The Magnetic Field. Concepts and Principles. Moving Charges. Permanent Magnets


 Valerie Wilkerson
 1 years ago
 Views:
Transcription
1 . The Magnetc Feld Concepts and Prncples Movng Charges All charged partcles create electrc felds, and these felds can be detected by other charged partcles resultng n electrc force. However, a completely dfferent feld, both qualtatvely and quanttatvely, s created when charged partcles move. Ths s the magnetc feld. All movng charged partcles create magnetc felds, and all movng charged partcles can detect magnetc felds resultng n magnetc force. Ths s n addton to the electrc feld that s always present surroundng charged partcles. Ths should strke you as rather strange. Whenever a charged partcle begns to move a completely new feld sprngs nto exstence (dstrbutng busness cards throughout the unverse). Other charged partcles, f they are at rest relatve to ths new feld, do not notce ths new feld and do not feel a magnetc force. Only f they move relatve to ths new feld can they sense ts exstence and feel a magnetc force. It s as f only whle n moton can they read the busness cards dstrbuted by the orgnal movng charge, and only whle n moton does the orgnal charge dstrbute these busness cards n the frst place! Does t sound strange yet? Why the magnetc feld exsts, and ts relatonshp to the electrc feld and relatve moton wll be explored later n the course. For now, we wll concentrate on learnng how to calculate the value of the magnetc feld at varous ponts surroundng movng charges. Next chapter, we wll learn how to calculate the value of the magnetc force actng on other charges movng relatve to a magnetc feld. Permanent Magnets I clamed above that the magnetc feld only exsts when the source charges that create t are movng. ut what about permanent magnets, lke the ones holdng your favorte physcs assgnments to your refrgerator? Where are the movng charges n those magnets? The smplest answer s that the electrons n orbt n each of the atoms of the materal create magnetc felds. In most materals, these mcroscopc magnetc felds are orented n random drectons and therefore cancel out when summed over all of the atoms n the materal. In some materals, however, these mcroscopc magnetc felds are correlated n ther orentaton and add together to yeld a measurable macroscopc feld (large enough to nteract wth the mcroscopc magnetc felds present n your refrgerator door). Although ths s a gross smplfcaton of what actually takes place, t s good enough for now. 1
2 The magnetc propertes of real materals are extremely complcated. In addton to the orbtal contrbuton to magnetc feld, ndvdual electrons and protons have an ntrnsc magnetc feld assocated wth them due to a property called spn. Moreover, even neutrons, wth no net electrc charge, have an ntrnsc magnetc feld surroundng them. To learn more about the mcroscopc bass of magnetsm, consder becomng a physcs major Electrc Current Movng electrc charges form an electrc current. We wll consder the source of all magnetc felds to be electrc current, whether that current s macroscopc and flows through a wre or whether t s mcroscopc and flows n orbt around an atomc nucleus. The smplest source of magnetc feld s electrc current flowng through a long, straght wre. In ths case, the magntude of the magnetc feld at a partcular pont n space s gven by the relaton, where 2 r 0 s the permeablty of free space, a constant equal to 1.26 x 106 Tm/A, s the source current, the electrc current that creates the magnetc feld, measured n amperes 1 (A), r s the dstance between the source current and the pont of nterest, and the drecton of the magnetc feld s tangent to a crcle centered on the source current, and located at the pont of nterest. (To determne ths tangent drecton, place your thumb n the drecton of current flow. The sense n whch the fngers of your rght hand curl s the drecton of the magnetc feld. For example, for current flowng out of the page, the magnetc fled s counterclockwse.) 1 One ampere s equal to one coulomb of charge flowng through the wre per second. 2
3 Another common source of magnetc feld s electrc current flowng through a crcular loop of wre. In ths case, the magntude of the magnetc feld at the center of the loop s gven by the relaton, where R s the radus of the loop, 0 2 R and the drecton of the magnetc feld s perpendcular to the loop. (To determne ths drecton, agan place your thumb n the drecton of current flow. The sense n whch the fngers of your rght hand curl s the drecton of the magnetc feld. For example, for current flowng counterclockwse around the loop the magnetc feld nsde the loop ponts out of the page, and the magnetc feld outsde of the loop ponts nto the page.) 3
4 . The Magnetc Feld Analyss Tools Long, Parallel Wres Fnd the magnetc feld at the ndcated pont. The long, parallel wres are separated by a dstance 4a The magnetc feld at ths pont wll be the vector sum of the magnetc feld from the left wre and the magnetc feld from the rght wre. For the left wre, I ve ndcated the drecton of the magnetc feld. Remember, wth your thumb pontng n the drecton of the current (out of the page), the drecton n whch the fngers of your rght hand curl s the drecton of the tangent vector (counterclockwse) The magntude of the magnetc feld from the left wre s: left left left 2 r 2 5a (2) 0 (2a) 2 ( a) 2 To determne the drecton of ths feld, notce that the magnetc feld vector s at the same angle relatve to the yaxs that the lne connectng ts locaton to the source current s relatve to the xaxs. Ths lne forms a rght trangle wth gven by: a tan 2a tan a a
5 Thus, leftx leftx leftx sn a (0.45) 5a a lefty lefty lefty cos a (0.89) 5a a Repeatng the analyss for the magntude of the feld from the rght wre gves: rght rght rght 0 2 r ( ) (2a) 5a 0 2 ( a) 2 Wth your thumb pontng n the drecton of the current (nto the page), the drecton n whch the fngers of your rght hand curl s the drecton of the tangent vector (clockwse). Notce that the magnetc feld s at the same angle relatve to the yaxs as before, although ths magnetc feld has postve x and ycomponents. a  2a Thus, rghtx rghtx rghtx sn a (0.45) 2 5a a rghty rghty rghty cos a (0.89) 2 5a a 5
6 The resultant magnetc feld at ths pont s the sum of the felds from the two source currents: x x x leftx rghtx a a a y y y lefty rghty a a a Thus, the magnetc feld s predomnately n the +ydrecton wth a slght leftward (x) component. The magntude of ths feld could be determned by Pythagoras theorem, and the exact angle of the resultng feld determned by the tangent functon. Loops of Wre The nner col conssts of 100 crcular loops of wre wth radus 10 cm carryng 3.0 A counterclockwse and the outer col conssts of 500 crcular loops of wre wth radus 25 cm carryng 1.5 A clockwse. Fnd the magnetc feld at the orgn. The magnetc feld at the orgn wll be the vector sum of the magnetc felds from the two cols. Each loop of the nner col produces: 0 2R 6 (1.26x10 )(3) 2(0.10) 18.9x10 Snce there are 100 dentcal loops of wre makng up ths col, the total feld produced by the nner col s: Ths feld s drected out of the page. 1.89x10 6 T T 100(18.9x T ) 6
7 Each outer col produces: Ths feld s drected nto the page. N( ) 2R 6 (1.26x10 )(1.5) 500 2(0.25) 1.89x10 3 T Snce the two cols produce equal magntude but opposte drected magnetc felds at the orgn, the net magnetc feld at the orgn s zero. (Ths does not mean, however, that the feld s equal to zero at any other ponts n space.) 7
8 . The Magnetc Feld Actvtes 8
9 Determne the drecton of the net magnetc feld at each of the ndcated ponts. The wres are long, perpendcular to the page, and carry constant current ether out of (+) or nto () the page. a. +  b
10 Determne the drecton of the net magnetc feld at each of the ndcated ponts. The wres are long, perpendcular to the page, and carry constant current ether out of (+) or nto () the page. a.   b
11 Determne the drecton of the net magnetc feld at each of the ndcated ponts. The wres are long, perpendcular to the page, and carry constant current ether out of (+) or nto () the page. a b
12 Determne the drecton of the net magnetc feld at each of the ndcated ponts. The wres are long, perpendcular to the page, and carry constant current ether out of (+) or nto () the page. a b
13 Determne the drecton of the net magnetc feld at each of the ndcated ponts. All fgures are planar and the wres are long and carry constant current n the drecton ndcated. a. b. 2 c. 3 d. 4 2 e
14 Determne the drecton of the net magnetc feld at each of the ndcated ponts. All fgures are planar and the wres are long, nsulated from each other, and carry constant current n the drecton ndcated. a. b. 2 c. d
15 Determne the drecton of the net magnetc feld at each of the ndcated ponts. The ponts are n the parallel or perpendcular plane passng through the center of each crcular hoop. a. b. c. d. 15 2
16 For each of the current dstrbutons below, ndcate the approxmate locaton(s), f any, where the magnetc feld s zero. The wres are long, perpendcular to the page, and carry constant current ether out of (+) or nto () the page. a. + + b. +  c d e
17 For each of the current dstrbutons below, ndcate the approxmate locaton(s), f any, where the magnetc feld s zero. The wres are long, perpendcular to the page, and carry constant current ether out of (+) or nto () the page. a b
18 For each of the current dstrbutons below, determne and clearly label the regons where the magnetc feld ponts nto and out of the plane of the page. All fgures are planar and the wres are long, nsulated from each other, and carry constant current n the drecton ndcated. a. b. 2 c. d
19 A par of long, parallel wres separated by 0.5 cm carry 1.0 A n opposte drectons. Fnd the magnetc feld drectly between the wres. +  Qualtatve Analyss On the graphc above, sketch the drecton of the magnetc feld at the requested pont. Explan why the magnetc feld ponts n ths drecton. Mathematcal Analyss 19
20 Four long, parallel wres wth spacng 1.5 cm each carry 350 ma. Fnd the magnetc feld at the center of the wre array Qualtatve Analyss On the graphc above, sketch the drecton of the magnetc feld at the requested pont. Explan why the magnetc feld ponts n ths drecton. Mathematcal Analyss 20
21 Fnd the magnetc feld at each of the ndcated ponts. The long, parallel wres are separated by a dstance 4a. a. b. c. +  d. Mathematcal Analyss 21
22 Fnd the magnetc feld at each of the ndcated ponts. The long, parallel wres are separated by a dstance 4a. a. b. c d. Mathematcal Analyss 22
23 The long, parallel wres at rght are separated by a dstance 2a. Fnd the magnetc feld at all ponts on the yaxs. + + Mathematcal Analyss Questons For all ponts on the yaxs, what should y equal? Does your functon agree wth ths observaton? At y = 0, what should x equal? Does your functon agree wth ths observaton? Sketch x below. Indcate the value of the functon at y = 0. y 23
24 The long, parallel wres at rght are separated by a dstance 2a. Fnd the magnetc feld at all ponts on the yaxs. +  Mathematcal Analyss Questons For all ponts on the yaxs, what should x equal? Does your functon agree wth ths observaton? Sketch y below. Indcate the value of the functon at y = 0. y 24
25 The long, parallel wres at rght are separated by a dstance 2a. Determne the locaton(s), f any, where the magnetc feld s zero Mathematcal Analyss 25
26 The long, parallel wres at rght are separated by a dstance 2a. Determne the locaton(s), f any, where the magnetc feld s zero Mathematcal Analyss 26
27 The long, parallel wres at rght are separated by a dstance 2a. Determne the locaton(s), f any, where the magnetc feld s zero Mathematcal Analyss 27
28 Fnd the magnetc feld at the orgn. The nner radus R col conssts of N loops of wre carryng current counterclockwse and the outer radus 3R col conssts of 2N loops of wre carryng current clockwse. Mathematcal Analyss 28
29 Fnd the magnetc feld at the orgn. The nner radus R col conssts of 3N loops of wre carryng current counterclockwse and the outer radus 3R col conssts of N loops of wre carryng current 2 counterclockwse. Mathematcal Analyss 29
30 A long wre carryng 2.0 A s bent nto a crcular loop of radus 5.0 cm as shown at rght. Fnd the magnetc feld at the center of the crcle. Mathematcal Analyss 30
Moment of a force about a point and about an axis
3. STATICS O RIGID BODIES In the precedng chapter t was assumed that each of the bodes consdered could be treated as a sngle partcle. Such a vew, however, s not always possble, and a body, n general, should
More information21 Vectors: The Cross Product & Torque
21 Vectors: The Cross Product & Torque Do not use our left hand when applng ether the rghthand rule for the cross product of two vectors dscussed n ths chapter or the rghthand rule for somethng curl
More informationLaws of Electromagnetism
There are four laws of electromagnetsm: Laws of Electromagnetsm The law of BotSavart Ampere's law Force law Faraday's law magnetc feld generated by currents n wres the effect of a current on a loop of
More informationRotation Kinematics, Moment of Inertia, and Torque
Rotaton Knematcs, Moment of Inerta, and Torque Mathematcally, rotaton of a rgd body about a fxed axs s analogous to a lnear moton n one dmenson. Although the physcal quanttes nvolved n rotaton are qute
More informationz(t) = z 1 (t) + t(z 2 z 1 ) z(t) = 1 + i + t( 2 3i (1 + i)) z(t) = 1 + i + t( 3 4i); 0 t 1
(4.): ontours. Fnd an admssble parametrzaton. (a). the lne segment from z + to z 3. z(t) z (t) + t(z z ) z(t) + + t( 3 ( + )) z(t) + + t( 3 4); t (b). the crcle jz j 4 traversed once clockwse startng at
More informationHALL EFFECT SENSORS AND COMMUTATION
OEM770 5 Hall Effect ensors H P T E R 5 Hall Effect ensors The OEM770 works wth threephase brushless motors equpped wth Hall effect sensors or equvalent feedback sgnals. In ths chapter we wll explan how
More informationExperiment 8 Two Types of Pendulum
Experment 8 Two Types of Pendulum Preparaton For ths week's quz revew past experments and read about pendulums and harmonc moton Prncples Any object that swngs back and forth can be consdered a pendulum
More informationGoals Rotational quantities as vectors. Math: Cross Product. Angular momentum
Physcs 106 Week 5 Torque and Angular Momentum as Vectors SJ 7thEd.: Chap 11.2 to 3 Rotatonal quanttes as vectors Cross product Torque expressed as a vector Angular momentum defned Angular momentum as a
More informationChapter 8. Rotational Equilibrium and Rotational Dynamics. ! = Fd. ! = Fr sin" !F x = 0 and!f y = 0. Wrench Demo. Torque is vector quantity.
Wrench emo hapter 8 Rotatonal Equlbrum and Rotatonal ynamcs Torque Torque,!, s tendency of a force to rotate object about some axs! = Fd F s the force d s the lever arm (or moment arm) Torque s vector
More informationGraph Theory and Cayley s Formula
Graph Theory and Cayley s Formula Chad Casarotto August 10, 2006 Contents 1 Introducton 1 2 Bascs and Defntons 1 Cayley s Formula 4 4 Prüfer Encodng A Forest of Trees 7 1 Introducton In ths paper, I wll
More informationSCALAR A physical quantity that is completely characterized by a real number (or by its numerical value) is called a scalar. In other words, a scalar
SCALAR A phscal quantt that s completel charactered b a real number (or b ts numercal value) s called a scalar. In other words, a scalar possesses onl a magntude. Mass, denst, volume, temperature, tme,
More informationMechanics of Rigid Body
Mechancs of Rgd Body 1. Introducton Knematcs, Knetcs and Statc 2. Knematcs. Types of Rgd Body Moton: Translaton, Rotaton General Plane Moton 3. Knetcs. Forces and Acceleratons. Energy and Momentum Methods.
More information1E6 Electrical Engineering AC Circuit Analysis and Power Lecture 12: Parallel Resonant Circuits
E6 Electrcal Engneerng A rcut Analyss and Power ecture : Parallel esonant rcuts. Introducton There are equvalent crcuts to the seres combnatons examned whch exst n parallel confguratons. The ssues surroundng
More informationPart 1. Electromagnetic Induction. Faraday s Law. Faraday s observation. Problem. Induced emf (Voltage) from changing Magnetic Flux.
Electromagnetc Inducton Part 1 Faraday s Law Chapter 1 Faraday s obseraton Electrc currents produce magnetc elds. 19 th century puzzle: Can magnetc elds produce currents? A statc magnet wll produce no
More informationPreLab 8. Torque balance & Rotational Dynamics. References (optional) 1. Review of concepts. Torque & Rotational Equilibrium
PreLab 8 orque balance & Rotatonal Dynamcs References (optonal) Physcs 121: pler & Mosca, Physcs for Scentsts and Engneers, 6 th edton, Vol. 1 (Red book). Chapter 9, sectons 92, 93, 94, example 911.
More informationHalliday/Resnick/Walker 7e Chapter 25 Capacitance
HRW 7e hapter 5 Page o 0 Hallday/Resnck/Walker 7e hapter 5 apactance. (a) The capactance o the system s q 70 p 35. pf. 0 (b) The capactance s ndependent o q; t s stll 3.5 pf. (c) The potental derence becomes
More informationToday in Physics 217: the divergence and curl theorems
Today n Physcs 217: the dvergence and curl theorems Flux and dvergence: proof of the dvergence theorem, à lá Purcell. rculaton and curl: proof of tokes theorem, also followng Purcell. ee Purcell, chapter
More informationQUANTUM MECHANICS, BRAS AND KETS
PH575 SPRING QUANTUM MECHANICS, BRAS AND KETS The followng summares the man relatons and defntons from quantum mechancs that we wll be usng. State of a phscal sstem: The state of a phscal sstem s represented
More informationHomework Solutions Physics 8B Spring 2012 Chpt. 32 5,18,25,27,36,42,51,57,61,76
Homework Solutons Physcs 8B Sprng 202 Chpt. 32 5,8,25,27,3,42,5,57,,7 32.5. Model: Assume deal connectng wres and an deal battery for whch V bat =. Please refer to Fgure EX32.5. We wll choose a clockwse
More informationCHAPTER 8 Potential Energy and Conservation of Energy
CHAPTER 8 Potental Energy and Conservaton o Energy One orm o energy can be converted nto another orm o energy. Conservatve and nonconservatve orces Physcs 1 Knetc energy: Potental energy: Energy assocated
More informationThe example below solves a system in the unknowns α and β:
The Fnd Functon The functon Fnd returns a soluton to a system of equatons gven by a solve block. You can use Fnd to solve a lnear system, as wth lsolve, or to solve nonlnear systems. The example below
More information( ) Homework Solutions Physics 8B Spring 09 Chpt. 32 5,18,25,27,36,42,51,57,61,76
Homework Solutons Physcs 8B Sprng 09 Chpt. 32 5,8,25,27,3,42,5,57,,7 32.5. Model: Assume deal connectng wres and an deal battery for whch V bat = E. Please refer to Fgure EX32.5. We wll choose a clockwse
More informationLinear Circuits Analysis. Superposition, Thevenin /Norton Equivalent circuits
Lnear Crcuts Analyss. Superposton, Theenn /Norton Equalent crcuts So far we hae explored tmendependent (resste) elements that are also lnear. A tmendependent elements s one for whch we can plot an / cure.
More informationwhere the coordinates are related to those in the old frame as follows.
Chapter 2  Cartesan Vectors and Tensors: Ther Algebra Defnton of a vector Examples of vectors Scalar multplcaton Addton of vectors coplanar vectors Unt vectors A bass of noncoplanar vectors Scalar product
More informationChapter 20 Rigid Body: Translation and Rotational Motion Kinematics for Fixed Axis Rotation
Chapter 20 Rgd Body: Translaton and Rotatonal Moton Knematcs for Fxed Axs Rotaton 201 Introducton 1 202 Constraned Moton: Translaton and Rotaton 1 2021 Rollng wthout slppng 5 Example 201 Bcycle Wheel Rollng
More informationFaraday's Law of Induction
Introducton Faraday's Law o Inducton In ths lab, you wll study Faraday's Law o nducton usng a wand wth col whch swngs through a magnetc eld. You wll also examne converson o mechanc energy nto electrc energy
More informationHYPOTHESIS TESTING OF PARAMETERS FOR ORDINARY LINEAR CIRCULAR REGRESSION
HYPOTHESIS TESTING OF PARAMETERS FOR ORDINARY LINEAR CIRCULAR REGRESSION Abdul Ghapor Hussn Centre for Foundaton Studes n Scence Unversty of Malaya 563 KUALA LUMPUR Emal: ghapor@umedumy Abstract Ths paper
More informationChapter 11 Torque and Angular Momentum
Chapter 11 Torque and Angular Momentum I. Torque II. Angular momentum  Defnton III. Newton s second law n angular form IV. Angular momentum  System of partcles  Rgd body  Conservaton I. Torque  Vector
More informationRotation and Conservation of Angular Momentum
Chapter 4. Rotaton and Conservaton of Angular Momentum Notes: Most of the materal n ths chapter s taken from Young and Freedman, Chaps. 9 and 0. 4. Angular Velocty and Acceleraton We have already brefly
More informationGeneral Physics (PHY 2130)
General Physcs (PHY 130) Lecture 15 Energy Knetc and potental energy Conservatve and nonconservatve orces http://www.physcs.wayne.edu/~apetrov/phy130/ Lghtnng Revew Last lecture: 1. Work and energy: work:
More information+ + +   This circuit than can be reduced to a planar circuit
MeshCurrent Method The meshcurrent s analog of the nodeoltage method. We sole for a new set of arables, mesh currents, that automatcally satsfy KCLs. As such, meshcurrent method reduces crcut soluton to
More informationThinking about Newton's Laws
Newtonan modellng In ths actvty you wll see how Newton s Laws of Moton are used to connect the moton of an object wth the forces actng on t. You wll practse applyng Newton s three laws n some real contexts.
More informationHÜCKEL MOLECULAR ORBITAL THEORY
1 HÜCKEL MOLECULAR ORBITAL THEORY In general, the vast maorty polyatomc molecules can be thought of as consstng of a collecton of two electron bonds between pars of atoms. So the qualtatve pcture of σ
More informationPing Pong Fun  Video Analysis Project
Png Pong Fun  Vdeo Analyss Project Objectve In ths experment we are gong to nvestgate the projectle moton of png pong balls usng Verner s Logger Pro Software. Does the object travel n a straght lne? What
More informationCHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES
CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES In ths chapter, we wll learn how to descrbe the relatonshp between two quanttatve varables. Remember (from Chapter 2) that the terms quanttatve varable
More informationIntroduction: Analysis of Electronic Circuits
/30/008 ntroducton / ntroducton: Analyss of Electronc Crcuts Readng Assgnment: KVL and KCL text from EECS Just lke EECS, the majorty of problems (hw and exam) n EECS 3 wll be crcut analyss problems. Thus,
More informationRecurrence. 1 Definitions and main statements
Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.
More informationElectric circuit components. Direct Current (DC) circuits
Electrc crcut components Capactor stores charge and potental energy, measured n Farads (F) Battery generates a constant electrcal potental dfference ( ) across t. Measured n olts (). Resstor ressts flow
More informationMultivariate EWMA Control Chart
Multvarate EWMA Control Chart Summary The Multvarate EWMA Control Chart procedure creates control charts for two or more numerc varables. Examnng the varables n a multvarate sense s extremely mportant
More informationThe mathematical representation of physical objects and relativistic Quantum Mechanics.
The mathematcal representaton of physcal obects and relatvstc Quantum Mechancs. Enrque Ordaz Romay 1 Facultad de Cencas Físcas, Unversdad Complutense de Madrd Abstract The mathematcal representaton of
More information9.1 The Cumulative Sum Control Chart
Learnng Objectves 9.1 The Cumulatve Sum Control Chart 9.1.1 Basc Prncples: Cusum Control Chart for Montorng the Process Mean If s the target for the process mean, then the cumulatve sum control chart s
More informationLoop Parallelization
  Loop Parallelzaton C52 Complaton steps: nested loops operatng on arrays, sequentell executon of teraton space DECLARE B[..,..+] FOR I :=.. FOR J :=.. I B[I,J] := B[I,J]+B[I,J] ED FOR ED FOR analyze
More informationPhysics problem solving (Key)
Name: Date: Name: Physcs problem solvng (Key) Instructons: 1.. Fnd one partner to work together. You can use your textbook, calculator and may also want to have scratch paper. 3. Work through the problems
More informationPart IB Paper 1: Mechanics Examples Paper Kinematics
Engneerng Trpos Part B SECOND YEAR Straghtforward questons are marked t Trpos standard questons are marked *. Part B Paper 1: Mechancs Examples Paper Knematcs 1 ~..~~." 'SSUED ON t 7 JAN 20t4
More informationChapter 12 Inductors and AC Circuits
hapter Inductors and A rcuts awrence B. ees 6. You may make a sngle copy of ths document for personal use wthout wrtten permsson. Hstory oncepts from prevous physcs and math courses that you wll need for
More informationGEOLOGIC STRUCTURES. I. Tectonic Forces (Forces that move and deform rocks, especially along plate boundaries.)
GEOLOGIC STRUCTURES Structural geology s the branch of geology that pertans to the shapes, arrangement, and nterrelatonshps of bedrock unts and the forces that cause them. Structural geologsts study the
More informationSolution of Algebraic and Transcendental Equations
CHAPTER Soluton of Algerac and Transcendental Equatons. INTRODUCTION One of the most common prolem encountered n engneerng analyss s that gven a functon f (, fnd the values of for whch f ( = 0. The soluton
More informationConversion between the vector and raster data structures using Fuzzy Geographical Entities
Converson between the vector and raster data structures usng Fuzzy Geographcal Enttes Cdála Fonte Department of Mathematcs Faculty of Scences and Technology Unversty of Combra, Apartado 38, 3 454 Combra,
More informationII. PROBABILITY OF AN EVENT
II. PROBABILITY OF AN EVENT As ndcated above, probablty s a quantfcaton, or a mathematcal model, of a random experment. Ths quantfcaton s a measure of the lkelhood that a gven event wll occur when the
More information8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by
6 CHAPTER 8 COMPLEX VECTOR SPACES 5. Fnd the kernel of the lnear transformaton gven n Exercse 5. In Exercses 55 and 56, fnd the mage of v, for the ndcated composton, where and are gven by the followng
More informationSupport Vector Machines
Support Vector Machnes Max Wellng Department of Computer Scence Unversty of Toronto 10 Kng s College Road Toronto, M5S 3G5 Canada wellng@cs.toronto.edu Abstract Ths s a note to explan support vector machnes.
More informationv a 1 b 1 i, a 2 b 2 i,..., a n b n i.
SECTION 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS 455 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS All the vector spaces we have studed thus far n the text are real vector spaces snce the scalars are
More informationUnderstanding the Genetics of Blood Groups
Name: Key Class: Date: Understandng the Genetcs of Blood Groups Objectves: understand the genetcs of blood types determne the ABO blood type of unknown smulated blood samples predct, usng punnett squares,
More informationPERRON FROBENIUS THEOREM
PERRON FROBENIUS THEOREM R. CLARK ROBINSON Defnton. A n n matrx M wth real entres m, s called a stochastc matrx provded () all the entres m satsfy 0 m, () each of the columns sum to one, m = for all, ()
More informationGenerator WarmUp Characteristics
NO. REV. NO. : ; ~ Generator WarmUp Characterstcs PAGE OF Ths document descrbes the warmup process of the SNAP27 Generator Assembly after the sotope capsule s nserted. Several nqures have recently been
More informationWhat is Candidate Sampling
What s Canddate Samplng Say we have a multclass or mult label problem where each tranng example ( x, T ) conssts of a context x a small (mult)set of target classes T out of a large unverse L of possble
More informationQuestions that we may have about the variables
Antono Olmos, 01 Multple Regresson Problem: we want to determne the effect of Desre for control, Famly support, Number of frends, and Score on the BDI test on Perceved Support of Latno women. Dependent
More informationEXPLORATION 2.5A Exploring the motion diagram of a dropped object
5 Acceleraton Let s turn now to moton that s not at constant elocty. An example s the moton of an object you release from rest from some dstance aboe the floor. EXPLORATION.5A Explorng the moton dagram
More information 573 A Possible Detector for the Study of Weak Interactions at Fermi Clash R. Singer Argonne National Laboratory
 573 A Possble Detector for the Study of Weak nteractons at Ferm Clash R. Snger Argonne Natonal Laboratory The purpose of ths paper s to pont out what weak nteracton phenomena may exst for centerofmass
More informationA machine vision approach for detecting and inspecting circular parts
A machne vson approach for detectng and nspectng crcular parts DuMng Tsa Machne Vson Lab. Department of Industral Engneerng and Management YuanZe Unversty, ChungL, Tawan, R.O.C. Emal: edmtsa@saturn.yzu.edu.tw
More information9 Arithmetic and Geometric Sequence
AAU  Busness Mathematcs I Lecture #5, Aprl 4, 010 9 Arthmetc and Geometrc Sequence Fnte sequence: 1, 5, 9, 13, 17 Fnte seres: 1 + 5 + 9 + 13 +17 Infnte sequence: 1,, 4, 8, 16,... Infnte seres: 1 + + 4
More informationEE201 Circuit Theory I 2015 Spring. Dr. Yılmaz KALKAN
EE201 Crcut Theory I 2015 Sprng Dr. Yılmaz KALKAN 1. Basc Concepts (Chapter 1 of Nlsson  3 Hrs.) Introducton, Current and Voltage, Power and Energy 2. Basc Laws (Chapter 2&3 of Nlsson  6 Hrs.) Voltage
More informationMean Molecular Weight
Mean Molecular Weght The thermodynamc relatons between P, ρ, and T, as well as the calculaton of stellar opacty requres knowledge of the system s mean molecular weght defned as the mass per unt mole of
More informationHarvard University Division of Engineering and Applied Sciences. Fall Lecture 3: The Systems Approach  Electrical Systems
Harvard Unversty Dvson of Engneerng and Appled Scences ES 45/25  INTRODUCTION TO SYSTEMS ANALYSIS WITH PHYSIOLOGICAL APPLICATIONS Fall 2000 Lecture 3: The Systems Approach  Electrcal Systems In the last
More informationLecture 2: Single Layer Perceptrons Kevin Swingler
Lecture 2: Sngle Layer Perceptrons Kevn Sngler kms@cs.str.ac.uk Recap: McCullochPtts Neuron Ths vastly smplfed model of real neurons s also knon as a Threshold Logc Unt: W 2 A Y 3 n W n. A set of synapses
More informationSIX WAYS TO SOLVE A SIMPLE PROBLEM: FITTING A STRAIGHT LINE TO MEASUREMENT DATA
SIX WAYS TO SOLVE A SIMPLE PROBLEM: FITTING A STRAIGHT LINE TO MEASUREMENT DATA E. LAGENDIJK Department of Appled Physcs, Delft Unversty of Technology Lorentzweg 1, 68 CJ, The Netherlands Emal: e.lagendjk@tnw.tudelft.nl
More informationb) The mean of the fitted (predicted) values of Y is equal to the mean of the Y values: c) The residuals of the regression line sum up to zero: = ei
Mathematcal Propertes of the Least Squares Regresson The least squares regresson lne obeys certan mathematcal propertes whch are useful to know n practce. The followng propertes can be establshed algebracally:
More informationProbablty of an Acute Trangle n the Twodmensonal Spaces of Constant Curvature Abstract The nterest n the statstcal theory of shape has arsen snce Ken
Probablty of an Acute Trangle n the Twodmensonal Spaces of Constant Curvature Afflated Hgh School of SCNU, Canton, Chna Student: Lv Zyuan, Guo Yuyu Advsor: We Jzhu  54  Probablty of an Acute Trangle
More informationVLSI Technology Dr. Nandita Dasgupta Department of Electrical Engineering Indian Institute of Technology, Madras
VLI Technology Dr. Nandta Dasgupta Department of Electrcal Engneerng Indan Insttute of Technology, Madras Lecture  11 Oxdaton I netcs of Oxdaton o, the unt process step that we are gong to dscuss today
More informationReview C: Work and Kinetic Energy
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department o Physcs 8.2 Revew C: Work and Knetc Energy C. Energy... 2 C.. The Concept o Energy... 2 C..2 Knetc Energy... 3 C.2 Work and Power... 4 C.2. Work Done by
More informationSolutions to First Midterm
rofessor Chrstano Economcs 3, Wnter 2004 Solutons to Frst Mdterm. Multple Choce. 2. (a) v. (b). (c) v. (d) v. (e). (f). (g) v. (a) The goods market s n equlbrum when total demand equals total producton,.e.
More information1. Measuring association using correlation and regression
How to measure assocaton I: Correlaton. 1. Measurng assocaton usng correlaton and regresson We often would lke to know how one varable, such as a mother's weght, s related to another varable, such as a
More information"Research Note" APPLICATION OF CHARGE SIMULATION METHOD TO ELECTRIC FIELD CALCULATION IN THE POWER CABLES *
Iranan Journal of Scence & Technology, Transacton B, Engneerng, ol. 30, No. B6, 789794 rnted n The Islamc Republc of Iran, 006 Shraz Unversty "Research Note" ALICATION OF CHARGE SIMULATION METHOD TO ELECTRIC
More information1. Give a reason why the Thomson plumpudding model does not agree with experimental observations.
[Problems] Walker, Physcs, 3 rd Edton Chapter 31 Conceptual Questons (Answers to oddnumbered Conceptual Questons can be ound n the back o the book, begnnng on page ANSxx.) 1. Gve a reason why the Thomson
More informationChapter 9. Linear Momentum and Collisions
Chapter 9 Lnear Momentum and Collsons CHAPTER OUTLINE 9.1 Lnear Momentum and Its Conservaton 9.2 Impulse and Momentum 9.3 Collsons n One Dmenson 9.4 TwoDmensonal Collsons 9.5 The Center of Mass 9.6 Moton
More informationImplementation of Deutsch's Algorithm Using Mathcad
Implementaton of Deutsch's Algorthm Usng Mathcad Frank Roux The followng s a Mathcad mplementaton of Davd Deutsch's quantum computer prototype as presented on pages  n "Machnes, Logc and Quantum Physcs"
More informationTHE METHOD OF LEAST SQUARES THE METHOD OF LEAST SQUARES
The goal: to measure (determne) an unknown quantty x (the value of a RV X) Realsaton: n results: y 1, y 2,..., y j,..., y n, (the measured values of Y 1, Y 2,..., Y j,..., Y n ) every result s encumbered
More informationChapter 4: Motion in Two Dimensions
Answers and Solutons. (a) Tme s a scalar quantt. (b) Dsplacement s a vector quantt. (c) Veloct s a vector quantt. (d) Speed s a scalar quantt.. An nspecton of the lengths, or magntudes, or the vectors
More informationESA Study Guide Year 10 Science
ES Study Gude Year 10 Scence Chapter 10: Electrc crcuts Conductors nsulators Questons from page 131 of ES Study Gude Year 10 Scence Understng 1. Explan the dfference between a good conductor of electrcty
More informationPLANAR GRAPHS. Plane graph (or embedded graph) A graph that is drawn on the plane without edge crossing, is called a Plane graph
PLANAR GRAPHS Basc defntons Isomorphc graphs Two graphs G(V,E) and G2(V2,E2) are somorphc f there s a onetoone correspondence F of ther vertces such that the followng holds:  u,v V, uv E, => F(u)F(v)
More informationgreatest common divisor
4. GCD 1 The greatest common dvsor of two ntegers a and b (not both zero) s the largest nteger whch s a common factor of both a and b. We denote ths number by gcd(a, b), or smply (a, b) when there s no
More informationCHAPTER 14 MORE ABOUT REGRESSION
CHAPTER 14 MORE ABOUT REGRESSION We learned n Chapter 5 that often a straght lne descrbes the pattern of a relatonshp between two quanttatve varables. For nstance, n Example 5.1 we explored the relatonshp
More informationChapter 6 Balancing of Rotating Masses
Chapter 6 Balancng of otatng Masses All rotors have soe eccentrct. Eccentrct s present when geoetrcal center of the rotor and the ass center do not concde along ther length (gure ). Eaples of rotors are
More informationHomework: 49, 56, 67, 60, 64, 74 (p. 234237)
Hoework: 49, 56, 67, 60, 64, 74 (p. 3437) 49. bullet o ass 0g strkes a ballstc pendulu o ass kg. The center o ass o the pendulu rses a ertcal dstance o c. ssung that the bullet reans ebedded n the pendulu,
More informationSection 15: Magnetic properties of materials
Physcs 97 Secton 15: Magnetc propertes of materals Defnton of fundamental quanttes When a materal medum s placed n a magnetc feld, the medum s magnetzed. Ths magnetzaton s descrbed by the magnetzaton vector
More informationEffects of ExtremeLow Frequency Electromagnetic Fields on the Weight of the Hg at the Superconducting State.
Effects of EtremeLow Frequency Electromagnetc Felds on the Weght of the at the Superconductng State. Fran De Aquno Maranhao State Unversty, Physcs Department, S.Lus/MA, Brazl. Copyrght 200 by Fran De
More informationAttention: This material is copyright Chris Hecker. All rights reserved.
Attenton: Ths materal s copyrght 19951997 Chrs Hecker. All rghts reserved. You have permsson to read ths artcle for your own educaton. You do not have permsson to put t on your webste (but you may lnk
More informationGeneral Physics (PHY 2130)
General Physcs (PHY 30) Lecture 8 Moentu Collsons Elastc and nelastc collsons http://www.physcs.wayne.edu/~apetro/phy30/ Lghtnng Reew Last lecture:. Moentu: oentu and pulse oentu conseraton Reew Proble:
More information) of the Cell class is created containing information about events associated with the cell. Events are added to the Cell instance
Calbraton Method Instances of the Cell class (one nstance for each FMS cell) contan ADC raw data and methods assocated wth each partcular FMS cell. The calbraton method ncludes event selecton (Class Cell
More informationME 563 HOMEWORK # 1 (Solutions) Fall 2010
ME 563 HOMEWORK # 1 (Solutons) Fall 2010 PROBLEM 1: (40%) Derve the equatons of moton for the three systems gven usng NewtonEuler technques (A, B, and C) and energy/power methods (A and B only). System
More information4088858 05 AUG 10 Rev L
SL Jack Tool Kt 1725150 [ ] Instructon Sheet 4088858 05 AUG 10 PROPER USE GUIDELINES Cumulatve Trauma Dsorders can result from the prolonged use of manually powered hand tools. Hand tools are ntended
More informationChapter 3 Group Theory p. 1  Remark: This is only a brief summary of most important results of groups theory with respect
Chapter 3 Group Theory p.  3. Compact Course: Groups Theory emark: Ths s only a bref summary of most mportant results of groups theory wth respect to the applcatons dscussed n the followng chapters. For
More informationx f(x) 1 0.25 1 0.75 x 1 0 1 1 0.04 0.01 0.20 1 0.12 0.03 0.60
BIVARIATE DISTRIBUTIONS Let be a varable that assumes the values { 1,,..., n }. Then, a functon that epresses the relatve frequenc of these values s called a unvarate frequenc functon. It must be true
More informationErrorPropagation.nb 1. Error Propagation
ErrorPropagaton.nb Error Propagaton Suppose that we make observatons of a quantty x that s subject to random fluctuatons or measurement errors. Our best estmate of the true value for ths quantty s then
More informationFormula of Total Probability, Bayes Rule, and Applications
1 Formula of Total Probablty, Bayes Rule, and Applcatons Recall that for any event A, the par of events A and A has an ntersecton that s empty, whereas the unon A A represents the total populaton of nterest.
More informationRECOGNIZING DIFFERENT TYPES OF STOCHASTIC PROCESSES
RECOGNIZING DIFFERENT TYPES OF STOCHASTIC PROCESSES JONG U. KIM AND LASZLO B. KISH Department of Electrcal and Computer Engneerng, Texas A&M Unversty, College Staton, TX 778418, USA Receved (receved date)
More information1 Example 1: Axisaligned rectangles
COS 511: Theoretcal Machne Learnng Lecturer: Rob Schapre Lecture # 6 Scrbe: Aaron Schld February 21, 2013 Last class, we dscussed an analogue for Occam s Razor for nfnte hypothess spaces that, n conjuncton
More informationSection C2: BJT Structure and Operational Modes
Secton 2: JT Structure and Operatonal Modes Recall that the semconductor dode s smply a pn juncton. Dependng on how the juncton s based, current may easly flow between the dode termnals (forward bas, v
More informationCalculating the high frequency transmission line parameters of power cables
< ' Calculatng the hgh frequency transmsson lne parameters of power cables Authors: Dr. John Dcknson, Laboratory Servces Manager, N 0 RW E B Communcatons Mr. Peter J. Ncholson, Project Assgnment Manager,
More informationChapter 6 Inductance, Capacitance, and Mutual Inductance
Chapter 6 Inductance Capactance and Mutual Inductance 6. The nductor 6. The capactor 6.3 Seresparallel combnatons of nductance and capactance 6.4 Mutual nductance 6.5 Closer look at mutual nductance Oerew
More information