Physics 217 Practice Final Exam: Solutions
|
|
- Amber Price
- 6 years ago
- Views:
Transcription
1 Physis 17 Ptie Finl Em: Solutions Fll This ws the Physis 17 finl em in Fll 199 Twenty-thee students took the em The vege soe ws 11 out of 15 (731%), nd the stndd devition 9 The high nd low soes wee 145 nd 75 If ny of these solutions seems obsue, plese ontt us so we n eplin it bette Poblem 1 (3 points) An infinite ylinde with dius R is hged unifomly, with hge density ρ, eept fo n infinite ylindil hole pllel to the ylinde's is The hole hs dius R nd is tngent to the eteio of the ylinde A shot hunk of the ylinde is shown in the ompnying figue E y Clulte the eleti field eveywhee inside the hole, nd sketh the lines of E on the figue ρ R Supepose now ylinde with hge density ρ on wide ylinde with hge density ρ to ete the hole; then supepose the fields fom these two hge distibutions The field inside unifomly hged infinite ylinde n be omputed by using Guss Lw, with ylindil Gussin sufe (dius s less thn the wie s dius, length ) oil with the wie: R y s s + E d = Qenlosed E πs = π ρπs E = πρs ( ) 4
2 Then, with E + s the field fom the wide ylinde nd now one, we hve (see figue): E s the field inside the E+ = πρs+, E = πρs, E= E + E = πρ s s = πρryˆ ( ) + + The field is onstnt, nd points stight up Multiply on the ight by 1ε to get the nswe in MKS units b An infinite ylindil wie with dius R ies unifom uent density J, eept inside n infinite ylindil hole pllel to the wie's is The hole hs dius R nd is tngent to the eteio of the wie A shot hunk of the wie is shown in the ompnying figue y B Clulte the mgneti field eveywhee inside the hole, nd sketh J the lines of B on the figue R Supepose now wie with uent density -J on wide ylinde with hge density J to ete the hole; then supepose the fields fom these two uent distibutions The field inside unifomdensity uent n be omputed by using Ampèe s Lw, with iul Ampèen loop (dius s less thn the wie s dius) oil with the wie: B d = Ienlosed πjs B πs= ( Jπs ) B = φˆ Then, with B + s the field fom the wide ylinde nd now one, we hve: B s the field inside the πjs+ πj πj B+ = φˆ+ = s+ ( sinφ+ ˆ + os φ+ yˆ) = ( y+ ˆ + + yˆ), π J B = ( y ˆ + yˆ ) But = = nd y = y + R= y (see oss setion figue in pt ), so + +
3 3 ( y ( y R) ) B πj ˆ ˆ ˆ ˆ πjr = B + + B = + + = ˆ y y The field is onstnt, nd points hoiontlly, to the left in the figue Reple the 1 with µ to get the nswe in MKS units An infinite ylindil flu tube with dius R ies unifom mgneti field B, pllel to the ylinde's is, eept inside n infinite ylindil hole pllel to the flu tube s is The hole hs dius R nd is tngent to the eteio of the flu tube A shot hunk of the flu tube is shown in the ompnying figue The mgneti field is eo inside the hole nd outside the flu tube, but whee it eists, it is inesing linely with time: B y E R t B( t) = B ˆ t Clulte the eleti field eveywhee inside the hole, nd sketh the lines of E on the figue Supepose now flu tube with mgneti field -B on wide flu tube with mgneti field B to ete the hole; then supepose the fields fom these two flu tubes The field inside unifom mgneti flu tube n be omputed by using Fdy s Lw, with iul Ampèen loop (dius s less thn the flu tube s dius) oil with the flu tube: 1 dφb E d = dt 1 db πsb Bs E πs= πs = E = φˆ dt t t Then, with E + s the field fom the wide flu tube nd now one, we hve: E s the field inside the Bs B E = φˆ = ˆ + yˆ, t t ( y ) B E = ( ( y R) ˆ + yˆ ), t
4 4 so ( y ( y R) ) E B B ˆ ˆ ˆ ˆ R = E + + E = + + = ˆ t y y t The field is onstnt, nd points hoiontlly, to the ight in the figue Eliminte the fto of 1 to get the nswe in MKS units Poblem (3 points) Clulte the eleti field t point on the is of unifomly-hged iul disk, distne fom the ile's ente The disk hs sufe hge density σ nd dius de Fo two infinitesiml elements the sme distne wy fom the is (s) on opposite sides ( φ nd φ+ π ), the hoiontl omponents of de nel nd the vetil () omponents dd; thus the ontibution to the eleti field fom ing with dius s nd width ds is dq osθ π sds de= ˆ =σ + s + s θ s ds σ Thus + sds du E = ˆπσ = ˆπσ = ˆ πσ u ( + s ) 3 3 u 1 + = πσ 1 ˆ + b The hged iul disk fom pt is set into ottion bout its is, with ngul fequeny ω Clulte the mgneti field B t point on the is distne fom the ente of the disk Agin, the hoiontl omponents nel nd vetil omponents dd, fo uent elements symmetilly pled bout the is, so db ω θ σ
5 5 ( σω)( π sds) 1 Kd 1 s db = os θ = s + + s Thus πσω sds B= ˆ 3 3 ( + s ) Not mny points would be lost by stopping hee, but we ll ssume we e tying fo pefet soe: πσω udu B= ˆ 3 Integte by pts, with ( ) 3 ( + u) dv = du + u, v = + u : πσω πσω u du B= ˆ uv vdu = ˆ + + u + u + dw πσω + w w + + πσω + ˆ πσω = ˆ + = ˆ + πσω = ˆ + + = + + Multiply on the ight by 1ε in pt, nd eple the 1 with µ in pt b, to get the nswes in MKS units Poblem 3 ( points) Conside the efeene point fo eleti potentil to be t infinity fo both pts of this poblem A onduting sphee with dius is in n infinite vuum Wht is its pitne? Conside it to y hge q; then, fo >,
6 6 q E= ˆ, qd q CV V = E d = = = C = Multiply on the ight by 1ε fo the MKS nswe b The sme sphee is pled in n infinite, wekly-onduting medium with esistivity ρ Wht is the esistne between the sphee nd infinity? If the ondutivity is smll enough, the eleti field is given simply by the eletostti vlue, so Fo ll But V >, then, π π σ q J = σ E= ˆ 1 I = J d = σq dφ dθsinθ = σq ( π)( ) = 4 πσq = q still, so, sine V lso = IR, R V 1 ρ = = = I σ Divide on the ight by 1ε fo the MKS nswe Poblem 4 (1 points) Clulte the mgneti field inside long solenoid with dius, N tuns pe unit length, nd uent I Use Ampèe s Lw with etngul loop, two sides pllel to the solenoid s is: B d = Ienlosed Bh = INh B= NIˆ,
7 7 whee I is the uent in eh tun of the solenoid, nd the dietion is long the oil s is in the dietion given by the ight hnd ule Reple the 1 with µ to get the nswe in MKS units b Inside the long solenoid nd pllel to it, thee is shot solenoid with dius b, N b tuns pe unit length, nd length Wht is the mutul indutne of the two solenoids? b It s esiest to wok out the flu in the smll oil fom the field in the lge one: Φ = = Bb BA b NIN b π b (flu theds Nb b NN b = I = MI, so M = NN b b loops) Reple the 1 with µ to get the nswe in MKS units Poblem 5 ( points) An infinite, hged, stight wie (hge pe unit length λ ) lies pllel to the is, nd pllel to two infinite, gounded onduting plnes whih inteset t 9 ngle The hged wie lies distne fom eh plne Clulte the eleti field E t point A, fom eh plne on the sme side s the line hge, nd t point B, fom eh plne but on the side opposite the line hge y A λ 1 λ λ 4 B 3 λ
8 8 Point B is inside the onduto, so the eleti field is eo thee Fo point A, use the method of imges Thee e thee imges of the line hge in the onduting plne, two with hge pe unit length λ nd one with λ, lbeled -4 in the figue bove The eleti field fo n infinite line hge n be lulted fom Guss Lw, using Gussin ylinde with dius s nd length h: E d = qenlosed λ E πsh= πλh E= s ˆ 4 s So we n supepose the fields fom the fou line hges t point A: E= E + E + E + E ˆ ˆ ˆ ˆ = λ + y + y ˆ ˆ ˆ ˆ + y + + y λ ˆ = ˆ y λ = ( ˆ + yˆ ) 3 Poblem 6 ( points) A sphee with dius R ies polition distne fom the ente P = K, whee K is onstnt nd is the veto Find the sufe nd volume bound hges σb = P( R) ˆ = KR, 1 d ρb = P = ( K ) = 3 K d Chek: the totl bound hge should ome out to eo, nd it does: q = R σb + πr ρb = KR KR = 3 b Clulte the fields E nd D eveywhee
9 9 Sine the hges e distibuted with spheil symmety, we n use Guss Lw with spheil gussin sufes With one of those dwn outside the sphee > R, we enlose no hge (see pt, bove), so ( ) E d = E =, D = E + P = Fo the inside of the sphee ( R) popotionl to its volume:, Gussin sphee enloses hge E d = qenlosed E = π ρb = π ( 3K) 3 3 E= K = 4 πp, D= E+ P= Note tht we ould hve done the whole poblem with D, beuse thee e no fee hges nd the polition is dil (ie P =, so D= ) Poblem 7 ( points) A iul wfe is mde of vey wekly onduting mteil with esistivity ρ nd dieleti onstnt ε Its dius is nd its thikness is ( ) Highly ondutive, metlli eletodes ove the iul fes Unde the ssumption tht the mteil s ondutivity doesn't ffet the pitne, lulte the esistne nd pitne of the wfe with its eletodes ρ, ε ρ ρ R = = A π εa ε C = = 4, Reple ε by ε to onvet to MKS b Suppose tht the wfe is hged up with bttey with voltge V, nd tht the bttey is disonneted t t = Wite one diffeentil eqution desibing the hge on the eletodes, nd the simil equtions desibing the potentil diffeene V ( t ), nd the eleti field E ( t) within the wfe
10 1 (Hint: The wfe's esistne nd pitne hve the sme potentil diffeene, nd n theefoe be epesented by two elements in pllel) Kihhoff s ule #, with the loop dwn ountelokwise, gives us Divide this esult though by C nd use q q + IR = ; C dq 1 dq + q = + q= dt RC dt ερ = CV to get dv + V = dt ερ + I dq = q dt + R C V The field is onstnt between the pltes; divide this lst esult by nd use V = E to get de + E = dt ερ Solve the diffeentil eqution to obtin the eleti field between the eletodes s funtion of time de de + E= dt ερ = E ερ E t ln = E ερ Et = Ee () t ερ d In tems of the esistivity nd dieleti onstnt of the mteil, wht is the time onstnt? Comment on the genelity of this esult, onsideing the dependene of the time onstnt on the shpe of the wfe The esult of pt n lso be witten s t τ ερ () = Ee, τ = Et Reple ε by ε to onvet to MKS Note tht the time onstnt doesn t hve ny ftos o vibles in it tht hve to do with the shpe of the wfe; this must dt
11 11 theefoe be genel esult fo the eltion of n eleti field in medium tht onduts
General 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 Applications of Integration
CHAPTER 7 Applitions of Integtion Setion 7. Ae of Region Between Two Cuves.......... Setion 7. Volume: The Disk Method................. Setion 7. Volume: The Shell Method................ Setion 7. A Length
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 informationThis immediately suggests an inverse-square law for a "piece" of current along the line.
Electomgnetic Theoy (EMT) Pof Rui, UNC Asheville, doctophys on YouTube Chpte T Notes The iot-svt Lw T nvese-sque Lw fo Mgnetism Compe the mgnitude of the electic field t distnce wy fom n infinite line
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 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 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 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 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 informationCHAPTER (6) Biot-Savart law Ampere s Circuital Law Magnetic Field Density Magnetic Flux
CAPTE 6 Biot-Svt w Ampee s Ciuit w Mgneti Fied Densit Mgneti Fu Soues of mgneti fied: - Pemnent mgnet - Fow of uent in ondutos -Time ving of eeti fied induing mgneti fied Cuent onfigutions: - Fiment uent
More informationDEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING FLUID MECHANICS III Solutions to Problem Sheet 3
DEPATMENT OF CIVIL AND ENVIONMENTAL ENGINEEING FLID MECHANICS III Solutions to Poblem Sheet 3 1. An tmospheic vote is moelle s combintion of viscous coe otting s soli boy with ngul velocity Ω n n iottionl
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 Cuent-Cying Conducto - Foce Between Pllel Conductos - Mgnetic Field of Cicul Cuent
More informationPhysics 218, Spring March 2004
Today in Physis 8: eleti dipole adiation II The fa field Veto potential fo an osillating eleti dipole Radiated fields and intensity fo an osillating eleti dipole Total satteing oss setion of a dieleti
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 informationPrerna Tower, Road No 2, Contractors Area, Bistupur, Jamshedpur , Tel (0657) ,
R Pen Towe Rod No Conttos Ae Bistupu Jmshedpu 8 Tel (67)89 www.penlsses.om IIT JEE themtis Ppe II PART III ATHEATICS SECTION I (Totl ks : ) (Single Coet Answe Type) This setion ontins 8 multiple hoie questions.
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 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 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 informationIn electrostatics, the electric field E and its sources (charges) are related by Gauss s law: Surface
Ampee s law n eletostatis, the eleti field E and its soues (hages) ae elated by Gauss s law: EdA i 4πQenl Sufae Why useful? When symmety applies, E an be easily omputed Similaly, in magnetism the magneti
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 informationThe Area of a Triangle
The e of Tingle tkhlid June 1, 015 1 Intodution In this tile we will e disussing the vious methods used fo detemining the e of tingle. Let [X] denote the e of X. Using se nd Height To stt off, the simplest
More informationAVS fiziks. Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES
ELECTROMAGNETIC THEORY SOLUTIONS GATE- Q. An insulating sphee of adius a aies a hage density a os ; a. The leading ode tem fo the eleti field at a distane d, fa away fom the hage distibution, is popotional
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 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 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 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 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 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 informationSPA7010U/SPA7010P: THE GALAXY. Solutions for Coursework 1. Questions distributed on: 25 January 2018.
SPA7U/SPA7P: THE GALAXY Solutions fo Cousewok Questions distibuted on: 25 Jnuy 28. Solution. Assessed question] We e told tht this is fint glxy, so essentilly we hve to ty to clssify it bsed on its spectl
More informationFluids & Bernoulli s Equation. Group Problems 9
Goup Poblems 9 Fluids & Benoulli s Eqution Nme This is moe tutoil-like 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 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 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 informationIllustrating the space-time coordinates of the events associated with the apparent and the actual position of a light source
Illustting the spe-time oointes of the events ssoite with the ppent n the tul position of light soue Benh Rothenstein ), Stefn Popesu ) n Geoge J. Spi 3) ) Politehni Univesity of Timiso, Physis Deptment,
More informationCourse Updates. Reminders: 1) Assignment #8 available. 2) Chapter 28 this week.
Couse Updtes http://www.phys.hwii.edu/~vne/phys7-sp1/physics7.html Remindes: 1) Assignment #8 vilble ) Chpte 8 this week Lectue 3 iot-svt s Lw (Continued) θ d θ P R R θ R d θ d Mgnetic Fields fom long
More information8.022 (E&M) Lecture 13. What we learned about magnetism so far
8.0 (E&M) Letue 13 Topis: B s ole in Mawell s equations Veto potential Biot-Savat law and its appliations What we leaned about magnetism so fa Magneti Field B Epeiments: uents in s geneate foes on hages
More information3.1 Magnetic Fields. Oersted and Ampere
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,
More informationInfluence of the Magnetic Field in the Solar Interior on the Differential Rotation
Influene of the gneti Fiel in the Sol Inteio on the Diffeentil ottion Lin-Sen Li * Deptment of Physis Nothest Noml Univesity Chnghun Chin * Coesponing utho: Lin-Sen Li Deptment of Physis Nothest Noml Univesity
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 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 informationMark Scheme (Results) January 2008
Mk Scheme (Results) Jnuy 00 GCE GCE Mthemtics (6679/0) Edecel Limited. Registeed in Englnd nd Wles No. 4496750 Registeed Office: One90 High Holbon, London WCV 7BH Jnuy 00 6679 Mechnics M Mk Scheme Question
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 ight-hnd ule to detemine the diection of the mgnetic foce on the chge. Emple 1 ˆ i = ˆ ˆ i
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 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 informationWinter 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 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 informationOptimization. x = 22 corresponds to local maximum by second derivative test
Optimiztion Lectue 17 discussed the exteme vlues of functions. This lectue will pply the lesson fom Lectue 17 to wod poblems. In this section, it is impotnt to emembe we e in Clculus I nd e deling one-vible
More informationCHAPTER 25 ELECTRIC POTENTIAL
CHPTE 5 ELECTIC POTENTIL Potential Diffeence and Electic Potential Conside a chaged paticle of chage in a egion of an electic field E. This filed exets an electic foce on the paticle given by F=E. When
More informationExperiment 1 Electric field and electric potential
Expeiment 1 Eleti field and eleti potential Pupose Map eleti equipotential lines and eleti field lines fo two-dimensional hage onfiguations. Equipment Thee sheets of ondutive papes with ondutive-ink eletodes,
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 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 information(conservation of momentum)
Dynamis of Binay Collisions Assumptions fo elasti ollisions: a) Eletially neutal moleules fo whih the foe between moleules depends only on the distane between thei entes. b) No intehange between tanslational
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 information( ) D x ( s) if r s (3) ( ) (6) ( r) = d dr D x
SIO 22B, Rudnick dpted fom Dvis III. Single vile sttistics The next few lectues e intended s eview of fundmentl sttistics. The gol is to hve us ll speking the sme lnguge s we move to moe dvnced topics.
More informationLecture 13 - Linking E, ϕ, and ρ
Lecture 13 - Linking E, ϕ, nd ρ A Puzzle... Inner-Surfce Chrge Density A positive point chrge q is locted off-center inside neutrl conducting sphericl shell. We know from Guss s lw tht the totl chrge on
More informationToday in Physics 122: getting V from E
Today in Physics 1: getting V fom E When it s best to get V fom E, athe than vice vesa V within continuous chage distibutions Potential enegy of continuous chage distibutions Capacitance Potential enegy
More informationMATH34032: Green s Functions, Integral Equations and the Calculus of Variations 1. 1 [(y ) 2 + yy + y 2 ] dx,
MATH3403: Green s Funtions, Integrl Equtions nd the Clulus of Vritions 1 Exmples 5 Qu.1 Show tht the extreml funtion of the funtionl I[y] = 1 0 [(y ) + yy + y ] dx, where y(0) = 0 nd y(1) = 1, is y(x)
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 informationChapter Seven Notes N P U1C7
Chpte Seven Notes N P UC7 Nme Peiod Setion 7.: Angles nd Thei Mesue In fling, hitetue, nd multitude of othe fields, ngles e used. An ngle is two diffeent s tht hve the sme initil (o stting) point. The
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 informationof Technology: MIT OpenCourseWare). (accessed MM DD, YYYY). License: Creative Commons Attribution- Noncommercial-Share Alike.
MIT OpenouseWe http://ocw.mit.edu 6.1/ESD.1J Electomgnetics nd pplictions, Fll 25 Plese use the following cittion fomt: Mkus Zhn, Eich Ippen, nd Dvid Stelin, 6.1/ESD.1J Electomgnetics nd pplictions, Fll
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 informationApplications of Definite Integral
Chpter 5 Applitions of Definite Integrl 5.1 Are Between Two Curves In this setion we use integrls to find res of regions tht lie between the grphs of two funtions. Consider the region tht lies between
More informationChapter Introduction to Partial Differential Equations
hpte 10.01 Intodtion to Ptil Diffeentil Eqtions Afte eding this hpte o shold be ble to: 1. identif the diffeene between odin nd ptil diffeentil eqtions.. identif diffeent tpes of ptil diffeentil eqtions.
More informationApplications of Definite Integral
Chpter 5 Applitions of Definite Integrl 5.1 Are Between Two Curves In this setion we use integrls to find res of regions tht lie between the grphs of two funtions. Consider the region tht lies between
More informationProblems set # 3 Physics 169 February 24, 2015
Prof. Anhordoqui Problems set # 3 Physis 169 Februry 4, 015 1. A point hrge q is loted t the enter of uniform ring hving liner hrge density λ nd rdius, s shown in Fig. 1. Determine the totl eletri flux
More informationTOPIC: Electrostatics and Magnetostatics (ENEL475) Q.1
TOPIC: Eletosttis nd Mgnetosttis (ENEL475 Q. We e inteested in inding the potentil ( t point on the -xis P = (0, 0, o uniom hge density ρ S distibuted on disk o dius = lying in the xy-plne nd ented ound
More informationLecture 4. Electric Potential
Lectue 4 Electic Ptentil In this lectue yu will len: Electic Scl Ptentil Lplce s n Pissn s Eutin Ptentil f Sme Simple Chge Distibutins ECE 0 Fll 006 Fhn Rn Cnell Univesity Cnsevtive Ittinl Fiels Ittinl
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 un-th distnce is 1.4 nd the th-moon 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 informationWelcome to Physics 272
Welcome to Physics 7 Bob Mose mose@phys.hawaii.edu http://www.phys.hawaii.edu/~mose/physics7.html To do: Sign into Masteing Physics phys-7 webpage Registe i-clickes (you i-clicke ID to you name on class-list)
More informationQuality control. Final exam: 2012/1/12 (Thur), 9:00-12:00 Q1 Q2 Q3 Q4 Q5 YOUR NAME
Qulity contol Finl exm: // (Thu), 9:-: Q Q Q3 Q4 Q5 YOUR NAME NOTE: Plese wite down the deivtion of you nswe vey clely fo ll questions. The scoe will be educed when you only wite nswe. Also, the scoe will
More information(a) Counter-Clockwise (b) Clockwise ()N (c) No rotation (d) Not enough information
m m m00 kg dult, m0 kg bby. he seesw stts fom est. Which diection will it ottes? ( Counte-Clockwise (b Clockwise ( (c o ottion ti (d ot enough infomtion Effect of Constnt et oque.3 A constnt non-zeo toque
More informationThe Wave Equation I. MA 436 Kurt Bryan
1 Introduction The Wve Eqution I MA 436 Kurt Bryn Consider string stretching long the x xis, of indeterminte (or even infinite!) length. We wnt to derive n eqution which models the motion of the string
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 informationr a + r b a + ( r b + r c)
AP Phsics C Unit 2 2.1 Nme Vectos Vectos e used to epesent quntities tht e chcteized b mgnitude ( numeicl vlue with ppopite units) nd diection. The usul emple is the displcement vecto. A quntit with onl
More information1 Introduction. K. Morawetz*, M. Gilbert and A. Trupp Induced Voltage in an Open Wire
Z. Ntufosh. 7; 7(7): 67 65 K. Mowetz*, M. Gilbet nd A. Tupp Indued Voltge in n Open Wie DOI.55/zn-7-6 Reeived My, 7; epted My, 7; peviously published online June, 7 Abstt: A puzzle ising fom Fdy s lw hs
More informationECE Microwave Engineering. Fall Prof. David R. Jackson Dept. of ECE. Notes 8. Waveguides Part 5: Coaxial Cable
ECE 5317-6351 Mirowve Engineering Fll 17 Prof. Dvid R. Jkson Dept. of ECE Notes 8 Wveguides Prt 5: Coil Cle 1 Coil Line: TEM Mode To find the TEM mode fields, we need to solve: ( ρφ) Φ, ; Φ ( ) V Φ ( )
More informationChapter 22 The Electric Field II: Continuous Charge Distributions
Chpte The lectic Field II: Continuous Chge Distibutions Conceptul Poblems [SSM] Figue -7 shows n L-shped object tht hs sides which e equl in length. Positive chge is distibuted unifomly long the length
More informationA NOTE ON THE POCHHAMMER FREQUENCY EQUATION
A note on the Pohhmme feqeny eqtion SCIENCE AND TECHNOLOGY - Reseh Jonl - Volme 6 - Univesity of Mitis Rédit Mitis. A NOTE ON THE POCHHAMMER FREQUENCY EQUATION by F.R. GOLAM HOSSEN Deptment of Mthemtis
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 informationPhysics 122, Fall September 2012
Physics 1, Fall 1 7 Septembe 1 Today in Physics 1: getting V fom E When it s best to get V fom E, athe than vice vesa V within continuous chage distibutions Potential enegy of continuous chage distibutions
More informationThe Double Integral. The Riemann sum of a function f (x; y) over this partition of [a; b] [c; d] is. f (r j ; t k ) x j y k
The Double Integrl De nition of the Integrl Iterted integrls re used primrily s tool for omputing double integrls, where double integrl is n integrl of f (; y) over region : In this setion, we de ne double
More informationMathematical Reflections, Issue 5, INEQUALITIES ON RATIOS OF RADII OF TANGENT CIRCLES. Y.N. Aliyev
themtil efletions, Issue 5, 015 INEQULITIES ON TIOS OF DII OF TNGENT ILES YN liev stt Some inequlities involving tios of dii of intenll tngent iles whih inteset the given line in fied points e studied
More informationEECE 260 Electrical Circuits Prof. Mark Fowler
EECE 60 Electicl Cicuits Pof. Mk Fowle Complex Numbe Review /6 Complex Numbes Complex numbes ise s oots of polynomils. Definition of imginy # nd some esulting popeties: ( ( )( ) )( ) Recll tht the solution
More information1.2. Linear Variable Coefficient Equations. y + b "! = a y + b " Remark: The case b = 0 and a non-constant can be solved with the same idea as above.
1 12 Liner Vrible Coefficient Equtions Section Objective(s): Review: Constnt Coefficient Equtions Solving Vrible Coefficient Equtions The Integrting Fctor Method The Bernoulli Eqution 121 Review: Constnt
More informationCHAPTER 2 ELECTROSTATIC POTENTIAL
1 CHAPTER ELECTROSTATIC POTENTIAL 1 Intoduction Imgine tht some egion of spce, such s the oom you e sitting in, is pemeted by n electic field (Pehps thee e ll sots of electiclly chged bodies outside the
More informationProperties and Formulas
Popeties nd Fomuls Cpte 1 Ode of Opetions 1. Pefom ny opetion(s) inside gouping symols. 2. Simplify powes. 3. Multiply nd divide in ode fom left to igt. 4. Add nd sutt in ode fom left to igt. Identity
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 informationTwo dimensional polar coordinate system in airy stress functions
I J C T A, 9(9), 6, pp. 433-44 Intentionl Science Pess Two dimensionl pol coodinte system in iy stess functions S. Senthil nd P. Sek ABSTRACT Stisfy the given equtions, boundy conditions nd bihmonic eqution.in
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 informationPreviously. Extensions to backstepping controller designs. Tracking using backstepping Suppose we consider the general system
436-459 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 informationMATHEMATICS IV 2 MARKS. 5 2 = e 3, 4
MATHEMATICS IV MARKS. If + + 6 + c epesents cicle with dius 6, find the vlue of c. R 9 f c ; g, f 6 9 c 6 c c. Find the eccenticit of the hpeol Eqution of the hpeol Hee, nd + e + e 5 e 5 e. Find the distnce
More information1. Viscosities: μ = ρν. 2. Newton s viscosity law: 3. Infinitesimal surface force df. 4. Moment about the point o, dm
3- Fluid Mecnics Clss Emple 3: Newton s Viscosit Lw nd Se Stess 3- Fluid Mecnics Clss Emple 3: Newton s Viscosit Lw nd Se Stess Motition Gien elocit field o ppoimted elocit field, we wnt to be ble to estimte
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 cuent-caying wie 165 Cuent loops and
More information( ) Make-up Tests. From Last Time. Electric Field Flux. o The Electric Field Flux through a bit of area is
Mon., 3/23 Wed., 3/25 Thus., 3/26 Fi., 3/27 Mon., 3/30 Tues., 3/31 21.4-6 Using Gauss s & nto to Ampee s 21.7-9 Maxwell s, Gauss s, and Ampee s Quiz Ch 21, Lab 9 Ampee s Law (wite up) 22.1-2,10 nto to
More informationUniversity of Illinois at Chicago Department of Physics. Electricity & Magnetism Qualifying Examination
E&M poblems Univesity of Illinois at Chicago Depatment of Physics Electicity & Magnetism Qualifying Examination Januay 3, 6 9. am : pm Full cedit can be achieved fom completely coect answes to 4 questions.
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 informationr r E x w, y w, z w, (1) Where c is the speed of light in vacuum.
ISSN: 77-754 ISO 900:008 Cetified Intentionl Jonl of Engineeing nd Innovtive Tehnology (IJEIT) olme, Isse 0, Apil 04 The Replement of the Potentils s Conseene of the Limittions Set by the Lw of the Self
More informationModule 4: Moral Hazard - Linear Contracts
Module 4: Mol Hzd - Line Contts Infomtion Eonomis (E 55) Geoge Geogidis A pinipl employs n gent. Timing:. The pinipl o es line ontt of the fom w (q) = + q. is the sly, is the bonus te.. The gent hooses
More informationSTD: XI MATHEMATICS Total Marks: 90. I Choose the correct answer: ( 20 x 1 = 20 ) a) x = 1 b) x =2 c) x = 3 d) x = 0
STD: XI MATHEMATICS Totl Mks: 90 Time: ½ Hs I Choose the coect nswe: ( 0 = 0 ). The solution of is ) = b) = c) = d) = 0. Given tht the vlue of thid ode deteminnt is then the vlue of the deteminnt fomed
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 hlf-filled by hemispheicl
More information