ECE 546 Lecture 02 Review of Electromagnetics
|
|
|
- Lilian Booth
- 5 years ago
- Views:
Transcription
1 C 546 Lecture 0 Review f lectrmagnetics Spring 018 Jse. Schutt-Aine lectrical & Cmputer ngineering University f Illinis jesa@illinis.edu C 546 Jse Schutt Aine 1
2 Printed Circuit Bard C 546 Jse Schutt Aine
3 High-Density Package C 546 Jse Schutt Aine 3
4 D H B lectrmagnetic Quantities lectric field (Vlts/m) lectric flux density (Culmbs/m ) Magnetic field (Amperes/m) Magnetic flux density (Webers/m ) J Current density (Amperes/m ) Charge density (Culmbs/m ) C 546 Jse Schutt Aine 4
5 Maxwell s quatins B t H J D t D Faraday s Law f Inductin Ampère s Law Gauss Law fr electric field B 0 Gauss Law fr magnetic field C 546 Jse Schutt Aine 5
6 Cnstitutive Relatins B H D Permittivity : Farads/m Permeability : Henries/m Free Space F / m H / m C 546 Jse Schutt Aine 6
7 D H J t Cntinuity quatin D H J J D t t 0 D J t 0 C 546 Jse Schutt Aine 7
8 lectrstatics t Assume n time dependence 0 0 Since 0, such that where is the scalar ptential with we get we get Pissn s quatin if n charge is present 0 Laplace s quatin C 546 Jse Schutt Aine 8
9 Integral Frm f M C dl BdS t S H dl J ds D ds t C S S S DdS dv V S BdS 0 C 546 Jse Schutt Aine 9
10 Bundary Cnditins nˆ 0 1 nˆ H H J 1 nˆ D D 1 1 nˆ B B 0 S S, H, D, B , H, D, B ˆn C 546 Jse Schutt Aine 10
11 Free Space Slutin H t H t 0 Faraday s Law f Inductin Ampère s Law Gauss Law fr electric field B 0 Gauss Law fr magnetic field C 546 Jse Schutt Aine 11
12 C 546 Jse Schutt Aine 1 H t t t Wave quatin t Wave quatin can shw that H H t
13 Wave quatin x y z t separating the cmpnents x x x x x y z t y y y y x y z t x y z t z z z z C 546 Jse Schutt Aine 13
14 Wave quatin Plane Wave (a) Assume that nly x exists y = z =0 (b) Only z spatial dependence x y 0 x x z t This situatin leads t the plane wave slutin In additin, assume a time harmnic dependence x j t e t then j C 546 Jse Schutt Aine 14
15 Plane Wave Slutin z x x slutin j z x e frward wave j z x e backward wave where prpagatin cnstant In the time dmain slutin x() t cst z frward traveling wave x() t cst z backward traveling wave C 546 Jse Schutt Aine 15
16 Plane Wave Characteristics where prpagatin cnstant 1 v prpagatin velcity In free space 1 8 vc 310 m/ s C 546 Jse Schutt Aine 16
17 Slutin fr Magnetic Field H jh t xˆ yˆ zˆ 1 1 H j j x y z x 0 0 j z If we assume that x ˆ e j z then H yˆ e j z If we assume that x ˆ e j z then H yˆ e intrinsic impedance f medium C 546 Jse Schutt Aine 17
18 Time-Average Pynting Vectr P() t t H t Pynting vectr W/m time average Pynting vectr W/m 1 T 1 T P P() t dt t H t dt T 0 T 0 We can shw that 1 Re * P H where and H are the phasrs f ( t) and H( t) respectively C 546 Jse Schutt Aine 18
19 H t H J t Material Medium J jh H J j : cnductivity f material medium ( 1 m 1 ) since H j j j 1 j 1 j r then 1 j C 546 Jse Schutt Aine 19
20 Wave in Material Medium 1 j 1 j is cmplex prpagatin cnstant j 1 j j assciated with attenuatin f wave assciated with prpagatin f wave C 546 Jse Schutt Aine 0
21 Wave in Material Medium Slutin: x ˆ e x ˆ e e z z jz decaying expnential 1 1 1/ 1 1 Magnetic field H yˆ e e z j z 1/ Cmplex intrinsic impedance j j C 546 Jse Schutt Aine 1
22 Wave in Material Medium Phase Velcity: Wavelength: v p 1 1 1/ 1 1 f 1/ Special Cases 1. Perfect dielectric 0 air, free space 0 and C 546 Jse Schutt Aine
23 Wave in Material Medium. Lssy dielectric Lss tangent: j 8 C 546 Jse Schutt Aine 3
24 Wave in Material Medium 3. Gd cnductrs Lss tangent: 1 j j j f f j f 1 j j C 546 Jse Schutt Aine 4
25 Material Medium attenuatin prpagatin d p H, xamples PC supercnd Gd cnductr f 1 j 1 f finite cpper Pr cnductr / 1 j finite Ice Perfect dielectric 0 / finite air C 546 Jse Schutt Aine 5
26 Radiatin - Vectr Ptential Assume time harmnicity ~ j H (1) H J j () D / (3) B 0 (4) j t e C 546 Jse Schutt Aine 6
27 Radiatin - Vectr Ptential Using the prperty: 0 anyvectr B 0 Asuch that AB A 0 A : vectr ptential ja j A 0 C 546 Jse Schutt Aine 7
28 vectr 0 vectr Vectr Ptential ja where is the scalar ptential Since a vectr is uniquely defined by its curl and its divergence, we can chse the divergence f A chse A such that A j 0 Lrentz cnditin C 546 Jse Schutt Aine 8
29 B J j AJ j j A A A J A j A j J A j Vectr Ptential A A J D Alembert s equatin C 546 Jse Schutt Aine 9
30 G r, r' Vectr Ptential Three-dimensinal free-space Green s functin j rr' e 4 r r' Vectr ptential A r V ' Jr' e 4 r r' j rr' dv' Frm A, get and H using Maxwell s equatins C 546 Jse Schutt Aine 30
31 Fr infinitesimal antenna, the current density is: J r zi dl ( x') ( y ') ( z ') ' ˆ A r z e ˆ 4 Idl r Vectr Ptential Calculating the vectr ptential, jr In spherical crdinates, zˆ rˆ cs ˆ sin C 546 Jse Schutt Aine 31
32 Vectr Ptential Idl ˆ ˆcs ˆ sin A r z r e 4 r Reslving int cmpnents, jr Idl cs A ˆ r z e 4 r jr A Idl 4 sin e r jr C 546 Jse Schutt Aine 3
33 and H Fields Calculate and H fields 1 H A 1 A H sin r A 0 sin H 1 1 A r ra r sin r 0 C 546 Jse Schutt Aine 33
34 and H Fields H 1 A ra r r r Idl 1 jr H j 1 e sin 4r jr 1 H j r r 1 H sin 1 sin j C 546 Jse Schutt Aine 34
35 and H Fields csidl 1 jr 1 r j 1 e 4 r jr j 1 rh 1 r r j j Idl sin 1 jr j e 4 r jr r j C 546 Jse Schutt Aine 35
36 and H Fields csidl 1 jr 1 r j 1 e 4 r jr j j Idl j r 1 1 e sin 1 4 r jr jr Idl 1 jr H j 1 e sin 4r jr C 546 Jse Schutt Aine 36
37 Far field : r r Far Field Apprximatin r r then, 0 r j Idl 4 r e jr sin H j Idl 4 r Nte that: e jr H sin,where C 546 Jse Schutt Aine 37
38 Far Field Apprximatin Characteristics f plane waves Unifrm cnstant phase lcus is a plane Cnstant magnitude Independent f Des nt decay Similarities between infinitesimal antenna far field radiated and plane wave (a) and H are perpendicular (b) and H are related by (c) is perpendicular t H C 546 Jse Schutt Aine 38
39 Pynting Vectr Pt t Ht Time-average Pynting vectr r TA pwer density 1 P Re H * and H here are PHASORS I dl ˆ rˆ P Re H r 4r sin C 546 Jse Schutt Aine 39
40 Time-Average Pwer Ttal pwer radiated (time-average) P= P ds with ds rr ˆ sindd 0 0 P= 0 0 I dl 4 r r sin sindd Idl P= 4 3 d sin 0 C 546 Jse Schutt Aine 40
41 Time-Average Pwer P= 4 Idl 3 4 Pynting Pwer Density Directive Gain = AveragePynting Pwer Density ver area f sphere with radius r Directive Gain = P P /4 r C 546 Jse Schutt Aine 41
42 Fr infinitesimal antenna, Directive Gain 3 Directive Gain sin Directivity I dl sin 4 r 4 I dl /4 r 3 4 C 546 Jse Schutt Aine 4
43 Directivity: gain in directin f maximum value Radiatin resistance: Frm 1 P P RI we have: rad I Fr infinitesimal antenna: Directivity R R rad 4 Idl dl I C 546 Jse Schutt Aine 43
44 Radiatin Resistance Fr free space, 10 R rad 80 dl (fr Hertzian diple) The radiatin resistance f an antenna is the value f a fictitius resistance that wuld dissipate an amunt f pwer equal t the radiated pwer P r when the current in the resistance is equal t the maximum current alng the antenna A high radiatin resistance is a desirable prperty fr an antenna C 546 Jse Schutt Aine 44
Schedule. Time Varying electromagnetic fields (1 Week) 6.1 Overview 6.2 Faraday s law (6.2.1 only) 6.3 Maxwell s equations
chedule Time Varying electrmagnetic fields (1 Week) 6.1 Overview 6.2 Faraday s law (6.2.1 nly) 6.3 Maxwell s equatins Wave quatin (3 Week) 6.5 Time-Harmnic fields 7.1 Overview 7.2 Plane Waves in Lssless
Power Flow in Electromagnetic Waves. The time-dependent power flow density of an electromagnetic wave is given by the instantaneous Poynting vector
Pwer Flw in Electrmagnetic Waves Electrmagnetic Fields The time-dependent pwer flw density f an electrmagnetic wave is given by the instantaneus Pynting vectr P t E t H t ( ) = ( ) ( ) Fr time-varying
Chapter 32. Maxwell s Equations and Electromagnetic Waves
Chapter 32 Maxwell s Equatins and Electrmagnetic Waves Maxwell s Equatins and EM Waves Maxwell s Displacement Current Maxwell s Equatins The EM Wave Equatin Electrmagnetic Radiatin MFMcGraw-PHY 2426 Chap32-Maxwell's
Chapter 6. Dielectrics and Capacitance
Chapter 6. Dielectrics and Capacitance Hayt; //009; 6- Dielectrics are insulating materials with n free charges. All charges are bund at mlecules by Culmb frce. An applied electric field displaces charges
ELECTROSTATIC FIELDS IN MATERIAL MEDIA
MF LCTROSTATIC FILDS IN MATRIAL MDIA 3/4/07 LCTURS Materials media may be classified in terms f their cnductivity σ (S/m) as: Cnductrs The cnductivity usually depends n temperature and frequency A material
ECE 598 JS Lecture 08 Lossy Transmission Lines
ECE 598 JS Lecture 8 Lssy Transmissin Lines Spring 22 Jse E. Schutt-Aine Electrical & Cmputer Engineering University f Illinis jesa@illinis.edu Lss in Transmissin Lines RF SOURCE Signal amplitude decreases
Preparatory School to the Winter College on Optics in Environmental Science January 2009
017-1 Preparatry Schl t the Winter Science 6-30 January 009 Review f lectrdynamics: Frm Maxwell's quatins t the lectrmagnetic waves Ashraf Zahid I. Quaid-I-Azam University Pakistan RVIW OF LCTODYNAMICS:
Chapter 8. The Steady Magnetic Field 8.1 Biot-Savart Law
hapter 8. The teady Magnetic Field 8. Bit-avart Law The surce f steady magnetic field a permanent magnet, a time varying electric field, a direct current. Hayt; /9/009; 8- The magnetic field intensity
ANTENNAS. Vector and Scalar Potentials. Maxwell's Equations. E = jωb. H = J + jωd. D = ρ (M3) B = 0 (M4) D = εe
ANTENNAS Vector and Scalar Potentials Maxwell's Equations E = jωb H = J + jωd D = ρ B = (M) (M) (M3) (M4) D = εe B= µh For a linear, homogeneous, isotropic medium µ and ε are contant. Since B =, there
37 Maxwell s Equations
37 Maxwell s quatins In this chapter, the plan is t summarize much f what we knw abut electricity and magnetism in a manner similar t the way in which James Clerk Maxwell summarized what was knwn abut
( ) ( ) ( ) ( ) ( z) ( )
EE433-08 Planer Micrwave Circuit Design Ntes Returning t the incremental sectin, we will nw slve fr V and I using circuit laws. We will assume time-harmnic excitatin. v( z,t ) = v(z)cs( ωt ) jωt { s }
(1.1) V which contains charges. If a charge density ρ, is defined as the limit of the ratio of the charge contained. 0, and if a force density f
1.0 Review f Electrmagnetic Field Thery Selected aspects f electrmagnetic thery are reviewed in this sectin, with emphasis n cncepts which are useful in understanding magnet design. Detailed, rigrus treatments
Chapter 2 GAUSS LAW Recommended Problems:
Chapter GAUSS LAW Recmmended Prblems: 1,4,5,6,7,9,11,13,15,18,19,1,7,9,31,35,37,39,41,43,45,47,49,51,55,57,61,6,69. LCTRIC FLUX lectric flux is a measure f the number f electric filed lines penetrating
Module 4: General Formulation of Electric Circuit Theory
Mdule 4: General Frmulatin f Electric Circuit Thery 4. General Frmulatin f Electric Circuit Thery All electrmagnetic phenmena are described at a fundamental level by Maxwell's equatins and the assciated
Kinetics of Particles. Chapter 3
Kinetics f Particles Chapter 3 1 Kinetics f Particles It is the study f the relatins existing between the frces acting n bdy, the mass f the bdy, and the mtin f the bdy. It is the study f the relatin between
Time varying fields and Maxwell's equations Chapter 9
Tie varying fields and Maxwell's equatins hapter 9 Dr. Naser Abu-Zaid Page 9/7/202 FARADAY LAW OF ELETROMAGNETI INDUTION A tie varying agnetic field prduces (induces) a current in a clsed lp f wire. The
!"#$%&'()%"*#%*+,-./-*+01.2(.* *!"#$%&"'(()'*+,"-'.'
!"#$%&'()%"*#%*+,-./-*+1.2(.*3+456789*!"#$%&"'(()'*+,"-'.' Dr. D. Shaun Blmfield Astrphysics Research Grup Trinity Cllege Dublin :-#*;
ECE 2100 Circuit Analysis
ECE 2100 Circuit Analysis Lessn 25 Chapter 9 & App B: Passive circuit elements in the phasr representatin Daniel M. Litynski, Ph.D. http://hmepages.wmich.edu/~dlitynsk/ ECE 2100 Circuit Analysis Lessn
Q1. In figure 1, Q = 60 µc, q = 20 µc, a = 3.0 m, and b = 4.0 m. Calculate the total electric force on q due to the other 2 charges.
Phys10 Secnd Majr-08 Zer Versin Crdinatr: Dr. I. M. Nasser Saturday, May 3, 009 Page: 1 Q1. In figure 1, Q = 60 µc, q = 0 µc, a = 3.0 m, and b = 4.0 m. Calculate the ttal electric frce n q due t the ther
ENGI 4430 Parametric Vector Functions Page 2-01
ENGI 4430 Parametric Vectr Functins Page -01. Parametric Vectr Functins (cntinued) Any nn-zer vectr r can be decmpsed int its magnitude r and its directin: r rrˆ, where r r 0 Tangent Vectr: dx dy dz dr
Chapter 23 Electromagnetic Waves Lecture 14
Chapter 23 Electrmagnetic Waves Lecture 14 23.1 The Discvery f Electrmagnetic Waves 23.2 Prperties f Electrmagnetic Waves 23.3 Electrmagnetic Waves Carry Energy and Mmentum 23.4 Types f Electrmagnetic
Short notes for Heat transfer
Furier s Law f Heat Cnductin Shrt ntes fr Heat transfer Q = Heat transfer in given directin. A = Crss-sectinal area perpendicular t heat flw directin. dt = Temperature difference between tw ends f a blck
Introduction: A Generalized approach for computing the trajectories associated with the Newtonian N Body Problem
A Generalized apprach fr cmputing the trajectries assciated with the Newtnian N Bdy Prblem AbuBar Mehmd, Syed Umer Abbas Shah and Ghulam Shabbir Faculty f Engineering Sciences, GIK Institute f Engineering
Chapter VII Electrodynamics
Chapter VII Electrdynamics Recmmended prblems: 7.1, 7., 7.4, 7.5, 7.7, 7.8, 7.10, 7.11, 7.1, 7.13, 7.15, 7.17, 7.18, 7.0, 7.1, 7., 7.5, 7.6, 7.7, 7.9, 7.31, 7.38, 7.40, 7.45, 7.50.. Ohm s Law T make a
Phys102 Final-061 Zero Version Coordinator: Nasser Wednesday, January 24, 2007 Page: 1
Crdinatr: Nasser Wednesday, January 4, 007 Page: 1 Q1. Tw transmitters, S 1 and S shwn in the figure, emit identical sund waves f wavelength λ. The transmitters are separated by a distance λ /. Cnsider
Q1. A) 48 m/s B) 17 m/s C) 22 m/s D) 66 m/s E) 53 m/s. Ans: = 84.0 Q2.
Phys10 Final-133 Zer Versin Crdinatr: A.A.Naqvi Wednesday, August 13, 014 Page: 1 Q1. A string, f length 0.75 m and fixed at bth ends, is vibrating in its fundamental mde. The maximum transverse speed
Figure 1a. A planar mechanism.
ME 5 - Machine Design I Fall Semester 0 Name f Student Lab Sectin Number EXAM. OPEN BOOK AND CLOSED NOTES. Mnday, September rd, 0 Write n ne side nly f the paper prvided fr yur slutins. Where necessary,
Chapter 9 Vector Differential Calculus, Grad, Div, Curl
Chapter 9 Vectr Differential Calculus, Grad, Div, Curl 9.1 Vectrs in 2-Space and 3-Space 9.2 Inner Prduct (Dt Prduct) 9.3 Vectr Prduct (Crss Prduct, Outer Prduct) 9.4 Vectr and Scalar Functins and Fields
ECE 6340 Intermediate EM Waves. Fall Prof. David R. Jackson Dept. of ECE. Notes 1
EE 6340 Intermediate EM Waves Fall 2016 Prof. David R. Jackson Dept. of EE Notes 1 1 Maxwell s Equations E D rt 2, V/m, rt, Wb/m T ( ) [ ] ( ) ( ) 2 rt, /m, H ( rt, ) [ A/m] B E = t (Faraday's Law) D H
Applying Kirchoff s law on the primary circuit. V = - e1 V+ e1 = 0 V.D. e.m.f. From the secondary circuit e2 = v2. K e. Equivalent circuit :
TRANSFORMERS Definitin : Transfrmers can be defined as a static electric machine which cnverts electric energy frm ne ptential t anther at the same frequency. It can als be defined as cnsists f tw electric
Honors Physics Final Review Summary
Hnrs Physics Final Review Summary Wrk Dne By A Cnstant Frce: Wrk describes a frce s tendency t change the speed f an bject. Wrk is dne nly when an bject mves in respnse t a frce, and a cmpnent f the frce
Q1. A string of length L is fixed at both ends. Which one of the following is NOT a possible wavelength for standing waves on this string?
Term: 111 Thursday, January 05, 2012 Page: 1 Q1. A string f length L is fixed at bth ends. Which ne f the fllwing is NOT a pssible wavelength fr standing waves n this string? Q2. λ n = 2L n = A) 4L B)
TECHNO INDIA BATANAGAR
TECHNO INDIA BATANAGAR ( DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING) QUESTION BANK- 2018 1.Vector Calculus Assistant Professor 9432183958.mukherjee@tib.edu.in 1. When the operator operates on
UIUC Physics 435 EM Fields & Sources I Fall Semester, 2007 Lecture Notes 24 Prof. Steven Errede LECTURE NOTES 24 MAXWELL S EQUATIONS
UIUC Physics 435 M Fields & urces I Fall eester, 7 Lecture Ntes 4 Prf. teven rrede LCTUR NOT 4 MAXWLL QUATION Thus far, we have the fllwing fur Maxwell equatins (in differential fr): ivergence and curl
Equilibrium of Stress
Equilibrium f Stress Cnsider tw perpendicular planes passing thrugh a pint p. The stress cmpnents acting n these planes are as shwn in ig. 3.4.1a. These stresses are usuall shwn tgether acting n a small
Chapter 3. AC Machinery Fundamentals. Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Chapter 3 AC Machinery Fundamentals 1 The Vltage Induced in a Rtating Lp e v B ind v = velcity f the cnductr B = Magnetic Flux Density vectr l = Length f the Cnductr Figure 3-1 A simple rtating lp in a
Information for Physics 1201 Midterm I Wednesday, February 20
My lecture slides are psted at http://www.physics.hi-state.edu/~humanic/ Infrmatin fr Physics 1201 Midterm I Wednesday, February 20 1) Frmat: 10 multiple chice questins (each wrth 5 pints) and tw shw-wrk
r r 1 r r 1 2 = q 1 p = qd and it points from the negative charge to the positive charge.
MP204, Important Equations page 1 Below is a list of important equations that we meet in our study of Electromagnetism in the MP204 module. For your exam, you are expected to understand all of these, and
Notes 19 Gradient and Laplacian
ECE 3318 Applied Electricity and Magnetism Spring 218 Prof. David R. Jackson Dept. of ECE Notes 19 Gradient and Laplacian 1 Gradient Φ ( x, y, z) =scalar function Φ Φ Φ grad Φ xˆ + yˆ + zˆ x y z We can
Supplementary Course Notes Adding and Subtracting AC Voltages and Currents
Supplementary Curse Ntes Adding and Subtracting AC Vltages and Currents As mentined previusly, when cmbining DC vltages r currents, we nly need t knw the plarity (vltage) and directin (current). In the
Chapter 3 Kinematics in Two Dimensions; Vectors
Chapter 3 Kinematics in Tw Dimensins; Vectrs Vectrs and Scalars Additin f Vectrs Graphical Methds (One and Tw- Dimensin) Multiplicatin f a Vectr b a Scalar Subtractin f Vectrs Graphical Methds Adding Vectrs
CHAPTER 2. COULOMB S LAW AND ELECTRONIC FIELD INTENSITY. 2.3 Field Due to a Continuous Volume Charge Distribution
CONTENTS CHAPTER 1. VECTOR ANALYSIS 1. Scalars and Vectors 2. Vector Algebra 3. The Cartesian Coordinate System 4. Vector Cartesian Coordinate System 5. The Vector Field 6. The Dot Product 7. The Cross
Phy 213: General Physics III 6/14/2007 Chapter 28 Worksheet 1
Ph 13: General Phsics III 6/14/007 Chapter 8 Wrksheet 1 Magnetic Fields & Frce 1. A pint charge, q= 510 C and m=110-3 m kg, travels with a velcit f: v = 30 ˆ s i then enters a magnetic field: = 110 T ˆj.
FIELD QUALITY IN ACCELERATOR MAGNETS
FIELD QUALITY IN ACCELERATOR MAGNETS S. Russenschuck CERN, 1211 Geneva 23, Switzerland Abstract The field quality in the supercnducting magnets is expressed in terms f the cefficients f the Furier series
Electric Current and Resistance
Electric Current and Resistance Electric Current Electric current is the rate f flw f charge thrugh sme regin f space The SI unit f current is the ampere (A) 1 A = 1 C / s The symbl fr electric current
Part a: Writing the nodal equations and solving for v o gives the magnitude and phase response: tan ( 0.25 )
+ - Hmewrk 0 Slutin ) In the circuit belw: a. Find the magnitude and phase respnse. b. What kind f filter is it? c. At what frequency is the respnse 0.707 if the generatr has a ltage f? d. What is the
MODULE 1. e x + c. [You can t separate a demominator, but you can divide a single denominator into each numerator term] a + b a(a + b)+1 = a + b
![MODULE 1. e x + c. [You can t separate a demominator, but you can divide a single denominator into each numerator term] a + b a(a + b)+1 = a + b](/thumbs/78/78051685.jpg "MODULE 1. e x + c. [You can t separate a demominator, but you can divide a single denominator into each numerator term] a + b a(a + b)+1 = a + b")
. REVIEW OF SOME BASIC ALGEBRA MODULE () Slving Equatins Yu shuld be able t slve fr x: a + b = c a d + e x + c and get x = e(ba +) b(c a) d(ba +) c Cmmn mistakes and strategies:. a b + c a b + a c, but
Introduction to Vector Calculus (29) SOLVED EXAMPLES. (d) B. C A. (f) a unit vector perpendicular to both B. = ˆ 2k = = 8 = = 8
Introduction to Vector Calculus (9) SOLVED EXAMPLES Q. If vector A i ˆ ˆj k, ˆ B i ˆ ˆj, C i ˆ 3j ˆ kˆ (a) A B (e) A B C (g) Solution: (b) A B (c) A. B C (d) B. C A then find (f) a unit vector perpendicular
PHYS College Physics II Final Examination Review
PHYS 1402- Cllege Physics II Final Examinatin Review The final examinatin will be based n the fllwing Chapters/Sectins and will cnsist f tw parts. Part 1, cnsisting f Multiple Chice questins, will accunt
Phys101 Final Code: 1 Term: 132 Wednesday, May 21, 2014 Page: 1
Phys101 Final Cde: 1 Term: 1 Wednesday, May 1, 014 Page: 1 Q1. A car accelerates at.0 m/s alng a straight rad. It passes tw marks that are 0 m apart at times t = 4.0 s and t = 5.0 s. Find the car s velcity
Basics of Electromagnetics Maxwell s Equations (Part - I)
Basics of Electromagnetics Maxwell s Equations (Part - I) Soln. 1. C A. dl = C. d S [GATE 1994: 1 Mark] A. dl = A. da using Stoke s Theorem = S A. ds 2. The electric field strength at distant point, P,
Review for the final exam (Math 127)
. Evaluate 3 tan tan 4 3 (b) (c) cs cs 4 7 3 sec cs 4 4 (d) cs tan 3 Review fr the final eam (Math 7). If sec, and 7 36, find cs, sin, tan, ct, csc tan (b) If, evaluate cs, sin 7 36 (c) Write the csc in
Chapter 4. Unsteady State Conduction
Chapter 4 Unsteady State Cnductin Chapter 5 Steady State Cnductin Chee 318 1 4-1 Intrductin ransient Cnductin Many heat transfer prblems are time dependent Changes in perating cnditins in a system cause
GAUSS' LAW E. A. surface
Prf. Dr. I. M. A. Nasser GAUSS' LAW 08.11.017 GAUSS' LAW Intrductin: The electric field f a given charge distributin can in principle be calculated using Culmb's law. The examples discussed in electric
ECE 497 JS Lecture - 14 Projects: FDTD & LVDS
ECE 497 JS Lecture - 14 Prjects: FDTD & LVDS Spring 2004 Jse E. Schutt-Aine Electrical & Cmputer Engineering University f Illinis jse@emlab.uiuc.edu 1 ECE 497 JS - Prjects All prjects shuld be accmpanied
Electromagnetic Field Theory Chapter 9: Time-varying EM Fields
Electromagnetic Field Theory Chapter 9: Time-varying EM Fields Faraday s law of induction We have learned that a constant current induces magnetic field and a constant charge (or a voltage) makes an electric
Lecture 6: Phase Space and Damped Oscillations
Lecture 6: Phase Space and Damped Oscillatins Oscillatins in Multiple Dimensins The preius discussin was fine fr scillatin in a single dimensin In general, thugh, we want t deal with the situatin where:
Copyright Paul Tobin 63
DT, Kevin t. lectric Circuit Thery DT87/ Tw-Prt netwrk parameters ummary We have seen previusly that a tw-prt netwrk has a pair f input terminals and a pair f utput terminals figure. These circuits were
TUTORIAL 7. Discussion of Quiz 2 Solution of Electrostatics part 1
TUTORIAL 7 Discussion of Quiz 2 Solution of Electrostatics part 1 Quiz 2 - Question 1! Postulations of Electrostatics %&''()(*+&,-$'.)/ : % (1)!! E # $$$$$$$$$$ & # (2)!" E # #! Static Electric field is
Physics 212. Lecture 12. Today's Concept: Magnetic Force on moving charges. Physics 212 Lecture 12, Slide 1
Physics 1 Lecture 1 Tday's Cncept: Magnetic Frce n mving charges F qv Physics 1 Lecture 1, Slide 1 Music Wh is the Artist? A) The Meters ) The Neville rthers C) Trmbne Shrty D) Michael Franti E) Radiatrs
Lecture 5: Equilibrium and Oscillations
Lecture 5: Equilibrium and Oscillatins Energy and Mtin Last time, we fund that fr a system with energy cnserved, v = ± E U m ( ) ( ) One result we see immediately is that there is n slutin fr velcity if
Unit-1 Electrostatics-1
1. Describe about Co-ordinate Systems. Co-ordinate Systems Unit-1 Electrostatics-1 In order to describe the spatial variations of the quantities, we require using appropriate coordinate system. A point
Fall 2013 Physics 172 Recitation 3 Momentum and Springs
Fall 03 Physics 7 Recitatin 3 Mmentum and Springs Purpse: The purpse f this recitatin is t give yu experience wrking with mmentum and the mmentum update frmula. Readings: Chapter.3-.5 Learning Objectives:.3.
Phys102 Second Major-102 Zero Version Coordinator: Al-Shukri Thursday, May 05, 2011 Page: 1
Crdinatr: Al-Shukri Thursday, May 05, 2011 Page: 1 1. Particles A and B are electrically neutral and are separated by 5.0 μm. If 5.0 x 10 6 electrns are transferred frm particle A t particle B, the magnitude
PHY 2054C Review guide Fall 2018 Chapter 17 Wave optics
PHY 2054C Review guide Fall 2018 Chapter 17 Wave ptics Light acts as a wave, ray, particle, and phtn. Refractive index n = c/v Light waves travel with speed c in a vacuum they slw dwn when they pass thrugh
Chapter 30. Inductance
Chapter 30 nductance 30. Self-nductance Cnsider a lp f wire at rest. f we establish a current arund the lp, it will prduce a magnetic field. Sme f the magnetic field lines pass thrugh the lp. et! be the
Sodium D-line doublet. Lectures 5-6: Magnetic dipole moments. Orbital magnetic dipole moments. Orbital magnetic dipole moments
Lectures 5-6: Magnetic diple mments Sdium D-line dublet Orbital diple mments. Orbital precessin. Grtrian diagram fr dublet states f neutral sdium shwing permitted transitins, including Na D-line transitin
Faculty of Engineering and Department of Physics Engineering Physics 131 Midterm Examination February 27, 2006; 7:00 pm 8:30 pm
Faculty f Engineering and Department f Physics Engineering Physics 131 Midterm Examinatin February 27, 2006; 7:00 pm 8:30 pm N ntes r textbks allwed. Frmula sheet is n the last page (may be remved). Calculatrs
Problem 1 Known: Dimensions and materials of the composition wall, 10 studs each with 2.5m high
Prblem Knwn: Dimensins and materials f the cmpsitin wall, 0 studs each with.5m high Unknwn:. Thermal resistance assciate with wall when surfaces nrmal t the directin f heat flw are isthermal. Thermal resistance
GENERAL FORMULAS FOR FLAT-TOPPED WAVEFORMS. J.e. Sprott. Plasma Studies. University of Wisconsin
GENERAL FORMULAS FOR FLAT-TOPPED WAVEFORMS J.e. Sprtt PLP 924 September 1984 Plasma Studies University f Wiscnsin These PLP Reprts are infrmal and preliminary and as such may cntain errrs nt yet eliminated.
Work, Energy, and Power
rk, Energy, and Pwer Physics 1 There are many different TYPES f Energy. Energy is expressed in JOULES (J 419J 4.19 1 calrie Energy can be expressed mre specifically by using the term ORK( rk The Scalar
Notes 18 Faraday s Law
EE 3318 Applied Electricity and Magnetism Spring 2018 Prof. David R. Jackson Dept. of EE Notes 18 Faraday s Law 1 Example (cont.) Find curl of E from a static point charge q y E q = rˆ 2 4πε0r x ( E sinθ
Numerical Simulation of the Thermal Resposne Test Within the Comsol Multiphysics Environment
Presented at the COMSOL Cnference 2008 Hannver University f Parma Department f Industrial Engineering Numerical Simulatin f the Thermal Respsne Test Within the Cmsl Multiphysics Envirnment Authr : C. Crradi,
Phys101 First Major-131 Zero Version Coordinator: Dr. A. A. Naqvi Wednesday, September 25, 2013 Page: 1
Phys11 First Majr-11 Zer Versin Crdinatr: Dr. A. A. Naqvi Wednesday, September 5, 1 Page: 1 Q1. Cnsider tw unifrm slid spheres A and B made f the same material and having radii r A and r B, respectively.
A Review of Basic Electromagnetic Theories
A Review of Basic Electromagnetic Theories Important Laws in Electromagnetics Coulomb s Law (1785) Gauss s Law (1839) Ampere s Law (1827) Ohm s Law (1827) Kirchhoff s Law (1845) Biot-Savart Law (1820)
Solution to HW14 Fall-2002
Slutin t HW14 Fall-2002 CJ5 10.CQ.003. REASONING AND SOLUTION Figures 10.11 and 10.14 shw the velcity and the acceleratin, respectively, the shadw a ball that underges unirm circular mtin. The shadw underges
Fields and Waves I. Lecture 3
Fields and Waves I ecture 3 Input Impedance n Transmissin ines K. A. Cnnr Electrical, Cmputer, and Systems Engineering Department Rensselaer Plytechnic Institute, Try, NY These Slides Were Prepared by
CBSE Board Class XII Physics Set 1 Board Paper 2008 (Solution)
CBSE Bard Class XII Physics Set 1 Bard Paper 2008 (Slutin) 1. The frce is given by F qv B This frce is at right angles t &. 2. Micrwaves. It is used in radar & cmmunicatin purpses. 3. Or As m e e m S,
Antennas and Propagation. Chapter 2: Basic Electromagnetic Analysis
Antennas and Propagation : Basic Electromagnetic Analysis Outline Vector Potentials, Wave Equation Far-field Radiation Duality/Reciprocity Transmission Lines Antennas and Propagation Slide 2 Antenna Theory
DHANALAKSHMI SRINIVASAN INSTITUTE OF RESEARCH AND TECHNOLOGY
DHANALAKSHMI SRINIVASAN INSTITUTE OF RESEARCH AND TECHNOLOGY SIRUVACHUR-621113 ELECTRICAL AND ELECTRONICS DEPARTMENT 2 MARK QUESTIONS AND ANSWERS SUBJECT CODE: EE 6302 SUBJECT NAME: ELECTROMAGNETIC THEORY
Coupled Inductors and Transformers
Cupled nductrs and Transfrmers Self-nductance When current i flws thrugh the cil, a magnetic flux is prduced arund it. d d di di v= = = dt di dt dt nductance: = d di This inductance is cmmnly called self-inductance,
TOPPER SAMPLE PAPER 2 Class XII- Physics
TOPPER SAMPLE PAPER 2 Class XII- Physics Time: Three Hurs Maximum Marks: 70 General Instructins (a) All questins are cmpulsry. (b) There are 30 questins in ttal. Questins 1 t 8 carry ne mark each, questins
Electric Field. Electric field direction Same direction as the force on a positive charge Opposite direction to the force on an electron
Electric Field Electric field Space surrounding an electric charge (an energetic aura) Describes electric force Around a charged particle obeys inverse-square law Force per unit charge Electric Field Electric
Radiation Integrals and Auxiliary Potential Functions
Radiation Integrals and Auxiliary Potential Functions Ranga Rodrigo June 23, 2010 Lecture notes are fully based on Balanis [?]. Some diagrams and text are directly from the books. Contents 1 The Vector
Yeu-Sheng Paul Shiue, Ph.D 薛宇盛 Professor and Chair Mechanical Engineering Department Christian Brothers University 650 East Parkway South Memphis, TN
Yeu-Sheng Paul Shiue, Ph.D 薛宇盛 Prfessr and Chair Mechanical Engineering Department Christian Brthers University 650 East Parkway Suth Memphis, TN 38104 Office: (901) 321-3424 Rm: N-110 Fax : (901) 321-3402
Chapter 7. Time-Varying Fields and Maxwell s Equations
Chapter 7. Time-arying Fields and Maxwell s Equations Electrostatic & Time arying Fields Electrostatic fields E, D B, H =J D H 1 E B In the electrostatic model, electric field and magnetic fields are not
ECE 107: Electromagnetism
ECE 107: Electromagnetism Set 7: Dynamic fields Instructor: Prof. Vitaliy Lomakin Department of Electrical and Computer Engineering University of California, San Diego, CA 92093 1 Maxwell s equations Maxwell
On Boussinesq's problem
Internatinal Jurnal f Engineering Science 39 (2001) 317±322 www.elsevier.cm/lcate/ijengsci On Bussinesq's prblem A.P.S. Selvadurai * Department f Civil Engineering and Applied Mechanics, McGill University,
POLARISATION VISUAL PHYSICS ONLINE. View video on polarisation of light
VISUAL PHYSICS ONLINE MODULE 7 NATURE OF LIGHT POLARISATION View vide n plarisatin f light While all the experimental evidence s far that supprts the wave nature f light, nne f it tells us whether light
Building to Transformations on Coordinate Axis Grade 5: Geometry Graph points on the coordinate plane to solve real-world and mathematical problems.
Building t Transfrmatins n Crdinate Axis Grade 5: Gemetry Graph pints n the crdinate plane t slve real-wrld and mathematical prblems. 5.G.1. Use a pair f perpendicular number lines, called axes, t define
AIR FORCE RESEARCH LABORATORY
AIR FORC RSARCH LABORATORY The xtinctin Theem as an xample f Reseach Vistas in Mathematical Optics Mach Richad A. Albanese Infmatin Opeatins and Applied Mathematics Human ffectiveness Diectate Bks City-Base
ME 458: Electronic Packaging and Materials Electromagnetic part Lecture note
ME 458: Electrnic Packaging and Materials Electrmagnetic part ecture nte I. What is Signal Integrity (SI) - Timing and quality f the signal - Higher signal bandwidth and small sie f packaging leads t increasingly
20 Faraday s Law and Maxwell s Extension to Ampere s Law
Chapter 20 Faraday s Law and Maxwell s Extensin t Ampere s Law 20 Faraday s Law and Maxwell s Extensin t Ampere s Law Cnsider the case f a charged particle that is ming in the icinity f a ming bar magnet
Sections 15.1 to 15.12, 16.1 and 16.2 of the textbook (Robbins-Miller) cover the materials required for this topic.
Tpic : AC Fundamentals, Sinusidal Wavefrm, and Phasrs Sectins 5. t 5., 6. and 6. f the textbk (Rbbins-Miller) cver the materials required fr this tpic.. Wavefrms in electrical systems are current r vltage
Physics 102. Second Midterm Examination. Summer Term ( ) (Fundamental constants) (Coulomb constant)
ε µ0 N mp T kg Kuwait University hysics Department hysics 0 Secnd Midterm Examinatin Summer Term (00-0) July 7, 0 Time: 6:00 7:0 M Name Student N Instructrs: Drs. bdel-karim, frusheh, Farhan, Kkaj, a,
Vector field and Inductance. P.Ravindran, PHY041: Electricity & Magnetism 19 February 2013: Vector Field, Inductance.
Vector field and Inductance Earth s Magnetic Field Earth s field looks similar to what we d expect if 11.5 there were a giant bar magnet imbedded inside it, but the dipole axis of this magnet is offset
Chapter 7. Time-Varying Fields and Maxwell s Equation
Chapter 7. Time-Varying Fields and Maxwell s Equation Electrostatic & Time Varying Fields Electrostatic fields E, D B, H =J D H 1 E B In the electrostatic model, electric field and magnetic fields are
Physics 2B Chapter 23 Notes - Faraday s Law & Inductors Spring 2018
Michael Faraday lived in the Lndn area frm 1791 t 1867. He was 29 years ld when Hand Oersted, in 1820, accidentally discvered that electric current creates magnetic field. Thrugh empirical bservatin and
Today in Physics 122: electrostatics review
Today in Physics 122: electrostatics review David Blaine takes the practical portion of his electrostatics midterm (Gawker). 11 October 2012 Physics 122, Fall 2012 1 Electrostatics As you have probably
( ) ( ) Pre-Calculus Team Florida Regional Competition March Pre-Calculus Team Florida Regional Competition March α = for 0 < α <, and
Flrida Reginal Cmpetitin March 08 Given: sin ( ) sin π α = fr 0 < α