ELECTRIC & MAGNETIC FIELDS I (STATIC FIELDS) ELC 205A
|
|
|
- Leon Tyler
- 5 years ago
- Views:
Transcription
1 LCTRIC & MAGNTIC FILDS I (STATIC FILDS) LC 05A D. Hanna A. Kils Assciate Pfess lectnics & Cmmnicatins ngineeing Depatment Faclty f ngineeing Cai Univesity Fall 0 f Static lecticity
2 lectic & Magnetic Fields I f Static lecticity Clmb s Law: Clmb q F F n q Q q mete Q F n q Q q 4 Pemittivity f fee space (F/m) / m 0 9 F / 36 m D. H. Kils, Fall 0
3 lectic & Magnetic Fields I f Static lecticity lectstatic Field Intensity ect: at p F q Q 4 / m p Q Field f a pint chage D. H. Kils, Fall 0
4 lectic & Magnetic Fields I f Static lecticity Spepsitin f lectstatic Field: i Q p at p N i q i 4 i i / m q i F Q nq at p q q i q N D. H. Kils, Fall 0
5 D. H. Kils, Fall 0 f Static lecticity lectic & Magnetic Fields I lectstatic Field f a cntinm f chages: x y z p at d dq 3 4 4
6 lectic & Magnetic Fields I f Static lecticity lectstatic Field Lines: The diectin f a field Line mst be in the diectin f the ttal field at the pint. The lines depat fm psitive chages and teminate n negative chages. The sface density f the lines cssing nmally an element f sface aea at a pint in space gives the magnitde f the field at this pint. The lines ae pen and nn-intesecting. D. H. Kils, Fall 0
7 lectic & Magnetic Fields I f Static lecticity lectstatic Field Lines f pint chages: Field Line f a psitive pint chage Field Line f a negative pint chage D. H. Kils, Fall 0
8 lectic & Magnetic Fields I f Static lecticity lectstatic Field Lines f a diple: D. H. Kils, Fall 0
9 lectic & Magnetic Fields I lectstatic Flx : f Static lecticity (.m) Definitin: The nmbe f field lines cssing nmally an aea f space in the field f electstatic system f chages d d ds ds ds ds cs ds S D. H. Kils, Fall 0 ds
10 lectic & Magnetic Fields I f Static lecticity lectstatic Flx Leaving a Pint Chage q : ds, S c ds q sin 0 0 d d 4 q 4 q q Clsed Sface S c D. H. Kils, Fall 0
11 lectic & Magnetic Fields I f Static lecticity Gass s Law f lectstatic Field: Statement: The ttal twad flx f the -field ve any clsed sface in fee space is eqal t the ttal chage enclsed by the sface divided by ds S c ds Q enclsed by S c Clsed Sface S c D. H. Kils, Fall 0
12 lectic & Magnetic Fields I f Static lecticity Gass s Law f lectstatic Field: q ds ds q ds 0 c S c q Clsed Sface S c D. H. Kils, Fall 0
13 lectic & Magnetic Fields I f Static lecticity Gass s Law f Distibted Chage: lmetic Chage distibtin: S c ds Sface Chage distibtin: S c ds S Linea Chage distibtin: S c ds L v s dv ds d D. H. Kils, Fall 0
14 lectic & Magnetic Fields I f Static lecticity Applicatins f Gass s Law: Field f a nifmly chaged spheical shell: Field inside the shell S c ds 4 0 a S s ds 0 Q a Gassian Sface Field tside the shell 4 Q 4 a Q Q 4 a D. H. Kils, Fall 0 a
15 lectic & Magnetic Fields I f Static lecticity Applicatins f Gass s Law: Field f a nifmly chaged slid sphee: Field inside the shell a a 3 C / m Field tside the shell a a 3 D. H. Kils, Fall 0 a
16 lectic & Magnetic Fields I f Static lecticity Applicatins f Gass s Law: Field f a nifmly chaged infinite cylindical shell: Field inside the shell S c ds a dz 0 0 L 0 L d 0 L C / a m dz Field tside the shell dz L a L dz D. H. Kils, Fall 0 a dz
17 lectic & Magnetic Fields I f Static lecticity Applicatins f Gass s Law: Field f a nifmly chaged infinite cylindical shell: L C / m L a L 0 a D. H. Kils, Fall 0
18 lectic & Magnetic Fields I f Static lecticity Applicatins f Gass s Law: Field f a nifmly chaged slid cylinde: Field inside the shell a a 3 C / m Field tside the shell a a D. H. Kils, Fall 0 a
19 lectic & Magnetic Fields I f Static lecticity Applicatins f Gass s Law: Field f a nifmly chaged infinite plane sface: S c ds Field abve the plane: Field belw the plane: S s ds s ds ds 0 ds s s z s z s C / m s s C / m z s ds z z D. H. Kils, Fall 0
20 lectic & Magnetic Fields I f Static lecticity Applicatins f Gass s Law: Field f a tw ppsitely chaged infinite plane sfaces: Field between the tw planes: s Field abve and belw the planes: z D. H. Kils, Fall s s s s s s s s z
21 lectic & Magnetic Fields I f Static lecticity Applicatins f Gass s Law: Cnclsin Gass s Law is a vey pwefl tl t calclate the electstatic field nly f symmetic chage distibtins. F nn-symmetic distibtins the integal in the LHS is vey difficlt t calclate, de t the difficlty t find a clsed sface f which the field is nmal t all its elements f sface aea D. H. Kils, Fall 0
22 lectic & Magnetic Fields I f Static lecticity Scala lectstatic Ptential ( ) : lementay wk dne by the electstatic fce when a chage Q mves fm P t P dw Fce F d Q d If the chage Q is mved by an extenal agent, hence the wk dne by the agent is: P Q d F P dw agent Q d dw agent Q d A scala qantity which depends nly n the field and the teminal pints D. H. Kils, Fall 0
23 lectic & Magnetic Fields I f Static lecticity Scala lectstatic Ptential ( ) : Definitin: The electstatic ptential diffeence is the wk dne by an extenal agent t mve a test chage Q fm P t P against the electstatic fce pe nit chage f Q P Q d F P P P dw agent Q P P d J lt / C Discss: The ptential diffeence is independent n the path between the tw pints. D. H. Kils, Fall 0
24 lectic & Magnetic Fields I f Static lecticity Scala lectstatic Ptential ( ) : The ptential diffeence is independent n the path between the tw pints. dw agent P P dw agent P P D. H. Kils, Fall 0
25 lectic & Magnetic Fields I f Static lecticity lectstatic Ptential at a pint in a finite system f chages d The LHS f the eqatin abve eads: The ptential f P in efeence t that f P P P P Q d F P In a system f finite chage distibtins we may assme that the ptential at infinity is ze and can be sed as a efeence t all ptentials in the system. p P d D. H. Kils, Fall 0
26 lectic & Magnetic Fields I f Static lecticity lectstatic Ptential f a pint in the field f a pint chage p P d P p P Q 4 d d sin d Q p Q 4 lt D. H. Kils, Fall 0
27 lectic & Magnetic Fields I f Static lecticity Spepsitin f lectstatic Ptential: i p i p N i qi 4 i lt q q q i q N D. H. Kils, Fall 0
28 x y z z y x,, z y x,, D. H. Kils, Fall 0 f Static lecticity lectic & Magnetic Fields I lectstatic Ptential f a cntinm f chages: p d dq 4 4 p z z y y x x dz dy dx / 4
29 lectic & Magnetic Fields I f Static lecticity lectstatic Ptential at a pint in an infinite system f chages HAS NO MANING Y can nly calclate the ptential diffeence between tw pints; since y may NOT assme that the ptential t be ze at infinity D. H. Kils, Fall 0
30 lectic & Magnetic Fields I f Static lecticity lectstatic Ptential diffeence between tw pints in an infinite line chage ds d S c L L P P L L L L d L ln L D. H. Kils, Fall 0 d P P
31 lectic & Magnetic Fields I Calclatin f f Static lecticity fm a given Ptential Fnctin ( x, y, z) The ptential fnctin is given while the magnitde and diectin f ae nknwns d d d d d cs d d cs Rate f change f ptential fnctin alng the diectin f d Maximm +ve if cs 80 D. H. Kils, Fall 0
32 lectic & Magnetic Fields I Calclatin f When 80 f Static lecticity d d fm a given Ptential Fnctin ( x, y, z) max The diectin f maximm incease f the ptential fnctin d d The magnitde f is eqal t the maximm ate f incease f the ptential fnctin The diectin f is ppsite t the diectin f the maximm ate f incease f the ptential fnctin D. H. Kils, Fall 0
33 lectic & Magnetic Fields I f Static lecticity The Gadient f a Scala Fnctin f ( x, y, z) A vect peat, peates pn a scala fnctin and defined by: f The diectin f is in the diectin f the maximm ate f incease f the fnctin f ( x, y, z) f The magnitde f is eqal t the maximm ate f incease f the fnctin f ( x, y, z) f f diectinf df d max f df d max D. H. Kils, Fall 0
34 lectic & Magnetic Fields I f Static lecticity Calclatin f fm a given Ptential Fnctin ( x, y, z) The magnitde f is eqal t the maximm ate f incease f the ptential fnctin The diectin f is ppsite t the diectin f the maximm ate f incease f the ptential fnctin D. H. Kils, Fall 0
35 D. H. Kils, Fall 0 f Static lecticity lectic & Magnetic Fields I xpansin f The Gadient f a Scala Fnctin ) Catesian Cdinates: z y x z f y f x f f ) Cylindical Cdinates: z z f f f f 3) Spheical Cdinates: f f f f sin
36 lectic & Magnetic Fields I xample: f Static lecticity D. H. Kils, Fall 0 Find the ptential fnctin and the electstatic field intensity n the axis f a hllw cicla disk f inne and te adii a and b espectively that caies a nifm chage density s C/m p s s z b a z z a b z z z x b a z z p( 0,0, z) R d d y
37 lectic & Magnetic Fields I f Static lecticity qiptential Sfaces: Sfaces ve which the ptential is cnstant f all pints n the sface ( ) Q 4 70 Field and eqiptential sfaces f a pint chage D. H. Kils, Fall 0
38 lectic & Magnetic Fields I f Static lecticity qiptential Sfaces: D. H. Kils, Fall 0
39 lectic & Magnetic Fields I f Static lecticity qiptential Sfaces: D. H. Kils, Fall 0
40 lectic & Magnetic Fields I f Static lecticity qiptential Sfaces: qiptential sface d ( x, y, z) d d S S d 0 cs 0 d S lectic field lines mst be pependicla t the eqiptential sfaces in a system f static chages D. H. Kils, Fall 0
41 lectic & Magnetic Fields I f Static lecticity qiptential Sfaces: qiptential sface Since, the diectin f is ppsite t the diectin f the maximm ate f incease f the ptential fnctin d S lectic field lines mst be diected fm the sface f highe ptential twads the sface f lwe ptential D. H. Kils, Fall 0
42 lectic & Magnetic Fields I f Static lecticity D. H. Kils, Fall 0
43 lectic & Magnetic Fields I f Static lecticity Cicital Law f Static lectic Field: P P d P P d d 0 Static electic field lines ae pen lines D. H. Kils, Fall 0
44 lectic & Magnetic Fields I f Static lecticity Ppeties f lectstatic Field Lines: The lines ae pen and nn-intesecting. The diectin f a field Line mst be in the diectin f the ttal field at the pint. The lines depat fm psitive chages and teminate n negative chages. The sface density f the lines cssing nmally an element f sface aea at a pint in space gives the magnitde f the field at this pint. The lines mst be pependicla t the eqiptential sfaces diected fm the sface f highe ptential t that f lwe ptential. D. H. Kils, Fall 0
A) N B) 0.0 N C) N D) N E) N
Cdinat: H Bahluli Sunday, Nvembe, 015 Page: 1 Q1. Five identical pint chages each with chage =10 nc ae lcated at the cnes f a egula hexagn, as shwn in Figue 1. Find the magnitude f the net electic fce
Electric Charge. Electric charge is quantized. Electric charge is conserved
lectstatics lectic Chage lectic chage is uantized Chage cmes in incements f the elementay chage e = ne, whee n is an intege, and e =.6 x 0-9 C lectic chage is cnseved Chage (electns) can be mved fm ne
CHAPTER 24 GAUSS LAW
CHAPTR 4 GAUSS LAW LCTRIC FLUX lectic flux is a measue f the numbe f electic filed lines penetating sme suface in a diectin pependicula t that suface. Φ = A = A csθ with θ is the angle between the and
A) 100 K B) 150 K C) 200 K D) 250 K E) 350 K
Phys10 Secnd Maj-09 Ze Vesin Cdinat: k Wednesday, May 05, 010 Page: 1 Q1. A ht bject and a cld bject ae placed in themal cntact and the cmbinatin is islated. They tansfe enegy until they each a final equilibium
A) (0.46 î ) N B) (0.17 î ) N
Phys10 Secnd Maj-14 Ze Vesin Cdinat: xyz Thusday, Apil 3, 015 Page: 1 Q1. Thee chages, 1 = =.0 μc and Q = 4.0 μc, ae fixed in thei places as shwn in Figue 1. Find the net electstatic fce n Q due t 1 and.
Introduction. Electrostatics
UNIVESITY OF TECHNOLOGY, SYDNEY FACULTY OF ENGINEEING 4853 Electmechanical Systems Electstatics Tpics t cve:. Culmb's Law 5. Mateial Ppeties. Electic Field Stength 6. Gauss' Theem 3. Electic Ptential 7.
Phy 213: General Physics III
Phy 1: Geneal Physics III Chapte : Gauss Law Lectue Ntes E Electic Flux 1. Cnside a electic field passing thugh a flat egin in space w/ aea=a. The aea vect ( A ) with a magnitude f A and is diected nmal
Fri. 10/23 (C14) Linear Dielectrics (read rest at your discretion) Mon. (C 17) , E to B; Lorentz Force Law: fields
Fi. 0/23 (C4) 4.4. Linea ielectics (ead est at yu discetin) Mn. (C 7) 2..-..2, 2.3. t B; 5..-..2 Lentz Fce Law: fields Wed. and fces Thus. (C 7) 5..3 Lentz Fce Law: cuents Fi. (C 7) 5.2 Bit-Savat Law HW6
Electric Fields and Electric Forces
Cpyight, iley 006 (Cutnell & Jhnsn 9. Ptential Enegy Chapte 9 mgh mgh GPE GPE Electic Fields and Electic Fces 9. Ptential Enegy 9. Ptential Enegy 9. The Electic Ptential Diffeence 9. The Electic Ptential
Example 11: The man shown in Figure (a) pulls on the cord with a force of 70
Chapte Tw ce System 35.4 α α 100 Rx cs 0.354 R 69.3 35.4 β β 100 Ry cs 0.354 R 111 Example 11: The man shwn in igue (a) pulls n the cd with a fce f 70 lb. Repesent this fce actin n the suppt A as Catesian
Summary chapter 4. Electric field s can distort charge distributions in atoms and molecules by stretching and rotating:
Summa chapte 4. In chapte 4 dielectics ae discussed. In thse mateials the electns ae nded t the atms mlecules and cannt am fee thugh the mateial: the electns in insulats ae n a tight leash and all the
The Gradient and Applications This unit is based on Sections 9.5 and 9.6, Chapter 9. All assigned readings and exercises are from the textbook
The Gadient and Applicatins This unit is based n Sectins 9.5 and 9.6 Chapte 9. All assigned eadings and eecises ae fm the tetbk Objectives: Make cetain that u can define and use in cntet the tems cncepts
EELE 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
CHAPTER GAUSS'S LAW
lutins--ch 14 (Gauss's Law CHAPTE 14 -- GAU' LAW 141 This pblem is ticky An electic field line that flws int, then ut f the cap (see Figue I pduces a negative flux when enteing and an equal psitive flux
Magnetism. Chapter 21
1.1 Magnetic Fields Chapte 1 Magnetism The needle f a cmpass is pemanent magnet that has a nth magnetic ple (N) at ne end and a suth magnetic ple (S) at the the. 1.1 Magnetic Fields 1.1 Magnetic Fields
Chapter 4. Energy and Potential
Chpte 4. Enegy nd Ptentil Hyt; 0/5/009; 4-4. Enegy Expended in Mving Pint Chge in n Electic Field The electic field intensity is defined s the fce n unit test chge. The fce exeted y the electic field n
Work, Energy, and Power. AP Physics C
k, Eneg, and Pwe AP Phsics C Thee ae man diffeent TYPES f Eneg. Eneg is expessed in JOULES (J) 4.19 J = 1 calie Eneg can be expessed me specificall b using the tem ORK() k = The Scala Dt Pduct between
5/20/2011. HITT An electron moves from point i to point f, in the direction of a uniform electric field. During this displacement:
5/0/011 Chapte 5 In the last lectue: CapacitanceII we calculated the capacitance C f a system f tw islated cnducts. We als calculated the capacitance f sme simple gemeties. In this chapte we will cve the
Physics 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
n Power transmission, X rays, lightning protection n Solid-state Electronics: resistors, capacitors, FET n Computer peripherals: touch pads, LCD, CRT
.. Cu-Pl, INE 45- Electmagnetics I Electstatic fields anda Cu-Pl, Ph.. INE 45 ch 4 ECE UPM Maagüe, P me applicatins n Pwe tansmissin, X as, lightning ptectin n lid-state Electnics: esists, capacits, FET
March 15. Induction and Inductance Chapter 31
Mach 15 Inductin and Inductance Chapte 31 > Fces due t B fields Lentz fce τ On a mving chage F B On a cuent F il B Cuent caying cil feels a tque = µ B Review > Cuents geneate B field Bit-Savat law = qv
ELECTROMAGNETIC INDUCTION PREVIOUS EAMCET BITS
P P Methd EECTOMAGNETIC INDUCTION PEVIOUS EAMCET BITS [ENGINEEING PAPE]. A cnduct d f length tates with angula speed ω in a unifm magnetic field f inductin B which is pependicula t its mtin. The induced
5.1 Moment of a Force Scalar Formation
Outline ment f a Cuple Equivalent System Resultants f a Fce and Cuple System ment f a fce abut a pint axis a measue f the tendency f the fce t cause a bdy t tate abut the pint axis Case 1 Cnside hizntal
Electromagnetic Waves
Chapte 3 lectmagnetic Waves 3.1 Maxwell s quatins and ectmagnetic Waves A. Gauss s Law: # clsed suface aea " da Q enc lectic fields may be geneated by electic chages. lectic field lines stat at psitive
Chapter 6. Dielectrics and Capacitance
Chapter 6. Dielectrics and Capacitance Hayt; //009; 6- Dielectrics are insulating materials with n free charges. All charges are bund at mlecules by Culmb frce. An applied electric field displaces charges
2. 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
Physics 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
Gauss 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
Announcements Candidates Visiting Next Monday 11 12:20 Class 4pm Research Talk Opportunity to learn a little about what physicists do
Wed., /11 Thus., /1 Fi., /13 Mn., /16 Tues., /17 Wed., /18 Thus., /19 Fi., / 17.7-9 Magnetic Field F Distibutins Lab 5: Bit-Savat B fields f mving chages (n quiz) 17.1-11 Pemanent Magnets 18.1-3 Mic. View
University Physics (PHY 2326)
Chapte Univesity Physics (PHY 6) Lectue lectostatics lectic field (cont.) Conductos in electostatic euilibium The oscilloscope lectic flux and Gauss s law /6/5 Discuss a techniue intoduced by Kal F. Gauss
Potential 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
Physics 111. Exam #1. January 26, 2018
Physics xam # Januay 6, 08 ame Please ead and fllw these instuctins caefully: Read all pblems caefully befe attempting t slve them. Yu wk must be legible, and the ganizatin clea. Yu must shw all wk, including
The Coriolis force. Atmospheric Motion. Newton s second law. dx 2. Dynamics. Newton s second law. Mass Acceleration = Force.
Atmspheic Mtin Dynamics Newtn s secnd law m F Mass Acceleatin = Fce x Themdynamics dx m dt = F TMD Lecte Cncened with changes in the intenal enegy and state f mist ai. Newtn s secnd law The Cilis fce Newtn
Faraday s Law (continued)
Faaday s Law (continued) What causes cuent to flow in wie? Answe: an field in the wie. A changing magnetic flux not only causes an MF aound a loop but an induced electic field. Can wite Faaday s Law: ε
Phys102 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
Chapter 15. ELECTRIC POTENTIALS and ENERGY CONSIDERATIONS
Ch. 15--Elect. Pt. and Enegy Cns. Chapte 15 ELECTRIC POTENTIALS and ENERGY CONSIDERATIONS A.) Enegy Cnsideatins and the Abslute Electical Ptential: 1.) Cnside the fllwing scenai: A single, fixed, pint
ENGI 1313 Mechanics I
ENGI 1313 Mechanics I Lectue 05: Catesian Vects Shawn Kenny, Ph.D., P.Eng. ssistant Pfess Faculty f Engineeing and pplied Science Memial Univesity f Newfundland spkenny@eng.mun.ca Chapte Objectives t eview
Physics 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
Welcome 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)
$ 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 =
Solution: (a) C 4 1 AI IC 4. (b) IBC 4
C A C C R A C R C R C sin 9 sin. A cuent f is maintaine in a single cicula lp f cicumfeence C. A magnetic fiel f is iecte paallel t the plane f the lp. (a) Calculate the magnetic mment f the lp. (b) What
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
PHYS 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
Chapter 12: Kinematics of a Particle 12.8 CURVILINEAR MOTION: CYLINDRICAL COMPONENTS. u of the polar coordinate system are also shown in
ME 01 DYNAMICS Chapte 1: Kinematics of a Paticle Chapte 1 Kinematics of a Paticle A. Bazone 1.8 CURVILINEAR MOTION: CYLINDRICAL COMPONENTS Pola Coodinates Pola coodinates ae paticlaly sitable fo solving
Outline. Steady Heat Transfer with Conduction and Convection. Review Steady, 1-D, Review Heat Generation. Review Heat Generation II
Steady Heat ansfe ebuay, 7 Steady Heat ansfe wit Cnductin and Cnvectin ay Caett Mecanical Engineeing 375 Heat ansfe ebuay, 7 Outline eview last lectue Equivalent cicuit analyses eview basic cncept pplicatin
Phys 332 Electricity & Magnetism Day 3. Note: I should have recommended reading section 1.5 (delta function) as well. rˆ rˆ
Phs 33 lecticit & Magnetism Da 3 Mn. 9/9 Wed. 9/ Thus 9/ Fi. 9/3 (C.-.5,.8). &.5;..-.. Gauss & Div, T Numeical Quadatue (C.-.5,.8)..3 Using Gauss (C.-.5,.8)..3-.. Using Gauss HW quipment Bing in ppt s
Electrostatics (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
Chapter 19 8/30/2010 ( ) Let s review what we have learned in PHY College Physics I. Electric Potential Energy and the Electric Potential
8/3/ Chapte 9 Electic Ptential Enegy and the Electic Ptential Gals Chapte 9 T undestand electical ptential enegy. T deine electicalptential. T study euiptential suaces. T study capacits and dielectics.
11. HAFAT İş-Enerji Power of a force: Power in the ability of a force to do work
MÜHENDİSLİK MEKNİĞİ. HFT İş-Eneji Pwe f a fce: Pwe in he abiliy f a fce d wk F: The fce applied n paicle Q P = F v = Fv cs( θ ) F Q v θ Pah f Q v: The velciy f Q ÖRNEK: İŞ-ENERJİ ω µ k v Calculae he pwe
Your 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,
Review: 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
Lecture 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
2 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
TUTORIAL 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
Honors Physics Final Review Summary
Hnrs Physics Final Review Summary Wrk Dne By A Cnstant Frce: Wrk describes a frce s tendency t change the speed f an bject. Wrk is dne nly when an bject mves in respnse t a frce, and a cmpnent f the frce
Today 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
Chapter 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
Chapter 4 Motion in Two and Three Dimensions
Chapte 4 Mtin in Tw and Thee Dimensins In this chapte we will cntinue t stud the mtin f bjects withut the estictin we put in chapte t me aln a staiht line. Instead we will cnside mtin in a plane (tw dimensinal
AIR FORCE RESEARCH LABORATORY
AIR FORC RSARCH LABORATORY The xtinctin Theem as an xample f Reseach Vistas in Mathematical Optics Mach Richad A. Albanese Infmatin Opeatins and Applied Mathematics Human ffectiveness Diectate Bks City-Base
ECE 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
From last times. MTE1 results. Quiz 1. GAUSS LAW for any closed surface. What is the Electric Flux? How to calculate Electric Flux?
om last times MTE1 esults Mean 75% = 90/120 Electic chages and foce Electic ield and was to calculate it Motion of chages in E-field Gauss Law Toda: Moe on Gauss law and conductos in electostatic equilibium
Today 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
Example
hapte Exaple.6-3. ---------------------------------------------------------------------------------- 5 A single hllw fibe is placed within a vey lage glass tube. he hllw fibe is 0 c in length and has a
CHAPTER 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
Math 209 Assignment 9 Solutions
Math 9 Assignment 9 olutions 1. Evaluate 4y + 1 d whee is the fist octant pat of y x cut out by x + y + z 1. olution We need a paametic epesentation of the suface. (x, z). Now detemine the nomal vecto:
ME 3600 Control Systems Frequency Domain Analysis
ME 3600 Cntl Systems Fequency Dmain Analysis The fequency espnse f a system is defined as the steady-state espnse f the system t a sinusidal (hamnic) input. F linea systems, the esulting utput is itself
Chapter 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
Charge in a Cavity of Conductor
Tdy s Pln Electic Ptentil Enegy (mesued in Jules Electic Ptentil Ptentil Enegy pe unit Chge (mesued in Vlts). Recll tht the electic field E is fce F pe unit chge. Cpcitnce BB Chge in Cvity f Cnduct A pticle
Hopefully 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
Surface and Interface Science Physics 627; Chemistry 542. Lecture 10 March 1, 2013
Suface and Inteface Science Physics 67; Chemisty 54 Lectue 0 Mach, 03 Int t Electnic Ppeties: Wk Functin,Theminic Electn Emissin, Field Emissin Refeences: ) Wduff & Delcha, Pp. 40-4; 46-484 ) Zangwill
Objectives: 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
Chapter 2 GAUSS LAW Recommended Problems:
Chapter GAUSS LAW Recmmended Prblems: 1,4,5,6,7,9,11,13,15,18,19,1,7,9,31,35,37,39,41,43,45,47,49,51,55,57,61,6,69. LCTRIC FLUX lectric flux is a measure f the number f electric filed lines penetrating
GAUSS' LAW E. A. surface
Prf. Dr. I. M. A. Nasser GAUSS' LAW 08.11.017 GAUSS' LAW Intrductin: The electric field f a given charge distributin can in principle be calculated using Culmb's law. The examples discussed in electric
Review. 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
PC 1342 Electricity and Magnetism - Notes Semester 2
PC 34 lecticity and Magnetism - Ntes Semeste ) lectic Chage and lectic Field Lectue: D. yan Andesn (Chapte, Yung and Feedman). Matte Simple. Cnducts, Semi-Cnducts and nsulats n slid state, the ute electn
Voltage ( = 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
q r 1 4πε Review: Two ways to find V at any point in space: Integrate E dl: Sum or Integrate over charges: q 1 r 1 q 2 r 2 r 3 q 3
Review: Lectue : Consevation of negy and Potential Gadient Two ways to find V at any point in space: Integate dl: Sum o Integate ove chages: q q 3 P V = i 4πε q i i dq q 3 P V = 4πε dq ample of integating
OBJECTIVE To investigate the parallel connection of R, L, and C. 1 Electricity & Electronics Constructor EEC470
Assignment 7 Paallel Resnance OBJECTIVE T investigate the paallel cnnectin f R,, and C. EQUIPMENT REQUIRED Qty Appaatus 1 Electicity & Electnics Cnstuct EEC470 1 Basic Electicity and Electnics Kit EEC471-1
Review 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
MEM202 Engineering Mechanics Statics Course Web site:
0 Engineeing Mechanics - Statics 0 Engineeing Mechanics Statics Cuse Web site: www.pages.dexel.edu/~cac54 COUSE DESCIPTION This cuse cves intemediate static mechanics, an extensin f the fundamental cncepts
PHYS 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
Physics 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
ELECTROSTATICS::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
Section 4.2 Radians, Arc Length, and Area of a Sector
Sectin 4.2 Radian, Ac Length, and Aea f a Sect An angle i fmed by tw ay that have a cmmn endpint (vetex). One ay i the initial ide and the the i the teminal ide. We typically will daw angle in the cdinate
ELECTROSTATIC FIELDS IN MATERIAL MEDIA
MF LCTROSTATIC FILDS IN MATRIAL MDIA 3/4/07 LCTURS Materials media may be classified in terms f their cnductivity σ (S/m) as: Cnductrs The cnductivity usually depends n temperature and frequency A material
1. Show that if the angular momentum of a boby is determined with respect to an arbitrary point A, then. r r r. H r A can be expressed by H r r r r
1. Shw that if the angula entu f a bb is deteined with espect t an abita pint, then H can be epessed b H = ρ / v + H. This equies substituting ρ = ρ + ρ / int H = ρ d v + ρ ( ω ρ ) d and epanding, nte
Target 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:
ELECTRIC FIELD. decos. 1 dq x.. Example:
ELECTRIC FIELD Example: Solution: A ing-shaped conducto with adius a caies a total positive chage Q unifomly distibuted on it. Find the electic field at a point P that lies on the axis of the ing at a
AE301 Aerodynamics I UNIT B: Theory of Aerodynamics
AE301 Aeodynamics I UNIT B: Theoy of Aeodynamics ROAD MAP... B-1: Mathematics fo Aeodynamics B-2: Flow Field Repesentations B-3: Potential Flow Analysis B-4: Applications of Potential Flow Analysis AE301
Q1. In figure 1, Q = 60 µc, q = 20 µc, a = 3.0 m, and b = 4.0 m. Calculate the total electric force on q due to the other 2 charges.
Phys10 Secnd Majr-08 Zer Versin Crdinatr: Dr. I. M. Nasser Saturday, May 3, 009 Page: 1 Q1. In figure 1, Q = 60 µc, q = 0 µc, a = 3.0 m, and b = 4.0 m. Calculate the ttal electric frce n q due t the ther
EM-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
Potential and Capacitance
Ptential and apacitance Electric Ptential Electric ptential (V) = Electric ptential energy (U e ) per unit charge () Define: ptential energy U e = 0 at infinity (r = ) lim U 0 r e Nte the similarity f
UIUC Physics 435 EM Fields & Sources I Fall Semester, 2007 Lecture Notes 14 Prof. Steven Errede LECTURE NOTES 14
UIU Physics 45 EM Fields & Suces I Fall Seeste, 007 Lectue Ntes 4 Pf. Steven Eede LETURE NOTES 4 THE MAROSOPI MAGNETI FIELD ASSOIATED WITH THE RELATIVE MOTION OF AN ELETRIALLY-HARGED POINT-LIKE PARTILE
Electric Potential Energy
Electic Ptentil Enegy Ty Cnsevtive Fces n Enegy Cnsevtin Ttl enegy is cnstnt n is sum f kinetic n ptentil Electic Ptentil Enegy Electic Ptentil Cnsevtin f Enegy f pticle fm Phys 7 Kinetic Enegy (K) nn-eltivistic
Physics 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
Prepared 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
Vector Calculus Identities
The Coope Union Depatment of Electical Engineeing ECE135 Engineeing Electomagnetics Vecto Analysis Mach 8, 2012 Vecto Calculus Identities A B B A A B C B C A C A B A B C B A C C A B fg f g + g f fg f G
Your 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
CHAPTER 2 ELECTRIC FIELD
lecticity-mgnetim Tutil (QU PROJCT) 9 CHAPTR LCTRIC FILD.. Intductin If we plce tet chge in the pce ne chged d, n electttic fce will ct n the chge. In thi ce we pek f n electic field in thi pce ( nlgy
WYSE Academic Challenge Sectional Mathematics 2006 Solution Set
WYSE Academic Challenge Sectinal 006 Slutin Set. Cect answe: e. mph is 76 feet pe minute, and 4 mph is 35 feet pe minute. The tip up the hill takes 600/76, 3.4 minutes, and the tip dwn takes 600/35,.70