Elements of Electromagnetics7th EditionSadiku Publisher: Oxford University PressISBN: 9780190698669
Elements of Electromagnetics
Solutions for Elements of Electromagnetics
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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, Elements of Electromagnetics, Seventh Edition, covers electrostatics, magnetostatics, fields, waves, and applications like transmission lines, waveguides, and antennas. The text also provides a balanced presentatio
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: 9780190698614
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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