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Quiz_1_2010_soltns
Course: MAC 2234, Spring 2012School: University of Florida
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#1 A QUIZ 9a x 4a z B 8a x 6a z Q1: Find the cross product of the vectors A and B a 9a x 4a z 8a x 6a z 54(a x) 32(a z ) 86a y a x z a y ay Q2: Find the dot product of the vectors A and B 9a x 4a z 8a x 6a z 72 24 48 Q3: Convert the coordinates cylindrical of P(1,135,5) to rectangular coordinates. xP 1/ 2, yP 1/ 2, z P 5 Q4: The vector A = 2a exists at the point P with spherical...
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#1
A QUIZ 9a x 4a z
B 8a x 6a z
Q1: Find the cross product of the vectors A and B
a
9a x 4a z 8a x 6a z 54(a x) 32(a z ) 86a y
a x
z
a y
ay
Q2: Find the dot product of the vectors A and B
9a x 4a z 8a x 6a z 72 24 48
Q3: Convert the coordinates cylindrical of P(1,135,5) to
rectangular coordinates.
xP 1/ 2, yP 1/ 2, z P 5
Q4: The vector A = 2a exists at the point P with spherical
coordinates given as r = 1, = 90, = 180. Express A in terms
of its rectangular components.
A 2a z
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University of Florida - MAC - 2234
= 3y + 8zQUIZ #1 = 5y 2zQ1: Find the dot product of the vectors and . = 3 5 + 8 (2) = 1Q2: Find the cross product of the vectors and .x y z = 0 38 = x (3 (2) 5 8) + y (8 0 (2) 0) + z (0 5 0 3) = 46x0 5 2Q3: Convert the rectangular coordinates o
University of Florida - MAC - 2234
A 5a x 3a yB 4a x 11a yQUIZ #1Q1: Find the cross product of the vectors A and B(5a x 3a y ) ( 4a x 11a y ) 55a z 12( a z ) 67a zQ2: Find the dot product of the vectors A and B(5a x 3a y ) ( 4a x 11a y ) 20 33 13Q3: Convert the cylindrical coordinat
University of Florida - MAC - 2234
QUIZ #2Q1: What is the total charge Q on the following finite surface 2 m, 1.5 , 0.5 z 0.5 mcharged with a uniform density s = 1012 C/m2.Q s 0.5 ( zmax zmin ) 1012 0.5 2 1 1012 CQ2: Find the E field vector (in RCS) at the point P(0,0,0) due toan inf
University of Florida - MAC - 2234
QUIZ #2Q1: What is the total charge Q in the volume0 r 0.1 m, 0 / 2, 0 2if the volume charge density v is constant and equal to 1012 C/m3.2 1512 1 43Q = v v = 10 10 =10 C233r30Q2: Find the flux density vector D (in RCS) at the point P(0,0,0)
University of Florida - MAC - 2234
QUIZ #2Q1: What is the total charge Q in the volume0 0.05 m, 0 / 2, 0.005 z 0.005 mif the volume charge density is v = 1010 C/m3.Q2: Find the E field vector (in RCS) at the point P(0,0,0) due to aninfinite planar charge of density s = 1010 C/m2 distr
University of Florida - MAC - 2234
QUIZ #2Q1: What is the total charge Q in the volume0 0.05 m, 0 / 2, 0.005 z 0.005 mif the volume charge density is uniform and v = 1010 C/m3.25102Q vV 10 ( 0.05 ) 0.01 / 4 1016 19.6 1016 C4Q2: Find the E-field vector (in RCS) at the point P(0,0
University of Florida - MAC - 2234
QUIZ #3Q1: Find the divergence of the following vectorD xa x ya y x 2 ya zDx Dy DzD 1 1 0 0xyzQ2: Find the total flux through a sphere of radius a = 1 m centeredat the origin (0,0,0) due to an infinite uniformly charged line alongthe x axis of
University of Florida - MAC - 2234
QUIZ #3Q1: Find the divergence of the vector D (given below) at the pointP(2, 2, 2). Coordinates are rectangular and in meters.11D = a x za y + 2 a zxy D = 1 / x 2 D P = 1 / 4 = 0.25Q2: An infinite uniformly charged line of density l = 1012 C/mi
University of Florida - MAC - 2234
QUIZ #3Q1: Find the charge density v if the flux density vector is givenin CCS as D ( 1a 2 a za z ) 1012 , C/m2 .11 F FzHelp: F ( F ) zQ2: The point charge Q1 = 1 pC is located at the point (0,0,0) andthe point charge Q2 = 5 pC is located at
University of Florida - MAC - 2234
QUIZ #3Q1: Find the charge density v if the flux density vector is givenin CCS as D ( 1a 2 a za z ) 1012 , C/m2 .11 D Dz v D( D )(001)1012 1 pC/m 3 zQ2: The point charge Q1 = 1 pC is located at the point (0,0,0) andthe point charge Q2 = 5 pC i
University of Florida - MAC - 2234
QUIZ #4Q1: The E-field inside a parallel-plate capacitor has magnitude 1kV/m. Find the voltage applied to the capacitor if the distancebetween the two plates is 1cm.V E D 1000 0.01 10 VQ2: The potential in a region of space is given as V = 0.5x2+2y,
University of Florida - MAC - 2234
QUIZ #4Q1. The voltage applied to a parallel-plate capacitor is 10 V. If thedistance between the two plates is 1 cm, find the E-field 0.2 cmaway from one of the plates.= 10 / 0.01 1000 VE=Q2. The potential in a region of space is given as V = 0.5x3
University of Florida - MAC - 2234
QUIZ #4Q1: Two infinite large metal plates are placed at z = 1 mm, and z= 2 mm. The voltages applied to the two plates are 3 V and 3 V,respectively. Find the E-field at the origin.Q2: The potential in a region of space is given as V = 5x2 + 2y3 + 2zV
University of Florida - MAC - 2234
QUIZ #4Q1: Two infinite large metal plates are placed at z = 1 mm, and z= 2 mm. The voltages applied to the two plates are 3 V and 3 V,respectively. Find the E-field at the origin.V6E is constant: E a z a z a z 2000 V/m3D3 10Q2: The potential i
University of Florida - MAC - 2234
QUIZ #5Q1: An infinite straight wire with current 0.5 A lies along the xaxis. The current flows in the positive x direction. Find themagnetic field vector H and the flux density vector B at the point P(0,0,0.5) m. ( 0 4 107 H/m)I0.51H a y a y a
University of Florida - MAC - 2234
QUIZ #5Q1: Two infinite straight wires parallel to the x axis are located at y =1 m, z = 0 and y = 2 m, z = 0, respectively. They have the samecurrent of 1 A flowing in the positive x direction. Find the magneticfield vector H and the flux density vec
University of Florida - PHY - 2049
University of Florida - PHY - 2049
Lecture 1Orthogonal CoordinateSystems and TransformationsSections: 1.3, 1.4, 1.5, 1.8, 1.9 (1.2, 1.6, 1.7 covered in T01)Homework: See homework fileLECTURE 1 slide 1Coordinates and Position Vector in RCSexamplezPzOP0xPxP ( xP , y P , z P )y
University of Florida - PHY - 2049
University of Florida - PHY - 2049
Lecture 2Coulombs Law, Charge DensitySections: 2.1, 2.2, 2.3, 2.4, 2.5Homework: See homework fileLECTURE 2slide1Electric Charge 1The electric charge is a fundamental property of matter. It ismeasured in coulombs (C). The electric-current unit amp
University of Florida - PHY - 2049
University of Florida - PHY - 2049
Lecture 3Total Charge:Line, Surface and Volume IntegralsSections: 1.8, 1.9, 2.3Homework: See homework fileLECTURE 3slide1Line Elements 1metric increment due to a differential change in position along a line2-D SPACEpolar CSrectangular CSyya
University of Florida - PHY - 2049
University of Florida - PHY - 2049
Lecture 4Vector Superposition:The Field of Standard ChargeDistributionsSections: 2.4, 2.5Homework: See homework fileLECTURE 4slide1E-field of Multiple Sources superposition means adding the individual contributions of sources superposition hold
University of Florida - PHY - 2049
University of Florida - PHY - 2049
Lecture 5Electric Flux and Flux Density,Gauss Law in Integral FormSections: 3.1, 3.2, 3.3Homework: See homework fileLECTURE 5slide1Faradays Experiment (1837), Flux charge transfer from inner to outer sphere electric induction: charge deposition
University of Florida - PHY - 2049
University of Florida - PHY - 2049
Lecture 6Divergence, Gauss Law inDifferential FormSections: 3.4, 3.5, 3.6, 3.7 (7th ed.) [3.4, 3.5, 3.6 (8th ed.)]Homework: See homework fileLECTURE 6slide1Flux 1flux is the net normal flow of the vector field F through a surface F ds F cos ds c
University of Florida - PHY - 2049
University of Florida - PHY - 2049
Lecture 7Electrostatic PotentialSections: 4.1, 4.2, 4.3, 4.4Homework: See homework fileLECTURE 7slide1Work: Definitiondifferential workW F L dW F dL FdL cos Ftotal work done from A to BBW F dL, JdLABLFAwork is positive if the applied f
University of Florida - PHY - 2049
University of Florida - PHY - 2049
Lecture 8Electrostatic Field and PotentialGradientSections: 4.5, 4.6Homework: See homework fileLECTURE 8slide1Conservative Property of Potential of Point Charge 1 the potential of a single point charge at the origin depends solelyon the radial d
University of Florida - PHY - 2049
University of Florida - PHY - 2049
Lecture 9Electrostatic Energy and EnergyDensitySections: 4.8Homework: See homework fileLECTURE 9slide1Energy of System of Point Charges 1 any system of charged bodies held static in relatively closeproximity contains potential energy the potent
University of Florida - PHY - 2049
Lecture 10Current DensityOhms Law in Differential FormSections: 5.1, 5.2, 5.3Homework: See homework fileLECTURE 10slide1Electric Direct Current ReviewDC is the flow of charge under Coulomb (electrostatic) forces inconductorsGeorg Simon Ohm was
University of Florida - PHY - 2049
Homework: Repeat for an infinite uniform line charge along the x-axis at z = 3, y = 0 (above ground plane).
University of Florida - PHY - 2049
Lecture 11Perfect Conductors, BoundaryConditions, Method of ImagesSections: 5.4, 5.5Homework: See homework fileLECTURE 11slide1Perfect Conductors 1 metals such as Cu, Ag, Al are closely approximated by theconcept of a perfect electric conductor
University of Florida - PHY - 2049
There are no hand-writtenexamples for Lecture 12LECTURE 12slide1
University of Florida - PHY - 2049
Lecture 12Dielectrics: Dipole, PolarizationSections: 4.7, 6.1 (in 8th ed.: 4.7, 5.7)Homework: See homework fileLECTURE 12slide1Electric Dipole and its Dipole Momentelectric dipole: two point charges of equal charge but oppositepolarity in close p
University of Florida - PHY - 2049
University of Florida - PHY - 2049
Lecture 13Boundary Conditions atDielectric InterfacesSections: 6.2 (in 8th ed.: 5.8)Homework: See homework fileLECTURE 13slide1BCs for the Tangential Field Components 1 we consider interfaces between two perfect ( = 0) dielectric regions use con
University of Florida - PHY - 2049
University of Florida - PHY - 2049
Lecture 14CapacitanceSections: 6.3, 6.4, 6.5 (8th ed.: 6.1, 6.2, 6.3, 6.4)Homework: See homework fileLECTURE 14slide1Definition of Capacitancecapacitance is a measure of the ability of the physical structure toaccumulate electrical free charge un
University of Florida - PHY - 2049
University of Florida - PHY - 2049
Lecture 15Magnetostatic Field Forcesand the Biot-Savart LawSections: 8.1, 9.1, 9.2Homework: See homework fileLECTURE 15slide1Magnetic Forces Review 1Ampres force law (motor equation)LFm IL(a I B), Nmagnetic fluxdensity vectorIBFmforce doe
University of Florida - EEL - 3111
238MICROWAVE AND RF DESIGN: A SYSTEMS APPROACH4.14SummaryIn this chapter a classical treatment of transmission lines was presented.Transmission lines are distributed elements and form the basis of microwavecircuits. A distinguishing feature is they
University of Florida - EEL - 3111
280MICROWAVE AND RF DESIGN: A SYSTEMS APPROACHSlow-Wave ModeThe third possible mode of propagation is the slow-wave mode [76, 77], forwhich the sectional equivalent circuit model of Figure 5-21(d) is applicable.This mode occurs when f is not so large
University of Florida - EEL - 3111
366MICROWAVE AND RF DESIGN: A SYSTEMS APPROACHmade in design, partly because of necessary simplications that mustbe made in modeling, but also because many of the material propertiesrequired in a detailed design can only be approximate. An example is
University of Florida - EEL - 3111
408MICROWAVE AND RF DESIGN: A SYSTEMS APPROACH7.16SummaryMany passive microwave elements exploit particular physical phenomena.Many make use of the characteristics of transmission lines. Each year newvariants of microwave elements are developed and
University of Florida - EEL - 3111
454MICROWAVE AND RF DESIGN: A SYSTEMS APPROACH8.10Exercises1. Repeat the analysis in Example 8.1 on Page419 for the case B = 1/L.2. Develop a two-element matching network forthe source/load conguration shown in theFigure below. The matching networ
University of Florida - EEL - 3111
COUPLED LINES AND APPLICATIONS9.13501SummaryCoupling from one transmission line to a nearby neighbor may often beundesirable. However, the effect can be exploited to realize a coupler thatdoes not have a lumped-element equivalent. This is one exampl
University of Florida - EEL - 3111
FILTERS591DRAIN BIASOUTPUTVGC FBSOURCE BIASFigure 10-90An active resonator circuit. After Karacaoglu and Robertson [167].the gate-source voltage. This induces a negative resistance that is adjustedthrough device selection and feedback capacitanc
University of Florida - EEL - 3111
10Note that Hx is out of phase with Eyand Hy is in phase with Ex. Explain.152224
University of Florida - EEL - 3111
University of Florida - EEL - 3111
University of Florida - EEL - 3111
Lecture 1Radio Systems: an OverviewSections: parts from 1.6, 1.7, 1.8, 3.10Acknowledgement: Most diagrams and plots are from M. Steers book Microwaveand RF DesignWhy Do We Need Microwave Engineers?all wireless links use RF and microwave circuits and