3.1 Magnetic Fields. Oersted and Ampere


 Gervase Woods
 4 years ago
 Views:
Transcription
1 3.1 Mgnetic Fields Oested nd Ampee The definition of mgnetic induction, B Fields of smll loop (dipole) Mgnetic fields in mtte: ) feomgnetism ) mgnetiztion, (M ) c) mgnetic susceptiility, m d) mgnetic field, H e) emnent nd induced M (hysteesis) Oested nd Ampee The ide tht the Eth hd some popety tht mde lodestone (mgnetic) neees lign in NS diection if the oot of the concept of mgnetic foce field. Oested found tht wie cying cuent lso ffected compss neee nd so estlished tht it is chges in motion tht cete the mgnetic foce field. Actully the fct is tht chges in motion poduce foce on othe chges in motion nd we descie this phenomenon y intoducing the concept of mgnetic field. Ampee fomulted the ide of the foce field when he found tht thee ws foce ceted etween two cuent cying wies: 1
2 Foce / unit length = II k In SI units, k = 0 / whee 0 = Lte this ws genelized so the foce could e clculted etween two cuent cying cicuits nd. F 0 II 4 1 The definition of mgnetic induction, B If we think of this foce s something hppening to cicuit cused y the totl effect of cicuit, we could ewite the expession fo F s F I 0 I
3 The tem in sque ckets is now popety of ; it is something ceted y cicuit which intects with the cuent in cicuit to poduce the foce on. It is defined s 'field' nd clled the mgnetic induction B. In S.I units, B is Tesl (T). In c.g.s units, B is in Guss (1.0 T = 10 4 guss). [In mny mgnetic suveys c.g.s unit clled the gmm () is used. 1.0 = 105 guss = 109 T (1.0 nt)]. The foce on n element of cuent then hs the fom: df I B nd if thee is cuent density, J, i.e. volume distiution of cuent, the expession fo B ecomes: 0 J B dv 4 V 1 (3.1.1) This simple fomul fo B ws deived y Biot nd Svt. The diection of the field follows the ight hnd ule  thum of ight hnd in diection of cuent then finges point in diection of B. Fom these definitions nd it of potentil theoy, we cn find the field fom smll loop of wie of dius cying cuent I fom: 3
4 0 1 B m 4 (3.1.) o, expnded whee 0 ( I) 0 ( I) B cos sin (3.1.3) m I IA This smll loop of cuent is clled mgnetic dipole nd m is clled the dipole moment of the loop. nd e unit vectos in the dil nd diections espectively. If you plot the field lines fom such dipole souce you get: 4
5 Mgnetic fields in mtte In simplistic clssicl view, ech tom of mtte, suounded y its shell of electons, looks like smll loop of cuent nd so hs mgnetic moment. If the toms e ndomly oiented, the net moment is zeo. If the toms line up, thee will e net moment, M, due to finite loop of mgnetiztion cuent I m s shown in the sketch: M = I m A Rigoously, the moment is computed fo cuents flowing ound volume V nd the mgnetiztion M is the moment pe unit volume. The individul loops my e lined up y n extenl field (like compss neee)  this is pmgnetism. They my e lined up opposite to the inducing field  dimgnetism. They my spontneously line up in smll goups clled domins  feomgnetism. The domins in tun my e lined up y n extenl field. In typicl minels the pmgnetic effect is dominnt ut wek. Minels contining ion, pticully mgnetite Fe 3 0 4, e stongly feomgnetic nd ccount fo the 5
6 mgnetiztion encounteed in ocks. When thee is mgnetiztion, thee is n dditionl cuent I m, o cuent density J m, which is dded to ny conventionl cuent tht might e pesent. In feomgnetic mteils the mgnetiztion M is ceted y the ppliction of mgnetic field  n pplied field cuses the domin mgnetiztions to line up. This dds mgnetiztion cuent J m, to ny othe cuent, J, tht might hve een thee so B is now function of J nd J m. 0 J Jm B 1 dv 4 With it of vecto clculus we cn show fom (1) tht B 0 J (3.1.4) nd with mgnetiztion V B J 0 J m nd with simil ppoch to tht used in defining J m nd M we find M (3.1.5) J m nd comining with (4) we get B M J 0 The quntity, B/ 0  M, whose cul is the 'fee' cuent density is defined s H  the mgnetic field intensity. B H 0 M nd so B = 0 ( H + M ) ( H nd M hve the sme units) Fo histoicl esons the sttement tht the induced mgnetiztion depends on the field hs een witten. 6
7 M = m H whee m is the mgnetic susceptiility. Becuse M nd H e in the sme units (Amp/m) m is dimensionless ut, e ceful, m SI units = 4 m cgs units Thee is one moe definition to complete this summy desciption of mgnetic field. B = 0 ( H + M ) = 0 ( H + m H ) = 0 ( 1 + m )H so B = H nd is the mgnetic pemeility. The eltionship etween M nd H is complex nd nonline nd is descied y hysteesis cuve, viz: 7
Winter 2004 OSU Sources of Magnetic Fields 1 Chapter 32
Winte 4 OSU 1 Souces Of Mgnetic Fields We lened two wys to clculte Electic Field Coulomb's Foce de 4 E da 1 dq Q enc ˆ ute Foce Clcultion High symmety Wht e the nlogous equtions fo the Mgnetic Field? Winte
More informationChapter 28 Sources of Magnetic Field
Chpte 8 Souces of Mgnetic Field  Mgnetic Field of Moving Chge  Mgnetic Field of Cuent Element  Mgnetic Field of Stight CuentCying Conducto  Foce Between Pllel Conductos  Mgnetic Field of Cicul Cuent
More informationPhysics 11b Lecture #11
Physics 11b Lectue #11 Mgnetic Fields Souces of the Mgnetic Field S&J Chpte 9, 3 Wht We Did Lst Time Mgnetic fields e simil to electic fields Only diffeence: no single mgnetic pole Loentz foce Moving chge
More informationCourse Updates. Reminders: 1) Assignment #8 available. 2) Chapter 28 this week.
Couse Updtes http://www.phys.hwii.edu/~vne/phys7sp1/physics7.html Remindes: 1) Assignment #8 vilble ) Chpte 8 this week Lectue 3 iotsvt s Lw (Continued) θ d θ P R R θ R d θ d Mgnetic Fields fom long
More informationU>, and is negative. Electric Potential Energy
Electic Potentil Enegy Think of gvittionl potentil enegy. When the lock is moved veticlly up ginst gvity, the gvittionl foce does negtive wok (you do positive wok), nd the potentil enegy (U) inceses. When
More informationELECTRO  MAGNETIC INDUCTION
NTRODUCTON LCTRO  MAGNTC NDUCTON Whenee mgnetic flu linked with cicuit chnges, n e.m.f. is induced in the cicuit. f the cicuit is closed, cuent is lso induced in it. The e.m.f. nd cuent poduced lsts s
More informationPhysics 604 Problem Set 1 Due Sept 16, 2010
Physics 64 Polem et 1 Due ept 16 1 1) ) Inside good conducto the electic field is eo (electons in the conducto ecuse they e fee to move move in wy to cncel ny electic field impessed on the conducto inside
More informationCollection of Formulas
Collection of Fomuls Electomgnetic Fields EITF8 Deptment of Electicl nd Infomtion Technology Lund Univesity, Sweden August 8 / ELECTOSTATICS field point '' ' Oigin ' Souce point Coulomb s Lw The foce F
More informationElectric Potential. and Equipotentials
Electic Potentil nd Euipotentils U Electicl Potentil Review: W wok done y foce in going fom to long pth. l d E dl F W dl F θ Δ l d E W U U U Δ Δ l d E W U U U U potentil enegy electic potentil Potentil
More informationWeek 8. Topic 2 Properties of Logarithms
Week 8 Topic 2 Popeties of Logithms 1 Week 8 Topic 2 Popeties of Logithms Intoduction Since the esult of ithm is n eponent, we hve mny popeties of ithms tht e elted to the popeties of eponents. They e
More informationSchool of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007
School of Electicl nd Compute Engineeing, Conell Univesity ECE 303: Electomgnetic Fields nd Wves Fll 007 Homewok 3 Due on Sep. 14, 007 by 5:00 PM Reding Assignments: i) Review the lectue notes. ii) Relevnt
More informationMagnetic Fields Due to Currents
PH C Fall 1 Magnetic Fields Due to Cuents Lectue 14 Chapte 9 (Halliday/esnick/Walke, Fundamentals of Physics 8 th edition) 1 Chapte 9 Magnetic Fields Due to Cuents In this chapte we will exploe the elationship
More informationSchool of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007
School of Electicl nd Compute Engineeing, Conell Univesity ECE 303: Electomgnetic Fields nd Wves Fll 007 Homewok 4 Due on Sep. 1, 007 by 5:00 PM Reding Assignments: i) Review the lectue notes. ii) Relevnt
More informationThis immediately suggests an inversesquare law for a "piece" of current along the line.
Electomgnetic Theoy (EMT) Pof Rui, UNC Asheville, doctophys on YouTube Chpte T Notes The iotsvt Lw T nvesesque Lw fo Mgnetism Compe the mgnitude of the electic field t distnce wy fom n infinite line
More information( ) ( ) ( ) ( ) ( ) # B x ( ˆ i ) ( ) # B y ( ˆ j ) ( ) # B y ("ˆ ( ) ( ) ( (( ) # ("ˆ ( ) ( ) ( ) # B ˆ z ( k )
Emple 1: A positie chge with elocit is moing though unifom mgnetic field s shown in the figues below. Use the ighthnd ule to detemine the diection of the mgnetic foce on the chge. Emple 1 ˆ i = ˆ ˆ i
More informationPhysics 1502: Lecture 2 Today s Agenda
1 Lectue 1 Phsics 1502: Lectue 2 Tod s Agend Announcements: Lectues posted on: www.phs.uconn.edu/~cote/ HW ssignments, solutions etc. Homewok #1: On Mstephsics this Fid Homewoks posted on Msteingphsics
More informationChapter 21: Electric Charge and Electric Field
Chpte 1: Electic Chge nd Electic Field Electic Chge Ancient Gees ~ 600 BC Sttic electicit: electic chge vi fiction (see lso fig 1.1) (Attempted) pith bll demonsttion: inds of popeties objects with sme
More informationSolutions to Midterm Physics 201
Solutions to Midtem Physics. We cn conside this sitution s supeposition of unifomly chged sphee of chge density ρ nd dius R, nd second unifomly chged sphee of chge density ρ nd dius R t the position of
More informationELECTROSTATICS. 4πε0. E dr. The electric field is along the direction where the potential decreases at the maximum rate. 5. Electric Potential Energy:
LCTROSTATICS. Quntiztion of Chge: Any chged body, big o smll, hs totl chge which is n integl multile of e, i.e. = ± ne, whee n is n intege hving vlues,, etc, e is the chge of electon which is eul to.6
More informationFI 2201 Electromagnetism
FI 1 Electomgnetism Alexnde A. Isknd, Ph.D. Physics of Mgnetism nd Photonics Resech Goup Electosttics ELECTRIC PTENTIALS 1 Recll tht we e inteested to clculte the electic field of some chge distiution.
More informationGeneral Physics II. number of field lines/area. for whole surface: for continuous surface is a whole surface
Genel Physics II Chpte 3: Guss w We now wnt to quickly discuss one of the moe useful tools fo clculting the electic field, nmely Guss lw. In ode to undestnd Guss s lw, it seems we need to know the concept
More informationChapter 7. Kleene s Theorem. 7.1 Kleene s Theorem. The following theorem is the most important and fundamental result in the theory of FA s:
Chpte 7 Kleene s Theoem 7.1 Kleene s Theoem The following theoem is the most impotnt nd fundmentl esult in the theoy of FA s: Theoem 6 Any lnguge tht cn e defined y eithe egul expession, o finite utomt,
More informationElectric Field F E. q Q R Q. ˆ 4 r r   Electric field intensity depends on the medium! origin
1 1 Electic Field + + q F Q R oigin E 0 0 F E ˆ E 4 4 R q Q R Q   Electic field intensity depends on the medium! Electic Flux Density We intoduce new vecto field D independent of medium. D E So, electic
More informationMagnetostatics. Magnetic Forces. = qu. BiotSavart Law H = Gauss s Law for Magnetism. Ampere s Law. Magnetic Properties of Materials. Inductance M.
Magnetic Foces BiotSavat Law Gauss s Law fo Magnetism Ampee s Law Magnetic Popeties of Mateials nductance F m qu d B d R 4 R B B µ 0 J Magnetostatics M. Magnetic Foces The electic field E at a point in
More informationPhysics Spring 2012 Announcements: Mar 07, 2012
Physics 00  Sping 01 Announcements: Ma 07, 01 HW#6 due date has been extended to the moning of Wed. Ma 1. Test # (i. Ma ) will cove only chaptes 0 and 1 All of chapte will be coveed in Test #4!!! Test
More informationAnswers to test yourself questions
Answes to test youself questions opic Descibing fields Gm Gm Gm Gm he net field t is: g ( d / ) ( 4d / ) d d Gm Gm Gm Gm Gm Gm b he net potentil t is: V d / 4d / d 4d d d V e 4 7 9 49 J kg 7 7 Gm d b E
More informationContinuous Charge Distributions
Continuous Chge Distibutions Review Wht if we hve distibution of chge? ˆ Q chge of distibution. Q dq element of chge. d contibution to due to dq. Cn wite dq = ρ dv; ρ is the chge density. = 1 4πε 0 qi
More information(A) 6.32 (B) 9.49 (C) (D) (E) 18.97
Univesity of Bhin Physics 10 Finl Exm Key Fll 004 Deptment of Physics 13/1/005 8:30 10:30 e =1.610 19 C, m e =9.1110 31 Kg, m p =1.6710 7 Kg k=910 9 Nm /C, ε 0 =8.8410 1 C /Nm, µ 0 =4π10 7 T.m/A Pt : 10
More informationMAGNETIC FIELD INTRODUCTION
MAGNETIC FIELD INTRODUCTION It was found when a magnet suspended fom its cente, it tends to line itself up in a nothsouth diection (the compass needle). The noth end is called the Noth Pole (Npole),
More informationRELATIVE KINEMATICS. q 2 R 12. u 1 O 2 S 2 S 1. r 1 O 1. Figure 1
RELAIVE KINEMAICS he equtions of motion fo point P will be nlyzed in two diffeent efeence systems. One efeence system is inetil, fixed to the gound, the second system is moving in the physicl spce nd the
More informationUnit 7: Sources of magnetic field
Unit 7: Souces of magnetic field Oested s expeiment. iot and Savat s law. Magnetic field ceated by a cicula loop Ampèe s law (A.L.). Applications of A.L. Magnetic field ceated by a: Staight cuentcaying
More informationPX3008 Problem Sheet 1
PX38 Poblem Sheet 1 1) A sphee of dius (m) contins chge of unifom density ρ (Cm 3 ). Using Guss' theoem, obtin expessions fo the mgnitude of the electic field (t distnce fom the cente of the sphee) in
More informationFriedmannien equations
..6 Fiedmnnien equtions FLRW metic is : ds c The metic intevl is: dt ( t) d ( ) hee f ( ) is function which detemines globl geometic l popety of D spce. f d sin d One cn put it in the Einstein equtions
More informationπ,π is the angle FROM a! TO b
Mth 151: 1.2 The Dot Poduct We hve scled vectos (o, multiplied vectos y el nume clled scl) nd dded vectos (in ectngul component fom). Cn we multiply vectos togethe? The nswe is YES! In fct, thee e two
More informationChapter 25: Current, Resistance and Electromotive Force. ~104 m/s Typical speeds ~ 10 6 m/s
Chpte 5: Cuent, esistnce nd lectomotive Foce Chge cie motion in conducto in two pts Constnt Acceletion F m q ndomizing Collisions (momentum, enegy) >esulting Motion http://phys3p.sl.psu.edu/phys_nim/m/ndom_wlk.vi
More informationCh 30  Sources of Magnetic Field! The BiotSavart Law! = k m. r 2. Example 1! Example 2!
Ch 30  Souces of Magnetic Field 1.) Example 1 Detemine the magnitude and diection of the magnetic field at the point O in the diagam. (Cuent flows fom top to bottom, adius of cuvatue.) Fo staight segments,
More informationanubhavclasses.wordpress.com CBSE Solved Test Papers PHYSICS Class XII Chapter : Electrostatics
CBS Solved Test Papes PHYSICS Class XII Chapte : lectostatics CBS TST PAPR01 CLASS  XII PHYSICS (Unit lectostatics) 1. Show does the foce between two point chages change if the dielectic constant of
More informationChapter 25: Current, Resistance and Electromotive Force. Charge carrier motion in a conductor in two parts
Chpte 5: Cuent, esistnce nd Electomotive Foce Chge cie motion in conducto in two pts Constnt Acceletion F m qe ndomizing Collisions (momentum, enegy) =>esulting Motion Avege motion = Dift elocity = v d
More informationElectrostatics. 1. Show does the force between two point charges change if the dielectric constant of the medium in which they are kept increase?
Electostatics 1. Show does the foce between two point chages change if the dielectic constant of the medium in which they ae kept incease? 2. A chaged od P attacts od R whee as P epels anothe chaged od
More informationChapter 2: Electric Field
P 6 Genel Phsics II Lectue Outline. The Definition of lectic ield. lectic ield Lines 3. The lectic ield Due to Point Chges 4. The lectic ield Due to Continuous Chge Distibutions 5. The oce on Chges in
More informationCHAPTER 18: ELECTRIC CHARGE AND ELECTRIC FIELD
ollege Physics Student s Mnul hpte 8 HAPTR 8: LTRI HARG AD LTRI ILD 8. STATI LTRIITY AD HARG: OSRVATIO O HARG. ommon sttic electicity involves chges nging fom nnocoulombs to micocoulombs. () How mny electons
More informationLecture 11: Potential Gradient and Capacitor Review:
Lectue 11: Potentil Gdient nd Cpcito Review: Two wys to find t ny point in spce: Sum o Integte ove chges: q 1 1 q 2 2 3 P i 1 q i i dq q 3 P 1 dq xmple of integting ove distiution: line of chge ing of
More informationMAGNETIC EFFECT OF CURRENT & MAGNETISM
TODUCTO MAGETC EFFECT OF CUET & MAGETM The molecul theo of mgnetism ws given b Webe nd modified lte b Ewing. Oested, in 18 obseved tht mgnetic field is ssocited with n electic cuent. ince, cuent is due
More informationWork, Potential Energy, Conservation of Energy. the electric forces are conservative: ur r
Wok, Potentil Enegy, Consevtion of Enegy the electic foces e consevtive: u Fd = Wok, Potentil Enegy, Consevtion of Enegy b b W = u b b Fdl = F()[ d + $ $ dl ] = F() d u Fdl = the electic foces e consevtive
More informationdx was area under f ( x ) if ( ) 0
13. Line Integls Line integls e simil to single integl, f ( x) dx ws e unde f ( x ) if ( ) 0 Insted of integting ove n intevl [, ] (, ) f xy ds f x., we integte ove cuve, (in the xyplne). **Figue  get
More information3. Magnetostatic fields
3. Magnetostatic fields D. Rakhesh Singh Kshetimayum 1 Electomagnetic Field Theoy by R. S. Kshetimayum 3.1 Intoduction to electic cuents Electic cuents Ohm s law Kichoff s law Joule s law Bounday conditions
More informationUnit 6. Magnetic forces
Unit 6 Mgnetic foces 6.1 ntoduction. Mgnetic field 6. Mgnetic foces on moving electic chges 6. oce on conducto with cuent. 6.4 Action of unifom mgnetic field on flt cuentcying loop. Mgnetic moment. Electic
More information10 Statistical Distributions Solutions
Communictions Engineeing MSc  Peliminy Reding 1 Sttisticl Distiutions Solutions 1) Pove tht the vince of unifom distiution with minimum vlue nd mximum vlue ( is ) 1. The vince is the men of the sques
More informationELECTROSTATICS::BHSEC MCQ 1. A. B. C. D.
ELETROSTATIS::BHSE 94 MQ. A moving electic chage poduces A. electic field only. B. magnetic field only.. both electic field and magnetic field. D. neithe of these two fields.. both electic field and magnetic
More informationTUTORIAL 9. Static magnetic field
TUTOIAL 9 Static magnetic field Vecto magnetic potential Null Identity % & %$ A # Fist postulation # " B such that: Vecto magnetic potential Vecto Poisson s equation The solution is: " Substitute it into
More informationSources of the Magnetic Field. Moving charges currents Ampere s Law Gauss Law in magnetism Magnetic materials
Souces of the Magnetic Field Moving chages cuents Ampee s Law Gauss Law in magnetism Magnetic mateials BiotSavat Law ˆ ˆ θ ds P db out I db db db db ds ˆ 1 I P db in db db ds sinθ db μ 4 π 0 Ids ˆ B μ0i
More information7.5Determinants in Two Variables
7.eteminnts in Two Vibles efinition of eteminnt The deteminnt of sque mti is el numbe ssocited with the mti. Eve sque mti hs deteminnt. The deteminnt of mti is the single ent of the mti. The deteminnt
More informationPhysics 2020, Spring 2005 Lab 5 page 1 of 8. Lab 5. Magnetism
Physics 2020, Sping 2005 Lab 5 page 1 of 8 Lab 5. Magnetism PART I: INTRODUCTION TO MAGNETS This week we will begin wok with magnets and the foces that they poduce. By now you ae an expet on setting up
More informationFourierBessel Expansions with Arbitrary Radial Boundaries
Applied Mthemtics,,,  doi:./m.. Pulished Online My (http://www.scirp.og/jounl/m) Astct FouieBessel Expnsions with Aity Rdil Boundies Muhmmd A. Mushef P. O. Box, Jeddh, Sudi Ai Emil: mmushef@yhoo.co.uk
More informationMagnetic Field. Conference 6. Physics 102 General Physics II
Physics 102 Confeence 6 Magnetic Field Confeence 6 Physics 102 Geneal Physics II Monday, Mach 3d, 2014 6.1 Quiz Poblem 6.1 Think about the magnetic field associated with an infinite, cuent caying wie.
More informationPhysics 505 Fall 2005 Midterm Solutions. This midterm is a two hour open book, open notes exam. Do all three problems.
Physics 55 Fll 5 Midtem Solutions This midtem is two hou open ook, open notes exm. Do ll thee polems. [35 pts] 1. A ectngul ox hs sides of lengths, nd c z x c [1] ) Fo the Diichlet polem in the inteio
More informationA moving charged particle creates a magnetic field vector at every point in space except at its position.
1 Pat 3: Magnetic Foce 3.1: Magnetic Foce & Field A. Chaged Paticles A moving chaged paticle ceates a magnetic field vecto at evey point in space ecept at its position. Symbol fo Magnetic Field mks units
More informationMagnetic Fields! Ch 29  Magnetic Fields & Sources! Magnets...! Earth s Magnetic Field!
Mgnetic Fields Ch 29  Mgnetic Fields & ources 1. The mgnetic field line hs the direction of the mgnetic field s its tngent t tht point. 2. The number of lines per unit re is proportionl to the mgnitude
More informationFluids & Bernoulli s Equation. Group Problems 9
Goup Poblems 9 Fluids & Benoulli s Eqution Nme This is moe tutoillike thn poblem nd leds you though conceptul development of Benoulli s eqution using the ides of Newton s 2 nd lw nd enegy. You e going
More informationPHY 114 A General Physics II 11 AM12:15 PM TR Olin 101
PHY 114 A Geneal Physics II 11 AM1:15 PM TR Olin 11 Plan fo Lectue 1 Chaptes 3): Souces of Magnetic fields 1. Pemanent magnets.biotsavat Law; magnetic fields fom a cuentcaying wie 3.Ampee Law 4.Magnetic
More informationChapter 25 Electric Potential
Chpte 5 lectic Potentil consevtive foces > potentil enegy  Wht is consevtive foce? lectic potentil = U / : the potentil enegy U pe unit chge is function of the position in spce Gol:. estblish the eltionship
More informationTopics for Review for Final Exam in Calculus 16A
Topics fo Review fo Finl Em in Clculus 16A Instucto: Zvezdelin Stnkov Contents 1. Definitions 1. Theoems nd Poblem Solving Techniques 1 3. Eecises to Review 5 4. Chet Sheet 5 1. Definitions Undestnd the
More informationCalculate the electric potential at B d2=4 m Calculate the electric potential at A d1=3 m 3 m 3 m
MTE : Ch 13 5:37pm on Oct 31 ltenate Exams: Wed Ch 13 6:3pm8:pm (people attending the altenate exam will not be allowed to go out of the oom while othes fom pevious exam ae still aound) Thu @ 9:1:3
More informationGeneral Physics (PHY 2140)
Genel Physics (PHY 40) Lightning Review Lectue 3 Electosttics Lst lectue:. Flux. Guss s s lw. simplifies computtion of electic fields Q Φ net Ecosθ ε o Electicl enegy potentil diffeence nd electic potentil
More informationPreviously. Extensions to backstepping controller designs. Tracking using backstepping Suppose we consider the general system
436459 Advnced contol nd utomtion Extensions to bckstepping contolle designs Tcking Obseves (nonline dmping) Peviously Lst lectue we looked t designing nonline contolles using the bckstepping technique
More information1 Using Integration to Find Arc Lengths and Surface Areas
Novembe 9, 8 MAT86 Week Justin Ko Using Integtion to Find Ac Lengths nd Sufce Aes. Ac Length Fomul: If f () is continuous on [, b], then the c length of the cuve = f() on the intevl [, b] is given b s
More information10 m, so the distance from the Sun to the Moon during a solar eclipse is. The mass of the Sun, Earth, and Moon are = =
Chpte 1 nivesl Gvittion 11 *P1. () The unth distnce is 1.4 nd the thmoon 8 distnce is.84, so the distnce fom the un to the Moon duing sol eclipse is 11 8 11 1.4.84 = 1.4 The mss of the un, th, nd Moon
More information6. Gravitation. 6.1 Newton's law of Gravitation
Gvittion / 1 6.1 Newton's lw of Gvittion 6. Gvittion Newton's lw of gvittion sttes tht evey body in this univese ttcts evey othe body with foce, which is diectly popotionl to the poduct of thei msses nd
More information16.1 Permanent magnets
Unit 16 Magnetism 161 Pemanent magnets 16 The magnetic foce on moving chage 163 The motion of chaged paticles in a magnetic field 164 The magnetic foce exeted on a cuentcaying wie 165 Cuent loops and
More informationHomework 3 MAE 118C Problems 2, 5, 7, 10, 14, 15, 18, 23, 30, 31 from Chapter 5, Lamarsh & Baratta. The flux for a point source is:
. Homewok 3 MAE 8C Poblems, 5, 7, 0, 4, 5, 8, 3, 30, 3 fom Chpte 5, msh & Btt Point souces emit nuetons/sec t points,,, n 3 fin the flux cuent hlf wy between one sie of the tingle (blck ot). The flux fo
More informationPhysics 2B Chapter 22 Notes  Magnetic Field Spring 2018
Physics B Chapte Notes  Magnetic Field Sping 018 Magnetic Field fom a Long Staight CuentCaying Wie In Chapte 11 we looked at Isaac Newton s Law of Gavitation, which established that a gavitational field
More informationPhysics 2112 Unit 14
Physics 2112 Unit 14 Today s Concept: What Causes Magnetic Fields d 0I ds ˆ 2 4 Unit 14, Slide 1 You Comments Can you give a summay fo eveything we use the ight hand ule fo? Wasn't too clea on this topic.
More informationElectricity & Magnetism Lecture 6: Electric Potential
Electicity & Mgnetism Lectue 6: Electic Potentil Tody s Concept: Electic Potenl (Defined in tems of Pth Integl of Electic Field) Electicity & Mgnesm Lectue 6, Slide Stuff you sked bout:! Explin moe why
More informationRadial geodesics in Schwarzschild spacetime
Rdil geodesics in Schwzschild spcetime Spheiclly symmetic solutions to the Einstein eqution tke the fom ds dt d dθ sin θdϕ whee is constnt. We lso hve the connection components, which now tke the fom using
More information7.2.3 Inductance. Neumann Formula for the Mutual Inductance. Important Things about Mutual Inductance
7..3 Inductnce Neumnn Fomul o the Mutul Inductnce Two loops o wie t est. A stedy cuent I ound loop ome psses though loop Φ Φ d ( A ) d A dl I dl A I dl ˆ Φ d nd dl ˆ Φ [ d ] I M I The constnt o popotionlity:
More information7.1 Integral as Net Change and 7.2 Areas in the Plane Calculus
7.1 Integrl s Net Chnge nd 7. Ares in the Plne Clculus 7.1 INTEGRAL AS NET CHANGE Notecrds from 7.1: Displcement vs Totl Distnce, Integrl s Net Chnge We hve lredy seen how the position of n oject cn e
More informationClass Summary. be functions and f( D) , we define the composition of f with g, denoted g f by
Clss Summy.5 Eponentil Functions.6 Invese Functions nd Logithms A function f is ule tht ssigns to ech element D ectly one element, clled f( ), in. Fo emple : function not function Given functions f, g:
More information3Axis Vector Magnet: Construction and Characterisation of Split Coils at RT. Semester Project Petar Jurcevic
3Axis Vecto Magnet: Constuction and Chaacteisation of Split Coils at RT Semeste Poject Peta Jucevic Outline Field Calculation and Simulation Constuction Details Field Calculations Chaacteization at RT
More informationMagnetic Field of a Wire
Magnetic Field of a Wie Fundamental Laws fo Calculating Bfield BiotSavat Law (long method, but woks always) Ampee s Law (high symmety) BField of a Staight Wie Fo a thin staight conducto caying cuent
More informationMath 4318 : Real Analysis II MidTerm Exam 1 14 February 2013
Mth 4318 : Rel Anlysis II MidTem Exm 1 14 Febuy 2013 Nme: Definitions: Tue/Flse: Poofs: 1. 2. 3. 4. 5. 6. Totl: Definitions nd Sttements of Theoems 1. (2 points) Fo function f(x) defined on (, b) nd fo
More information(1) It increases the break down potential of the surrounding medium so that more potential can be applied and hence more charge can be stored.
Cpcito Cpcito: Cpcito ( o conense ) is evice fo stoing chge. It essentilly consists of two conucting sufces such s two pltes o two spheicl shell o two cylines etc. kept exctly pllel to ech othe septe y
More informationOn the Eötvös effect
On the Eötvös effect Mugu B. Răuţ The im of this ppe is to popose new theoy bout the Eötvös effect. We develop mthemticl model which loud us bette undestnding of this effect. Fom the eqution of motion
More informationThe Formulas of Vector Calculus John Cullinan
The Fomuls of Vecto lculus John ullinn Anlytic Geomety A vecto v is n ntuple of el numbes: v = (v 1,..., v n ). Given two vectos v, w n, ddition nd multipliction with scl t e defined by Hee is bief list
More informationPHYS 1444 Lecture #5
Shot eview Chapte 24 PHYS 1444 Lectue #5 Tuesday June 19, 212 D. Andew Bandt Capacitos and Capacitance 1 Coulom s Law The Fomula QQ Q Q F 1 2 1 2 Fomula 2 2 F k A vecto quantity. Newtons Diection of electic
More informationReview of Mathematical Concepts
ENEE 322: Signls nd Systems view of Mthemticl Concepts This hndout contins ief eview of mthemticl concepts which e vitlly impotnt to ENEE 322: Signls nd Systems. Since this mteil is coveed in vious couses
More informationLecture 10. Solution of Nonlinear Equations  II
Fied point Poblems Lectue Solution o Nonline Equtions  II Given unction g : R R, vlue such tht gis clled ied point o the unction g, since is unchnged when g is pplied to it. Whees with nonline eqution
More informationSection 35 SHM and Circular Motion
Section 35 SHM nd Cicul Motion Phsics 204A Clss Notes Wht do objects do? nd Wh do the do it? Objects sometimes oscillte in simple hmonic motion. In the lst section we looed t mss ibting t the end of sping.
More informationProf. Anchordoqui Problems set # 12 Physics 169 May 12, 2015
Pof. Anchodoqui Poblems set # 12 Physics 169 My 12, 2015 1. Two concentic conducting sphees of inne nd oute dii nd b, espectively, cy chges ±Q. The empty spce between the sphees is hlffilled by hemispheicl
More informationFI 2201 Electromagnetism
FI 2201 Electomagnetism Alexande A. Iskanda, Ph.D. Physics of Magnetism and Photonics Reseach Goup Electodynamics ELETROMOTIVE FORE AND FARADAY S LAW 1 Ohm s Law To make a cuent flow, we have to push the
More informationPY208 Matter & Interactions Final Exam S2005
PY Matte & Inteactions Final Exam S2005 Name (pint) Please cicle you lectue section below: 003 (Ramakishnan 11:20 AM) 004 (Clake 1:30 PM) 005 (Chabay 2:35 PM) When you tun in the test, including the fomula
More information9.4 The response of equilibrium to temperature (continued)
9.4 The esponse of equilibium to tempetue (continued) In the lst lectue, we studied how the chemicl equilibium esponds to the vition of pessue nd tempetue. At the end, we deived the vn t off eqution: d
More informationAntennas & Propagation
Antennas & Popagation 1 Oveview of Lectue II Wave Equation Example Antenna Radiation Retaded potential THE KEY TO ANY OPERATING ANTENNA ot H = J +... Suppose: 1. Thee does exist an electic medium,
More informationReview for 2 nd Midterm
Review fo 2 nd Midtem Midtem2! Wednesday Octobe 29 at 6pm Section 1 N100 BCC (Business College) Section 2 158 NR (Natual Resouces) Allowed one sheet of notes (both sides) and calculato Coves Chaptes 2731
More informationThe Law of BiotSavart & RHR P θ
The Law of iotsavat & RHR P R dx x Jeanaptiste iot élix Savat Phys 122 Lectue 19 G. Rybka Recall: Potential Enegy of Dipole Wok equied to otate a cuentcaying loop in a magnetic field Potential enegy
More informationElectric Charge and Field
lectic Chage and ield Chapte 6 (Giancoli) All sections ecept 6.0 (Gauss s law) Compaison between the lectic and the Gavitational foces Both have long ange, The electic chage of an object plas the same
More informationNSIBTS indices calculation procedure
ICES Dt Cente DATRAS 1.1 NSIBTS indices 2013 DATRAS Pocedue Document NSIBTS indices clcultion pocedue Contents Genel... 2 I Rw ge dt CA > Agelength key by RFA fo defined ge nge ALK... 4 II Rw length
More informationAlgebra Based Physics. Gravitational Force. PSI Honors universal gravitation presentation Update Fall 2016.notebookNovember 10, 2016
Newton's Lw of Univesl Gvittion Gvittionl Foce lick on the topic to go to tht section Gvittionl Field lgeb sed Physics Newton's Lw of Univesl Gvittion Sufce Gvity Gvittionl Field in Spce Keple's Thid Lw
More informationPhysics 122, Fall October 2012
hsics 1, Fall 1 3 Octobe 1 Toda in hsics 1: finding Foce between paallel cuents Eample calculations of fom the iot Savat field law Ampèe s Law Eample calculations of fom Ampèe s law Unifom cuents in conductos?
More informationSources of Magnetic Fields (chap 28)
Souces of Magnetic Fields (chap 8) In chapte 7, we consideed the magnetic field effects on a moving chage, a line cuent and a cuent loop. Now in Chap 8, we conside the magnetic fields that ae ceated by
More informationCurrent, Resistance and
Cuent, Resistance and Electomotive Foce Chapte 25 Octobe 2, 2012 Octobe 2, 2012 Physics 208 1 Leaning Goals The meaning of electic cuent, and how chages move in a conducto. What is meant by esistivity
More information