University Physics (PHY 2326)
|
|
- Clarence Small
- 5 years ago
- Views:
Transcription
1 Chapte Univesity Physics (PHY 6) Lectue lectostatics lectic field (cont.) Conductos in electostatic euilibium The oscilloscope lectic flux and Gauss s law /6/5
2 Discuss a techniue intoduced by Kal F. Gauss ( ) to calculate electic fields. euies symmetic chage distibutions. Techniue based on the notion of electical flux. Flux Numbe of objects passing though a suface /6/5
3 To intoduce the notion of flux, conside a situation whee the electic field is unifom in magnitude and diection. Conside also that the field lines coss a suface of aea A which is pependicula to the field. The numbe of field lines pe unit of aea is constant. The flux, F, is defined as the poduct of the field magnitude by the aea cossed by the field lines. FA Aea=A /6/5
4 Units: Nm /C in SI units. Find the electic flux though the aea A = m, which is pependicula to an electic field = N/C FA Answe: F = 44 Nm/C. /6/5 4
5 If the suface is not pependicula to the field, the expession of the field becomes: FAcos Whee is the angle between the field and a nomal to the suface. N /6/5 5
6 emak: When an aea is constucted such that a closed suface is fomed, we shall adopt the convention that the flux lines passing into the inteio of the volume ae negative and those passing out of the inteio of the volume ae positive. /6/5 6
7 Question: Calculate the flux of a constant field (along x) though a cube of side L. y x z /6/5 7
8 Question: Calculate the flux of a constant field (along x) though a cube of side L. easoning: Dealing with a composite, closed suface. Sum of the fluxes though all sufaces. Flux of field going in is negative Flux of field going out is positive. is paallel to all sufaces except sufaces labeled and. So only those suface contibute to the flux. y x z /6/5 8
9 Question: Calculate the flux of a constant field (along x) though a cube of side L. easoning: Dealing with a composite, closed suface. Sum of the fluxes though all sufaces. Flux of field going in is negative Flux of field going out is positive. is paallel to all sufaces except sufaces labeled and. So only those suface contibute to the flux. Solution: F A F A cos L cos L Fnet L L y x z /6/5 9
10 The net flux passing though a closed suface suounding a chage Q is popotional to the magnitude of Q: F Acos Q net In fee space, the constant of popotionality is /e o whee e o is called the pemittivity of of fee space. eo 9 4 k Nm / C e /6/5
11 The net flux passing though any closed suface is eual to the net chage inside the suface divided by e o. F Acos net Q e o /6/5
12 The field lines emitted by a chage ae popotional to the size of the chage. Theefoe, the electic field must be popotional to the size of the chage In ode to count the field lines, we must enclose the chages in some geometical suface (one that we choose) /6/5
13 Mathematically F F Chage enclosed within bounding limits of this closed suface integal da enclosed e e /6/5
14 Fluxes, Fluxes, Fluxes /6/5 4
15 Shapes Sphee Cylinde Pillbox /6/5 5
16 Sphee When to use: aound spheical objects (duh!) and point chages Hey! What if an object is not one of these objects? Closed suface integal yields: da (4 is the adius of the geometical object that you ae ceating ) /6/5 6
17 /6/5 7 Sphee xample ) (4 ) (4 4 ) 4 )( ( : A A da A A sphee Inside the enclosed enclosed e e What if you had a sphee of adius, b, which contained a mateial whose chage density depend on the adius, fo example, =A whee A is a constant with appopiate units? ) (4 ) (4 4 ) 4 )( ( : b A b A da b A b Ab sphee Outside the enclosed total e e At =b, both of these expessions should be eual
18 When to use: aound cylindical objects and line chages Closed suface integal yields: da ( L) L is the adius of the geometical object that you ae ceating and L is the length of the cylinde 8
19 What if you had an infinitely long line of chage with a linea chage density, l? (L) da (L) enclosed l e ll ll e o l e ˆ 9
20 When to use: aound flat sufaces and sheets of chage Closed suface integal yields: da A A is the aea of the pillbox
21 If excess chage is placed on an isolated conducto, the chage esides on the suface. Why? If thee is an -field inside the conducto then it would exet foces on the fee electons which would then be in motion. This is NOT electostatic. Theefoe, if thee is no -field inside, then, by Gauss s Law, the chage enclosed inside must be zeo If the chages ae not on the outside, you ae only left with the suface A caveat to this is that -field lines must be pependicula to the suface else fee chages would move.
22 A Let n o A A So A A A A da enclosed ˆ ) )( ( e e e A
23 Let A A So A da enclosed A e e A A o A nˆ e So a conducto has x the electic field stength as the infinite sheet of chage
24 ecall the Divegence of a field of vectos Div( v) v Div=+lage Div= How much the vecto diveges aound a given point 4
25 v d A place of high divegence is like a faucet v Bounded suface of some egion da Suspiciously like LHS of Gauss s Law Sum of the faucets in a volume = Sum of the wate going thu the suface 5
26 so da e enclosed e d enclosed e and enclosed d So how the -field speads out fom a point depends on the amount of chage density at that point
27 Poblem A chage, +, is suounded by a thin, spheical shell of adius, a, which has a chage density of on its suface. This shell is, in tun, suounded by anothe thin shell of adius, b, which has a suface chage of +. Find the electic fields in egion : <a egion : a<= <=b egion : > b b + a - + /6/5 7
28 I choose spheical! So da (4 ) 8
29 enclosed = ) ( ˆ 4 ) ( 4 4 a outwad adially enclosed e e e e 9 + a b - +
30 enclosed =+(4a )*(-) 4 4 a enclosed 4e ( adially 4e e 4a e outwad) 4a ˆ ( a b) b + a - +
31 enclosed =+(4a )*(- )+ (4b )*() enclosed 4 4a 4b 4e ( adially 4e e 4a outwad) 4b 4a 4b ˆ ( a b) e b + a - +
32 An electic filed given by =4i-(y +)j pieces the Gaussian cube shown below. ( is in newtons/coulomb and y is metes). What net chage is enclosed by the Gaussian cube? y x z X=. m X=. m
33 Planes y 4 6.y-z: Nomal to +x.x-z: Nomal to y.y-z: Nomal to x 4.x-z: Nomal to +y 5.x-y: Nomal to +z x 6.x-y: Nomal to -z z X=. m 5 X=. m
34 6 5 4 da da da da da da da da enclosed enclosed enclosed e e e 4
35 but da 4xˆ da y dz xdydz ˆ yˆ 4dy 5 4** 6 egion, in which the nomal vecto points in the opposite diection, will have a value of -6
36 4 Since is pependicula to sides 5 & 6, the esult is zeo. yˆ dxdz dz yˆ dxdz dz enclosed ( y ( y y y ) dx ) dx 6()() 4 6(4 )() 7 N m da C 48e 48(8.85 ) 4. C 6
37 The figue below shows a coss-section of two thin concentic cylindes with adii of a and b whee b>a. The cylindes eual and opposite chages pe unit length of l. a) Pove that = fo >a b) Pove that = fo >b c) Pove that, fo a<<b, a l b l e l 7
38 I choose cylindical! So da ( L) 8
39 enclosed = da (L) l l (L) a b 9
40 enclosed =ll (L) da (L) e l ll e a l b l 4
41 enclosed =ll-ll= da (L) l l (L) a b This is the pinciple of a coaxial cable 4
42 A vey long, solid insulating cylinde with adius has a cylindical hole with adius, a, boed along its entie length. The axis of the hole is a distance b fom the axis of the cylinde, whee a<b<. The solid mateial of the cylinde has a unifom chage density, p. Find the magnitude and diection of the electic field inside the hole and show that is unifom ove the entie hole. b a 4
43 L L L L da enclosed e e e e ˆ ) ( ) ( 4
44 we can tanslate coodinates by =-b Whee b is the diection and distance of the cente of the off-axis cylinde is a vecto fom the oigin b da ( ' L) enclosed (L) e e e ' ' e ' L ' ˆ e b L ' 44
45 b b b b hole hole axis off solid hole axis off solid e e e e e e e e 45 All of these ae constants and do not depend on.
46 W Fo gavity : W U U ab b a U F ds U Gmem d U Gmem Gmem Gmem o U Gmem Gmm Gmem 46
47 F F G C Gm m k e ˆ ˆ so k U 47
48 Potential is actually potential enegy pe unit chage =U/ olts ()= Joule/Coulomb o J/C ecall -field units wee N/C N N J C C C N m J m Now we have a new unit fo electic field: /m So now we see that the electic field is expession of how the voltage is changing ove space 48
49 It is a SCALA! But it can tell us about the -field and Foces! 49
50 U k k Point chage (I put the minus sign in ) i k i i Collection of point chages k d Distibution of chage 5
51 Take and divide by : W ab W b a ab b a F ds U F ds U Wa b b a ds b ds Potential diffeence between point A and point B a 5
52 k/ k/ -field Lines lectic field lines ae always pependicula to euipotential sufaces 5
53 ecall that all the chage of an isolated conducto esides on the suface All excess chage placed on an isolated conducto will distibute itself so that the suface will come to same potential because: If thee is moe o less chage between two points on the suface, thee will be cuent flow until euilibium e-established Futhemoe, the electic field lines must be pependicula to the suface at evey point Because if thee wee components tangential to the suface, thee would be 5
54 ecall d d o d x ds : b a d d dx ds x dx d d d holdingy, z constant y dy x dx x d y dy z dz z dz 54
55 xˆ x yˆ y zˆ z 55
56 56
57 ecall: W ab b a F ds b a ds But the wok done is independent of path Just like in gavity 57
58 What if: W aa a a F ds a a ds Well, fom point a to point a seems facetious, what about to? Such an integal is called a closed path integal and is expessed ds 58
59 ecall Cul(v) Cul( v) v Cul= Cul= Cul=+, out of page (ight Hand ule) 59
60 vda v ds 6
61 If ds then Because da ds 6
62 Needless to say, Gauss s Law woks well fo shapes: Sphee Cylinde Big, Flat Sufaces But what if you have a funny shape? 6
63 ecall that What is this uantity? and so e e 6
64 64 ˆ ˆ ˆ ˆ ˆ ˆ z y x so x x x z z y y x x z z y y x x z z y y x x
65 o u k e This euation applies to many physical systems Gavitation Heat flow M Quantum Mechanics 65
66 A numeical method to solve Laplace s euation Method of elaxation Method of ecusion Finite lement Method Big Bothes Discete Odinate (eacto physics) Finite Diffeence Time Domain (F engineeing) euies Known bounday conditions The ability to beak geomety into small egula shaped volume elements Compute with sufficient memoy (PM) 66
67 Based on neaest neighbo aveaging 5 5 5??=(5+++)/4 =.5 This is the estimate of the voltage in this suae 67
68 Loop thu multiple times You save the new values in a tempoay aay The new values eplace the old values and you loop again Fo -d objects, thee ae 6 sufaces 68
69 By a simple aveage, you ae assuming pefect conduction Fo diffeent mateials, you can slow up the tansfe of voltage, heat, etc by using Heat: diffeent themal conductivity values lecticity: diffeent electical conductivity values Fluids: diffeent viscosities 69
70
71 In the figue below, point P is at the cente of the ectangle. With = at infinity, what is the net electic potential at P due to the six chaged paticles? +5 d - d - d P d + d - d +5 7
72 d d d/ s d P d d + d - d +5 7
73 i i d k s k P d d d d d d s d d/ s k 5 d k s k 5 6 s k 4
74 i i d k d k s d k s d s s d s k
75 A chage is distibuted unifomly thoughout a spheical volume of adius,. a) Setting = at infinity shown that the potential at a distance fom the cente, whee < is given by 8e b) What is the potential diffeence between a point on the suface and the sphee s cente? 75
76 76 da outside outside enclosed outside ˆ 4 4 e e e da inside inside inside enclosed inside ˆ 4 ˆ e e e e e
77 77 d d ds f i i f outside ˆ ˆ 4 e e e e
78 78 d ds in in in in inside ˆ 4 ˆ e e e e e e e
79 79 ) ( in e e e e e e e e e
80 8 at Cente Cente ) ( 8 e e e e e
81 ˆ 4 But d d inside e e e e e at in 8e Same as pevious Same as pevious
82 The electic potential at points in a space ae given by =x -y +5z What is the magnitude and diection of the electic field at the point (,,-)? 8
83 8 C N z y x z y x z z y y x x z y x /.6 5 5ˆ ˆ ˆ ) (,, ˆ ) 5( ˆ 6() 4() ˆ ) (,,
84 (,, ) xˆ yˆ 5ˆ z tan tan y x ( ) 5 Diection w..t +x axis cos z whee x y z.6 cos Diection w..t +z axis 84
85 Thee +. C chages fom an euilateal tiangle,.7 m on a side. Using enegy that is supplied at a ate of.8 kw, how many days would be euied to move one of the chages to the midpoint of the line joining the othe two chages? 85
86 .C Initially, this chage is.7 m fom the othe two chages.7 m.7 m.c.85 m.85 m.7 m.c Finally, this chage is.85 m fom the othe two chages 86
87 87 C m L whee L k L k L k L k L k L k L k L k L k i f f i i f
88 k U L 9 (9x )(.) U.7 whee L.7m.C 5x 6 J 88
89 P=W/t W=-U So.8 kw= 8 J/s And t= U/P=5x 6 /8 t=8,699 s o 5 hous o. days 89
Gauss Law. Physics 231 Lecture 2-1
Gauss Law Physics 31 Lectue -1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing
More informationFlux. Area Vector. Flux of Electric Field. Gauss s Law
Gauss s Law Flux Flux in Physics is used to two distinct ways. The fist meaning is the ate of flow, such as the amount of wate flowing in a ive, i.e. volume pe unit aea pe unit time. O, fo light, it is
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 information2 E. on each of these two surfaces. r r r r. Q E E ε. 2 2 Qencl encl right left 0
Ch : 4, 9,, 9,,, 4, 9,, 4, 8 4 (a) Fom the diagam in the textbook, we see that the flux outwad though the hemispheical suface is the same as the flux inwad though the cicula suface base of the hemisphee
More informationObjectives: After finishing this unit you should be able to:
lectic Field 7 Objectives: Afte finishing this unit you should be able to: Define the electic field and explain what detemines its magnitude and diection. Wite and apply fomulas fo the electic field intensity
More informationChapter 21: Gauss s Law
Chapte : Gauss s Law Gauss s law : intoduction The total electic flux though a closed suface is equal to the total (net) electic chage inside the suface divided by ε Gauss s law is equivalent to Coulomb
More informationToday s Plan. Electric Dipoles. More on Gauss Law. Comment on PDF copies of Lectures. Final iclicker roll-call
Today s Plan lectic Dipoles Moe on Gauss Law Comment on PDF copies of Lectues Final iclicke oll-call lectic Dipoles A positive (q) and negative chage (-q) sepaated by a small distance d. lectic dipole
More informationPotential Energy. The change U in the potential energy. is defined to equal to the negative of the work. done by a conservative force
Potential negy The change U in the potential enegy is defined to equal to the negative of the wok done by a consevative foce duing the shift fom an initial to a final state. U = U U = W F c = F c d Potential
More informationElectrostatics (Electric Charges and Field) #2 2010
Electic Field: The concept of electic field explains the action at a distance foce between two chaged paticles. Evey chage poduces a field aound it so that any othe chaged paticle expeiences a foce when
More informationAlgebra-based Physics II
lgebabased Physics II Chapte 19 Electic potential enegy & The Electic potential Why enegy is stoed in an electic field? How to descibe an field fom enegetic point of view? Class Website: Natual way of
More information2. Electrostatics. Dr. Rakhesh Singh Kshetrimayum 8/11/ Electromagnetic Field Theory by R. S. Kshetrimayum
2. Electostatics D. Rakhesh Singh Kshetimayum 1 2.1 Intoduction In this chapte, we will study how to find the electostatic fields fo vaious cases? fo symmetic known chage distibution fo un-symmetic known
More informationPhysics 2212 GH Quiz #2 Solutions Spring 2016
Physics 2212 GH Quiz #2 Solutions Sping 216 I. 17 points) Thee point chages, each caying a chage Q = +6. nc, ae placed on an equilateal tiangle of side length = 3. mm. An additional point chage, caying
More informationUNIT 3:Electrostatics
The study of electic chages at est, the foces between them and the electic fields associated with them. UNIT 3:lectostatics S7 3. lectic Chages and Consevation of chages The electic chage has the following
More informationChapter 22 The Electric Field II: Continuous Charge Distributions
Chapte The lectic Field II: Continuous Chage Distibutions A ing of adius a has a chage distibution on it that vaies as l(q) l sin q, as shown in Figue -9. (a) What is the diection of the electic field
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 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 informationModule 05: Gauss s s Law a
Module 05: Gauss s s Law a 1 Gauss s Law The fist Maxwell Equation! And a vey useful computational technique to find the electic field E when the souce has enough symmety. 2 Gauss s Law The Idea The total
More informationGauss s Law Simulation Activities
Gauss s Law Simulation Activities Name: Backgound: The electic field aound a point chage is found by: = kq/ 2 If thee ae multiple chages, the net field at any point is the vecto sum of the fields. Fo a
More information13. The electric field can be calculated by Eq. 21-4a, and that can be solved for the magnitude of the charge N C m 8.
CHAPTR : Gauss s Law Solutions to Assigned Poblems Use -b fo the electic flux of a unifom field Note that the suface aea vecto points adially outwad, and the electic field vecto points adially inwad Thus
More informationObjects usually are charged up through the transfer of electrons from one object to the other.
1 Pat 1: Electic Foce 1.1: Review of Vectos Review you vectos! You should know how to convet fom pola fom to component fom and vice vesa add and subtact vectos multiply vectos by scalas Find the esultant
More informationCHAPTER 10 ELECTRIC POTENTIAL AND CAPACITANCE
CHAPTER 0 ELECTRIC POTENTIAL AND CAPACITANCE ELECTRIC POTENTIAL AND CAPACITANCE 7 0. ELECTRIC POTENTIAL ENERGY Conside a chaged paticle of chage in a egion of an electic field E. This filed exets an electic
More informationChapter 23: GAUSS LAW 343
Chapte 23: GAUSS LAW 1 A total chage of 63 10 8 C is distibuted unifomly thoughout a 27-cm adius sphee The volume chage density is: A 37 10 7 C/m 3 B 69 10 6 C/m 3 C 69 10 6 C/m 2 D 25 10 4 C/m 3 76 10
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 informationReview. Electrostatic. Dr. Ray Kwok SJSU
Review Electostatic D. Ray Kwok SJSU Paty Balloons Coulomb s Law F e q q k 1 Coulomb foce o electical foce. (vecto) Be caeful on detemining the sign & diection. k 9 10 9 (N m / C ) k 1 4πε o k is the Coulomb
More informationPHYS 2135 Exam I February 13, 2018
Exam Total /200 PHYS 2135 Exam I Febuay 13, 2018 Name: Recitation Section: Five multiple choice questions, 8 points each Choose the best o most nealy coect answe Fo questions 6-9, solutions must begin
More informationTarget Boards, JEE Main & Advanced (IIT), NEET Physics Gauss Law. H. O. D. Physics, Concept Bokaro Centre P. K. Bharti
Page 1 CONCPT: JB-, Nea Jitenda Cinema, City Cente, Bokao www.vidyadishti.og Gauss Law Autho: Panjal K. Bhati (IIT Khaagpu) Mb: 74884484 Taget Boads, J Main & Advanced (IIT), NT 15 Physics Gauss Law Autho:
More informationPhysics 235 Chapter 5. Chapter 5 Gravitation
Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus
More informationΦ E = E A E A = p212c22: 1
Chapte : Gauss s Law Gauss s Law is an altenative fomulation of the elation between an electic field and the souces of that field in tems of electic flux. lectic Flux Φ though an aea A ~ Numbe of Field
More informationAP Physics Electric Potential Energy
AP Physics lectic Potential negy Review of some vital peviously coveed mateial. The impotance of the ealie concepts will be made clea as we poceed. Wok takes place when a foce acts ove a distance. W F
More informationHopefully Helpful Hints for Gauss s Law
Hopefully Helpful Hints fo Gauss s Law As befoe, thee ae things you need to know about Gauss s Law. In no paticula ode, they ae: a.) In the context of Gauss s Law, at a diffeential level, the electic flux
More informationLook over Chapter 22 sections 1-8 Examples 2, 4, 5, Look over Chapter 16 sections 7-9 examples 6, 7, 8, 9. Things To Know 1/22/2008 PHYS 2212
PHYS 1 Look ove Chapte sections 1-8 xamples, 4, 5, PHYS 111 Look ove Chapte 16 sections 7-9 examples 6, 7, 8, 9 Things To Know 1) What is an lectic field. ) How to calculate the electic field fo a point
More informationLecture 8 - Gauss s Law
Lectue 8 - Gauss s Law A Puzzle... Example Calculate the potential enegy, pe ion, fo an infinite 1D ionic cystal with sepaation a; that is, a ow of equally spaced chages of magnitude e and altenating sign.
More informationPHY2061 Enriched Physics 2 Lecture Notes. Gauss Law
PHY61 Eniched Physics Lectue Notes Law Disclaime: These lectue notes ae not meant to eplace the couse textbook. The content may be incomplete. ome topics may be unclea. These notes ae only meant to be
More information$ i. !((( dv vol. Physics 8.02 Quiz One Equations Fall q 1 q 2 r 2 C = 2 C! V 2 = Q 2 2C F = 4!" or. r ˆ = points from source q to observer
Physics 8.0 Quiz One Equations Fall 006 F = 1 4" o q 1 q = q q ˆ 3 4" o = E 4" o ˆ = points fom souce q to obseve 1 dq E = # ˆ 4" 0 V "## E "d A = Q inside closed suface o d A points fom inside to V =
More informationElectric field generated by an electric dipole
Electic field geneated by an electic dipole ( x) 2 (22-7) We will detemine the electic field E geneated by the electic dipole shown in the figue using the pinciple of supeposition. The positive chage geneates
More informationModule 5: Gauss s Law 1
Module 5: Gauss s Law 1 4.1 lectic Flux... 4-4. Gauss s Law... 4-3 xample 4.1: Infinitely Long Rod of Unifom Chage Density... 4-8 xample 4.: Infinite Plane of Chage... 4-9 xample 4.3: Spheical Shell...
More informationExam 1. Exam 1 is on Tuesday, February 14, from 5:00-6:00 PM.
Exam 1 Exam 1 is on Tuesday, Febuay 14, fom 5:00-6:00 PM. Testing Cente povides accommodations fo students with special needs I must set up appointments one week befoe exam Deadline fo submitting accommodation
More informationCh 30 - Sources of Magnetic Field! The Biot-Savart 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 informationEM-2. 1 Coulomb s law, electric field, potential field, superposition q. Electric field of a point charge (1)
EM- Coulomb s law, electic field, potential field, supeposition q ' Electic field of a point chage ( ') E( ) kq, whee k / 4 () ' Foce of q on a test chage e at position is ee( ) Electic potential O kq
More informationReview for Midterm-1
Review fo Midtem-1 Midtem-1! Wednesday Sept. 24th at 6pm Section 1 (the 4:10pm class) exam in BCC N130 (Business College) Section 2 (the 6:00pm class) exam in NR 158 (Natual Resouces) Allowed one sheet
More informationPhysics 1502: Lecture 4 Today s Agenda
1 Physics 1502: Today s genda nnouncements: Lectues posted on: www.phys.uconn.edu/~cote/ HW assignments, solutions etc. Homewok #1: On Mastephysics today: due next Fiday Go to masteingphysics.com and egiste
More informationB. Spherical Wave Propagation
11/8/007 Spheical Wave Popagation notes 1/1 B. Spheical Wave Popagation Evey antenna launches a spheical wave, thus its powe density educes as a function of 1, whee is the distance fom the antenna. We
More information(Sample 3) Exam 1 - Physics Patel SPRING 1998 FORM CODE - A (solution key at end of exam)
(Sample 3) Exam 1 - Physics 202 - Patel SPRING 1998 FORM CODE - A (solution key at end of exam) Be sue to fill in you student numbe and FORM lette (A, B, C) on you answe sheet. If you foget to include
More informationChapter 4 Gauss s Law
Chapte 4 Gauss s Law 4.1 lectic Flux... 1 4. Gauss s Law... xample 4.1: Infinitely Long Rod of Unifom Chage Density... 7 xample 4.: Infinite Plane of Chage... 9 xample 4.3: Spheical Shell... 11 xample
More information17.1 Electric Potential Energy. Equipotential Lines. PE = energy associated with an arrangement of objects that exert forces on each other
Electic Potential Enegy, PE Units: Joules Electic Potential, Units: olts 17.1 Electic Potential Enegy Electic foce is a consevative foce and so we can assign an electic potential enegy (PE) to the system
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 informationYour Comments. Do we still get the 80% back on homework? It doesn't seem to be showing that. Also, this is really starting to make sense to me!
You Comments Do we still get the 8% back on homewok? It doesn't seem to be showing that. Also, this is eally stating to make sense to me! I am a little confused about the diffeences in solid conductos,
More informationEELE 3331 Electromagnetic I Chapter 4. Electrostatic fields. Islamic University of Gaza Electrical Engineering Department Dr.
EELE 3331 Electomagnetic I Chapte 4 Electostatic fields Islamic Univesity of Gaza Electical Engineeing Depatment D. Talal Skaik 212 1 Electic Potential The Gavitational Analogy Moving an object upwad against
More informationReview: Electrostatics and Magnetostatics
Review: Electostatics and Magnetostatics In the static egime, electomagnetic quantities do not vay as a function of time. We have two main cases: ELECTROSTATICS The electic chages do not change postion
More informationPhys102 Second Major-182 Zero Version Monday, March 25, 2019 Page: 1
Monday, Mach 5, 019 Page: 1 Q1. Figue 1 shows thee pais of identical conducting sphees that ae to be touched togethe and then sepaated. The initial chages on them befoe the touch ae indicated. Rank the
More informationChapter 22: Electric Fields. 22-1: What is physics? General physics II (22102) Dr. Iyad SAADEDDIN. 22-2: The Electric Field (E)
Geneal physics II (10) D. Iyad D. Iyad Chapte : lectic Fields In this chapte we will cove The lectic Field lectic Field Lines -: The lectic Field () lectic field exists in a egion of space suounding a
More informationECE 3318 Applied Electricity and Magnetism. Spring Prof. David R. Jackson ECE Dept. Notes 13
ECE 338 Applied Electicity and Magnetism ping 07 Pof. David R. Jackson ECE Dept. Notes 3 Divegence The Physical Concept Find the flux going outwad though a sphee of adius. x ρ v0 z a y ψ = D nˆ d = D ˆ
More informationChapter 13 Gravitation
Chapte 13 Gavitation In this chapte we will exploe the following topics: -Newton s law of gavitation, which descibes the attactive foce between two point masses and its application to extended objects
More informationVoltage ( = Electric Potential )
V-1 of 10 Voltage ( = lectic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage
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 informationPage 1 of 6 Physics II Exam 1 155 points Name Discussion day/time Pat I. Questions 110. 8 points each. Multiple choice: Fo full cedit, cicle only the coect answe. Fo half cedit, cicle the coect answe and
More informationPhysics 2A Chapter 10 - Moment of Inertia Fall 2018
Physics Chapte 0 - oment of netia Fall 08 The moment of inetia of a otating object is a measue of its otational inetia in the same way that the mass of an object is a measue of its inetia fo linea motion.
More information7.2. Coulomb s Law. The Electric Force
Coulomb s aw Recall that chaged objects attact some objects and epel othes at a distance, without making any contact with those objects Electic foce,, o the foce acting between two chaged objects, is somewhat
More informationF = net force on the system (newton) F,F and F. = different forces working. E = Electric field strength (volt / meter)
All the Impotant Fomulae that a student should know fom. XII Physics Unit : CHAPTER - ELECTRIC CHARGES AND FIELD CHAPTER ELECTROSTATIC POTENTIAL AND CAPACITANCE S. Fomula No.. Quantization of chage Q =
More informationELECTROSTATICS::BHSEC MCQ 1. A. B. C. D.
ELETROSTATIS::BHSE 9-4 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 informationPHYS 1444 Section 501 Lecture #7
PHYS 1444 Section 51 Lectue #7 Wednesday, Feb. 8, 26 Equi-potential Lines and Sufaces Electic Potential Due to Electic Dipole E detemined fom V Electostatic Potential Enegy of a System of Chages Capacitos
More information! E da = 4πkQ enc, has E under the integral sign, so it is not ordinarily an
Physics 142 Electostatics 2 Page 1 Electostatics 2 Electicity is just oganized lightning. Geoge Calin A tick that sometimes woks: calculating E fom Gauss s law Gauss s law,! E da = 4πkQ enc, has E unde
More informationPhysics 122, Fall October 2012
Today in Physics 1: electostatics eview David Blaine takes the pactical potion of his electostatics midtem (Gawke). 11 Octobe 01 Physics 1, Fall 01 1 Electostatics As you have pobably noticed, electostatics
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 informationMAGNETIC FIELD INTRODUCTION
MAGNETIC FIELD INTRODUCTION It was found when a magnet suspended fom its cente, it tends to line itself up in a noth-south diection (the compass needle). The noth end is called the Noth Pole (N-pole),
More informationPrepared by: M. S. KumarSwamy, TGT(Maths) Page - 1 -
Pepaed by: M. S. KumaSwamy, TGT(Maths) Page - - ELECTROSTATICS MARKS WEIGHTAGE 8 maks QUICK REVISION (Impotant Concepts & Fomulas) Chage Quantization: Chage is always in the fom of an integal multiple
More information1. THINK Ampere is the SI unit for current. An ampere is one coulomb per second.
Chapte 4 THINK Ampee is the SI unit fo cuent An ampee is one coulomb pe second EXPRESS To calculate the total chage though the cicuit, we note that A C/s and h 6 s ANALYZE (a) Thus, F I HG K J F H G I
More informationPhysics 2B Chapter 22 Notes - Magnetic Field Spring 2018
Physics B Chapte Notes - Magnetic Field Sping 018 Magnetic Field fom a Long Staight Cuent-Caying Wie In Chapte 11 we looked at Isaac Newton s Law of Gavitation, which established that a gavitational field
More informationF Q E v B MAGNETOSTATICS. Creation of magnetic field B. Effect of B on a moving charge. On moving charges only. Stationary and moving charges
MAGNETOSTATICS Ceation of magnetic field. Effect of on a moving chage. Take the second case: F Q v mag On moving chages only F QE v Stationay and moving chages dw F dl Analysis on F mag : mag mag Qv. vdt
More information? this lecture. ? next lecture. What we have learned so far. a Q E F = q E a. F = q v B a. a Q in motion B. db/dt E. de/dt B.
PHY 249 Lectue Notes Chapte 32: Page 1 of 12 What we have leaned so fa a a F q a a in motion F q v a a d/ Ae thee othe "static" chages that can make -field? this lectue d/? next lectue da dl Cuve Cuve
More informationAP Physics - Coulomb's Law
AP Physics - oulomb's Law We ve leaned that electons have a minus one chage and potons have a positive one chage. This plus and minus one business doesn t wok vey well when we go in and ty to do the old
More informationElectrostatics. 3) positive object: lack of electrons negative object: excess of electrons
Electostatics IB 12 1) electic chage: 2 types of electic chage: positive and negative 2) chaging by fiction: tansfe of electons fom one object to anothe 3) positive object: lack of electons negative object:
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 informationChapter Sixteen: Electric Charge and Electric Fields
Chapte Sixteen: Electic Chage and Electic Fields Key Tems Chage Conducto The fundamental electical popety to which the mutual attactions o epulsions between electons and potons ae attibuted. Any mateial
More informationDEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS TSOKOS LESSON 10-1 DESCRIBING FIELDS Essential Idea: Electic chages and masses each influence the space aound them and that influence can be epesented
More informationEM Boundary Value Problems
EM Bounday Value Poblems 10/ 9 11/ By Ilekta chistidi & Lee, Seung-Hyun A. Geneal Desciption : Maxwell Equations & Loentz Foce We want to find the equations of motion of chaged paticles. The way to do
More informationIntroduction: Vectors and Integrals
Intoduction: Vectos and Integals Vectos a Vectos ae chaacteized by two paametes: length (magnitude) diection a These vectos ae the same Sum of the vectos: a b a a b b a b a b a Vectos Sum of the vectos:
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 informationPhysics 11 Chapter 20: Electric Fields and Forces
Physics Chapte 0: Electic Fields and Foces Yesteday is not ous to ecove, but tomoow is ous to win o lose. Lyndon B. Johnson When I am anxious it is because I am living in the futue. When I am depessed
More informationarxiv: v1 [physics.pop-ph] 3 Jun 2013
A note on the electostatic enegy of two point chages axiv:1306.0401v1 [physics.pop-ph] 3 Jun 013 A C Tot Instituto de Física Univesidade Fedeal do io de Janeio Caixa Postal 68.58; CEP 1941-97 io de Janeio,
More informationElectromagnetic Theory 1
/ lectomagnetic Theoy uestion : lectostatic Potential negy A sphee of adius caies a positive chage density ρ constant Obviously the spheical coodinates system is appopiate hee Take - C m - and cm τ a)
More informationReview of Potential Energy. The Electric Potential. Plotting Fields and Potentials. Electric Potential of a Point Charge
eview of Potential negy Potential enegy U() can be used to descibe a consevative foce. efeence point (U) can be chosen fo convenience. Wok done by F : W F d s F d (1D) Change in P.. : U U f U i W Foce
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 informationKinetic energy, work, and potential energy. Work, the transfer of energy: force acting through distance: or or
ENERGETICS So fa we have been studying electic foces and fields acting on chages. This is the dynamics of electicity. But now we will tun to the enegetics of electicity, gaining new insights and new methods
More informationPhysics 107 TUTORIAL ASSIGNMENT #8
Physics 07 TUTORIAL ASSIGNMENT #8 Cutnell & Johnson, 7 th edition Chapte 8: Poblems 5,, 3, 39, 76 Chapte 9: Poblems 9, 0, 4, 5, 6 Chapte 8 5 Inteactive Solution 8.5 povides a model fo solving this type
More informationYour Comments. Conductors and Insulators with Gauss's law please...so basically everything!
You Comments I feel like I watch a pe-lectue, and agee with eveything said, but feel like it doesn't click until lectue. Conductos and Insulatos with Gauss's law please...so basically eveything! I don't
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 information18.1 Origin of Electricity 18.2 Charged Objects and Electric Force
1 18.1 Oigin of lecticity 18. Chaged Objects and lectic Foce Thee ae two kinds of electic chage: positive and negative. The SI unit of electic chage is the coulomb (C). The magnitude of the chage on an
More informationJ. N. R E DDY ENERGY PRINCIPLES AND VARIATIONAL METHODS APPLIED MECHANICS
J. N. E DDY ENEGY PINCIPLES AND VAIATIONAL METHODS IN APPLIED MECHANICS T H I D E DI T IO N JN eddy - 1 MEEN 618: ENEGY AND VAIATIONAL METHODS A EVIEW OF VECTOS AND TENSOS ead: Chapte 2 CONTENTS Physical
More informationElectricity Revision ELECTRICITY REVISION KEY CONCEPTS TERMINOLOGY & DEFINITION. Physical Sciences X-Sheets
Electicity Revision KEY CONCEPTS In this session we will focus on the following: Stating and apply Coulomb s Law. Defining electical field stength and applying the deived equations. Dawing electical field
More information(r) = 1. Example: Electric Potential Energy. Summary. Potential due to a Group of Point Charges 9/10/12 1 R V(r) + + V(r) kq. Chapter 23.
Eample: Electic Potential Enegy What is the change in electical potential enegy of a eleased electon in the atmosphee when the electostatic foce fom the nea Eath s electic field (diected downwad) causes
More informationworking pages for Paul Richards class notes; do not copy or circulate without permission from PGR 2004/11/3 10:50
woking pages fo Paul Richads class notes; do not copy o ciculate without pemission fom PGR 2004/11/3 10:50 CHAPTER7 Solid angle, 3D integals, Gauss s Theoem, and a Delta Function We define the solid angle,
More informationQualifying Examination Electricity and Magnetism Solutions January 12, 2006
1 Qualifying Examination Electicity and Magnetism Solutions Januay 12, 2006 PROBLEM EA. a. Fist, we conside a unit length of cylinde to find the elationship between the total chage pe unit length λ and
More informationCHECK YOUR GRASP. +q +2q A B. D 2q +q
J-Physics XCIS 1 CHCK YOU GASP SLCT TH COCT ALTNATIV (ONLY ON COCT ANSW) 1. Using mass (M), length (L), time (T) and cuent as fundamental uantities, the dimension of pemittivity is : ML T A M 1 L T 4 A
More informationSchool of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007
School of Electical and Compute Engineeing, Conell Univesity ECE 303: Electomagnetic Fields and Waves Fall 007 Homewok 8 Due on Oct. 19, 007 by 5:00 PM Reading Assignments: i) Review the lectue notes.
More informationMagnetic fields (origins) CHAPTER 27 SOURCES OF MAGNETIC FIELD. Permanent magnets. Electric currents. Magnetic field due to a moving charge.
Magnetic fields (oigins) CHAPTER 27 SOURCES OF MAGNETC FELD Magnetic field due to a moving chage. Electic cuents Pemanent magnets Magnetic field due to electic cuents Staight wies Cicula coil Solenoid
More informationContinuous Charge Distributions: Electric Field and Electric Flux
8/30/16 Quiz 2 8/25/16 A positive test chage qo is eleased fom est at a distance away fom a chage of Q and a distance 2 away fom a chage of 2Q. How will the test chage move immediately afte being eleased?
More informationPhys-272 Lecture 17. Motional Electromotive Force (emf) Induced Electric Fields Displacement Currents Maxwell s Equations
Phys-7 Lectue 17 Motional Electomotive Foce (emf) Induced Electic Fields Displacement Cuents Maxwell s Equations Fom Faaday's Law to Displacement Cuent AC geneato Magnetic Levitation Tain Review of Souces
More information8.022 (E&M) - Lecture 2
8.0 (E&M) - Lectue Topics: Enegy stoed in a system of chages Electic field: concept and poblems Gauss s law and its applications Feedback: Thanks fo the feedback! caed by Pset 0? Almost all of the math
More informationCharges, Coulomb s Law, and Electric Fields
Q&E -1 Chages, Coulomb s Law, and Electic ields Some expeimental facts: Expeimental fact 1: Electic chage comes in two types, which we call (+) and (). An atom consists of a heavy (+) chaged nucleus suounded
More information