculation: Given that, the magnetic field intensity for air is, H1=10ax+15ay−3az A/m The magnetic...Calculation: Write the general expression to calculate the magnetic field intensity. H=12K×an (1)...Calculation: Consider the expression to find induced emf in a coil. Vemf=−Ndψdt Here, ψ is the flux...Calculation: Write the generalized forms of Maxwell’s four Equations. ∇⋅D=ρv (1) ∇⋅B=0 (2) ∇×E=−∂B∂t...Calculation: Write Maxwell’s Equations for a linear, homogeneous medium in terms of Es and Hs....Calculation: Find ∇⋅A. ∇⋅A=(∂∂xax+∂∂yay+∂∂zaz)⋅[40sin(ωt+10x)az]=∂∂z[40sin(ωt+10x)]=0 Find ∇×A....Calculation: Write the generalized form of Maxwell’s third Equation. ∇×E=−∂B∂t=−∂μH∂t {∵B=μH}=−μ∂H∂t...Calculation: Write the expression has to be satisfied by the given magnetic vector potential....Description: Write the expression of the given waveform: Ex=cos(ωt−βz) (1) Rewrite the expression in...Calculation: Write the expression for electric field component of given EM wave. E=40ρsin(ωt−2z)aρ...Calculation: Write the expression for given magnetic field in the air. H=4sin(ωt−5x)ay A/m (1)...Calculation: Write the expression for given incident electric field in region 1. Ei=5cos(108t+βy)az...Calculation: Write the expression for incident electric field in medium-1. Ei=60cos(ωt−β1z)ax V/m...Calculation: Write the expression for given incident electric field in medium-1 (air)....Calculation: Write the expression for given incident electric field in medium-1 (air)....Calculation: Consider the expression of reflection coefficient in the parallel polarization of...Calculation: Consider the expression to find the incidence angle. cos(θi)=ak⋅an Rearrange the...Calculation: Consider the expression to find the incidence angle. cos(θi)=ak⋅an Rearrange the...Calculation: A transmission line is described in terms of its line parameters, which are its...Calculation: Consider the general expression of input impedance for a lossless line....Calculation: Consider the general expression for line parameter R of a planar line. R=2wδσc (1)...Calculation: Consider the general expression for characteristic impedance of the line. Zo=R+jωLG+jωC...Calculation: Find the value of electrical length of the line. βl=14×100=25 rad=25×57.2958 {∵1...Calculation: Refer to the mentioned Figure given in the textbook. The relation between the input and...Calculation: Refer to Figure given in the textbook. Consider the general expression for input...Calculation: Consider the general formula for transformed load impedance at stub position z=−d....Calculation: Given, width is w=1.5 cm and h=1 cm. The ratio of line width to the substrate thickness...Description: Generally, transmission lines are used to guide the Electromagnetic (EM) energy from...Calculation: Given that the cutoff frequency fc of TE10 mode is 5 GHz and TE01 mode is 12 GHz. For...Calculation: Given dimensions a×b for the waveguide is 7.2 cm×3.4 cm, since a>b, the dominant...Calculation: Given dimensions a×b for the copper waveguide is 1 cm×2 cm. Write the expression to...Calculation: Given that the complex permittivity is , εc=16εo(1−j10−4) εc=16εo−j(16εo×10−4) (1)...Calculation: Write the expression to calculate the cutoff frequency for TE10 mode. fc=u′2a (1) Here,...Calculation: Given dimensions a×b for the waveguide is 2.5 cm×1.5 cm, since a>b, the dominant...Calculation: Write the general expression to calculate the speed. speed=distancetime (1) Rearrange...Calculation: Given that, As=50e−jβrrax where r2=x2+y2+z2. Using vector transformation (in spherical...Calculation: Using the mentioned equation given in the textbook,...Calculation: Consider the mentioned equation given in the textbook, dAzs=μIocosβzdz4πr'e−jβr' (1)...Calculation: Write the general relationship between the electric and magnetic field intensity....Calculation: Write the general expression to calculate the directivity (D). D=UmaxUave (1) Here,...Calculation: Write the general expression to calculate the directivity (D). D=UmaxUave (1) Here,...Calculation: Consider the given expression for the electric field. E=0.3ax−0.4ay V/m (1) Write the...Calculation: Refer to Figure 14-60 in the textbook for the two-element region. For element 1, local...Calculation: Refer to Figure 14-61 in the textbook for the two-element region. Modify Figure 14-61...Calculation: Refer to Figure 14-62 in the textbook for the two-element mesh. For element 1, local...Calculation: Consider the given equations. 3x1−x2−2x3=1 (1) −x1+6x2−3x3=0 (2) −2x1−3x2+6x3=6 (3)...

# More Editions of This Book

Corresponding editions of this textbook are also available below:

Elements of Electromagnetics

5th Edition

ISBN: 9780195387759

Elements of Electromagnetics

7th Edition

ISBN: 9780190698669

EBK ELEMENTS OF ELECTROMAGNETICS

6th Edition

ISBN: 8220101369376

Elements of Electromagnetics (The Oxford Series in Electrical and Computer Engineering)

6th Edition

ISBN: 9780199321384

Elements of Electromagnetics

6th Edition

ISBN: 9780190213879

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