Lesson 07 Electrostatics in Materials

Size: px
Start display at page:

Download "Lesson 07 Electrostatics in Materials"

Transcription

1 Electomagnetcs P7-1 Lesson 07 Electostatcs n Mateals Intoducton Mateals consst of atoms, whch ae made u of nucle (oste chages) and electons (negate chages). As a esult, the total electc feld must be modfed n the esence of mateals. We usually classfy mateals nto thee tyes: 1) Conductos: The electons n the outemost shells of the atoms ae ey loosely held and can feely mgate among atoms due to themal exctaton at oom temeatues. These electons ae shaed by all atoms. ) Delectcs: All electons ae confned wthn the nne shells of atoms, and can hadly mgate een by alyng a stong exctaton. 3) emconductos: Outemost electons ae modeately confned, whch may not mgate due to themal exctaton but become moable when alyng an extenal electc feld. Fg (a) Enegy leels and bands. (b) Band dagams of nsulato, semconducto, and metal. In tems of quantum theoy, the electons of an atom can only stay at dscete enegy leels (Fg. 7-1a, left). When a lage numbe of atoms aggegate n odeed manne (cystallne sold), each enegy leel slts nto densely saced leels (enegy band ). The allowed enegy bands can be oelaed o seaated by fobdden enegy ga (Fg. 7-1a, ght). Electc chaactestcs of mateals deend on the band stuctue and how they ae flled by the electons at the temeatue of 0 K (Fg. 7-1b):

2 Electomagnetcs P7-1) Conductos: Bands ae oelaed, o the conducton band s atally flled. ) Delectcs: Enegy ga s lage, and the conducton band s emty. 3) emconductos: Enegy ga s small, and the conducton band s emty. In ths lesson, we wll dscuss the feld behaos both nsde some mateal and on the nteface of dffeent mateals. 7.1 tatc Electc Feld n the Pesence of Conductos Chage and electc feld nsde a conducto Assume that some oste (o negate) chages ae ntoduced n the nteo of a conducto. Intally an electc feld wll be set u, whch wll ush the fee chages away fom one anothe by Coulomb s foce and modfy the electc feld dstbuton by tuns. Ths chage-feld nteacton ocess wll contnue untl: (1) all the chages each the conducto suface (no way to leae): ρ = 0, (7.1) and () the suface chages edstbute themseles such that no electc feld exsts nsde the conducto: E = 0 (7.) Eq. (7.) can be justfed by: 1) If E 0 somewhee nsde the conducto, the electc otental V ( ) s non-unfom. Ths wll esult n a contadcton that wok has to be done to moe fee chages. ) The fee chage dstbuton that leads to E = 0 actually coesonds to the lowest system enegy,.e., a state of equlbum (Lesson 9). Fo good conductos lke coe, the tme equed to each the equlbum s only n the ode of sec (Lesson 10).

3 Electomagnetcs P7-3 A-conducto nteface nce the chages on the conducto suface wll not be at est f thee s tangental electc feld comonent, the suface electc feld only has nomal comonent n the equlbum. goous bounday condtons (BCs) ae deed by alyng eq s (6.3), (6.4) wth esect to the dffeental contou abcda and the thn ll box (Fg. 7-) acoss the a-conducto nteface, esectely. Fg. 7-. Dffeental contou and ll box used to dee BCs on the a-conducto nteface (afte DKC). 1) Tangental BC: By eq s (6.4), (7.), E dl = E Δw + 0 Δw = 0, abcda Δh 0 t ) Nomal BC: BC: By eq s (6.3), (7.1-3), E = 0 (7.3) t E ds = E ρ Δ Δ =, s n Δh 0 ε 0 ρ s ε 0 E =, (7.4) n whee E n s n the nomal decton fom the conducto to the a. Examle 7-1: Consde a ont chage + located at the cente of a shecal conductng shell of fnte thckness (Fg. 7-3a). Fnd E, V nsde and outsde the shell.

4 Electomagnetcs P7-4 Fg (a) The geomety of a conductng shee. The coesondng (b) adal comonents of E (dashed), and (c) electc otental V. Ans: Because of the shecal symmety of the souce, we hae E a = E () eeywhee, and the Gaussan sufaces ae concentc shecal sufaces centeed at the ogn. < : E ds = E ( ) ( 4π ) =, E ( ) =. 3 ε 0 4 πε 0 () Fo < < o : By eq. (7.), E = 0, E ds = 0 (1) Fo fo any enclosed suface nsde the shell. Ths mles that fee chages of must be nduced on the nne suface of the shell. By the conseaton of chages and eq. (7.1), fee chages of + must be nduced on the oute suface of the shell. (3) Fo > o : The total chage enclosed by a Gaussan suface 1 s +, E ( ) =. 4 πε 0 The cue of E = E () s shown n Fg. 7-3b. One can dee the electc otental dstbuton V () by lne ntegal of E (Fg. 7-3c).

5 Electomagnetcs P tatc Electc Feld n the Pesence of Delectcs Concet of nduced doles A delectc molecule could be non-ola (e.g., H, CH 4 ) o ola (e.g., H O, HCl, NH 3, O 3 ), deendng on whethe thee s nonzeo electc dole moment [eq. (6.17)]. Howee, a delectc bulk made u of a lage numbe of andomly oented molecules (ola o non-ola) tycally has no macoscoc dole moment n the absence of extenal electc feld. When an electc feld s aled, the bound chages of the delectcs cannot feely mgate to the suface. Instead, (1) each non-ola molecule s olazed fo the ostely chaged nucle and negately chaged electons ae slghtly dslaced n ooste dectons (dstoton of electon cloud). () Most of the nddual dole moments (ectos) ae algned n the same decton due to the electc toque. In ethe case, a macoscoc dole moment emeges. Fg A coss secton of a olazed delectc medum (afte DKC). Although an electc dole s neutal n ensemble, t odes nonzeo otental and electc feld [eq s (6.18), (6.16)], whch wll modfy the total feld nsde and outsde delectcs. Polazaton ecto and equalent chage denstes To analyze the effect of nduced doles, we defne a (mcoscoc) olazaton ecto P as

6 Electomagnetcs P7-6 the olume densty of electc dole moment: k P lm (7.5) Δ 0 Δ whee k denotes the kth dole moment nsde a dffeental olume Δ. If the olazaton ecto P s nhomogeneous (.e., aes wth oston) somewhee, thee must exst net (bound) olazaton chage at that oston. Ths henomenon can be llustated n two cases. Fg (a) The model to deduce the olazaton suface chage densty. (b) Net olazaton olume chage exsts whee the olazaton ecto P s nhomogeneous. 1) The olazaton ecto P s dscontnuous on the a-delectc nteface, whee thee must exst net olazaton chage (Fg. 7-5a). To quanttately model ths henomenon, consde a dffeental aalleleed V bounded by a closed suface b, whee the dole moment of each molecule s = qd. The to suface of has a unt outwad b nomal ecto a n a n and an aea of Δ. The effecte heght of the aalleleed V s d. The net olazaton chage wthn V s: Δ = nq ( d a ) Δ = ( P a ) Δ n whee n (1/m 3 ) s the numbe densty of molecules. The coesondng olazaton n,

7 Electomagnetcs P7-7 suface chage densty Δ Δ s: s P a ρ = n (C/m ) (7.6) ) Consde two doles wth dffeent olazaton ectos P 1, P n the nteo of a dffeental olume V bounded by a closed suface (Fg. 7-5b). Although each nddual dole s electcally neutal, some net chage can exst on the nteface due to ncomlete cancellaton of the olazaton chage between adjacent doles. To mantan the electc neutalty, must be equal n magntude but ooste n sgn to the total suface olazaton chage s1 + s. Let ρ eesent the olazaton olume chage densty, ( P an ) ds = P ds = ( P) V ρ d. By eq s (7.6), (5.4), = d = V. The equement of ( + ) ( P) s1 s s1 + s = esults n: ρ = (C/m 3 ) (7.7) <Comment> 1) Eq. (7.6) can be egaded as a secal case of eq. (7.7) on the a-delectc nteface, whee the degence of the olazaton ecto P s nfnte. ) Equalent olazaton chage denstes ρ s, ρ can be used n collaboaton wth eq s (6.10), (6.15) to ealuate the electc feld and otental contbuted by olazed delectcs. Electc flux densty In the esence of delectc mateals, the total electc feld would be ceated by both the fee and olazaton chages. Fundamental ostulate eq. (6.1) s thus modfed as:

8 Electomagnetcs P7-8 ρ + ρ E =. By eq. (7.7), we hae: D = ρ, (7.8) D ε 0 ε E + P (C/m ), (7.9) = 0 whee the electc flux densty D chaactezes the contbuton fom the fee chages. The ntegal fom of eq. (7.8) (Gauss s law) becomes: D ds = (7.10) Fo lnea, homogeneous, and sotoc delectcs, the olazaton ecto s ootonal to the electc feld (by the elastc sng model): P = ε 0 χee, (7.11) whee the electc suscetblty χ e s a dmensonless quantty ndeendent of magntude (lnea), oston (homogeneous), and decton (sotoc) of E. By eq s (7.9), (7.11), D = εe, (7.1) whee the emttty of the medum ε s defned as: ( 1+ χe ) ε 0 ε = (7.13) <Comment> The stategy s usng a sngle constant ε to elace the tedous nduced doles, olazaton ecto, and equalent olazaton chages n detemnng the total electc feld. Examle 7-: Consde a aallel-late caacto. (1) D descbes the suface densty of fee chages on the conductng lates. () P descbes the suface densty of olazaton chages.

9 Electomagnetcs P7-9 (3) ε E 0 descbes the suface densty of total chage o uncomensated fee chage. Fg Physcal meanngs of electc flux densty D, olazaton ecto P, and electc feld ntensty E llustated n the examle of a aallel-late caacto (afte C. C. u). Examle 7-3: A ont chage + at the cente of a shecal delectc shell of emttty ε ε 0 (Fg. 7-7a), whee χe ε = 1 + s the elate emttty. Fnd D, E, V, P, and ρ s. Fg (a) The geomety of a delectc shee. The coesondng (b) adal comonents of D (sold), ε E (dashed), P (dash-dot), and (c) electc otental 0 V.

10 Electomagnetcs P7-10 Ans: (1) By shecal symmety, D a = D (). By eq. (7.10) and the fact that delectc mateals contbute to no fee chage: D ds = D ( ) ( 4π ) = D ( ) =, fo all > 0. 4 π () By shecal symmety, E a = E (). By eq. (7.1),, E ( ) =, whee 4 πε ε ε 0, fo < < ε = ε 0, othewse 0. (3) V () s deed by ntegaton of E (). (4) By eq. (7.9), P = D ε E = a P ( ), whee P ( ) = D ( ) ε 0E ( ), 0 1 ( 1 ε ) P ( ) = 4π 0, othewse, fo < < 0. (5) By eq (7.6), the suface olazaton chage densty becomes: ρ s a = 1 1 ( 1 ε ) ( a ) = ( 1 ε ) ( 1 1 ε ) π 4 4π o ( > 0), fo = o 4π ( < 0), fo = ; The total olazaton suface chage s: s = ρ = s 1 1 ( 1 ε ) ( 4π ) = ( 1 ε ) 4π 1 ( 1 ε ) ( > 0), fo = o ( < 0), fo = ; They ceate a adally nwad E to educe the total electc feld n the delectcs. 7.3 Geneal Bounday Condtons fo Electc Felds Deaton As n a-conducto nteface, we aly the ntegal foms of the two fundamental ostulates on the dffeental contou abcda and the thn ll box wth Δh 0 acoss the nteface of

11 Electomagnetcs P7-11 two delectc meda (Fg. 7-8) to dee the BCs fo the tangental and nomal comonents of the electc feld. Fg Dffeental contou and ll box used to dee geneal BCs (afte DKC). E dl = E Δw + E Δw, 1) Tangental BC: By eq. (6.4), ( ) ( ) 0 abcda E t Et ) Nomal BC: BC: By eq. (7.10), D ds = a 1 t t = 1 = (7.14), ( D a + D a )( Δ ) = ρ Δ 1 n ( D1 D ) = ρs n n1 s, (7.15) Eq. (7.15) can also be wtten as: D ρ 1 n D n = s, whee n D ( = 1, ) denotes comonent of medum 1). D n the decton of a n (unt nomal ecto dected fom medum to <Comment> 1) Eq s (7.3), (7.4) ae secal cases of eq s (7.14), (7.15), whee { E D } 0, = ae used. ) Only fee suface chage densty ρ s counts n eq. (7.15). If the two ntefacng meda ae both delectcs, ρ s = 0, D1 n = Dn. 3) Eq s (7.14), (7.15) eman ald een the felds ae tme-ayng (Lesson 14, o Ch 7 of the textbook). BCs exlan why most otcal comonents (wth mateal ntefaces) ae olazaton -deendent.

24-2: Electric Potential Energy. 24-1: What is physics

24-2: Electric Potential Energy. 24-1: What is physics D. Iyad SAADEDDIN Chapte 4: Electc Potental Electc potental Enegy and Electc potental Calculatng the E-potental fom E-feld fo dffeent chage dstbutons Calculatng the E-feld fom E-potental Potental of a

More information

CSJM University Class: B.Sc.-II Sub:Physics Paper-II Title: Electromagnetics Unit-1: Electrostatics Lecture: 1 to 4

CSJM University Class: B.Sc.-II Sub:Physics Paper-II Title: Electromagnetics Unit-1: Electrostatics Lecture: 1 to 4 CSJM Unvesty Class: B.Sc.-II Sub:Physcs Pape-II Ttle: Electomagnetcs Unt-: Electostatcs Lectue: to 4 Electostatcs: It deals the study of behavo of statc o statonay Chages. Electc Chage: It s popety by

More information

Physics 11b Lecture #2. Electric Field Electric Flux Gauss s Law

Physics 11b Lecture #2. Electric Field Electric Flux Gauss s Law Physcs 11b Lectue # Electc Feld Electc Flux Gauss s Law What We Dd Last Tme Electc chage = How object esponds to electc foce Comes n postve and negatve flavos Conseved Electc foce Coulomb s Law F Same

More information

iclicker Quiz a) True b) False Theoretical physics: the eternal quest for a missing minus sign and/or a factor of two. Which will be an issue today?

iclicker Quiz a) True b) False Theoretical physics: the eternal quest for a missing minus sign and/or a factor of two. Which will be an issue today? Clce Quz I egsteed my quz tansmtte va the couse webste (not on the clce.com webste. I ealze that untl I do so, my quz scoes wll not be ecoded. a Tue b False Theoetcal hyscs: the etenal quest fo a mssng

More information

ALL QUESTIONS ARE WORTH 20 POINTS. WORK OUT FIVE PROBLEMS.

ALL QUESTIONS ARE WORTH 20 POINTS. WORK OUT FIVE PROBLEMS. GNRAL PHYSICS PH -3A (D. S. Mov) Test (/3/) key STUDNT NAM: STUDNT d #: -------------------------------------------------------------------------------------------------------------------------------------------

More information

A. Thicknesses and Densities

A. Thicknesses and Densities 10 Lab0 The Eath s Shells A. Thcknesses and Denstes Any theoy of the nteo of the Eath must be consstent wth the fact that ts aggegate densty s 5.5 g/cm (ecall we calculated ths densty last tme). In othe

More information

Chapter 23: Electric Potential

Chapter 23: Electric Potential Chapte 23: Electc Potental Electc Potental Enegy It tuns out (won t show ths) that the tostatc foce, qq 1 2 F ˆ = k, s consevatve. 2 Recall, fo any consevatve foce, t s always possble to wte the wok done

More information

3.1 Electrostatic Potential Energy and Potential Difference

3.1 Electrostatic Potential Energy and Potential Difference 3. lectostatc Potental negy and Potental Dffeence RMMR fom mechancs: - The potental enegy can be defned fo a system only f consevatve foces act between ts consttuents. - Consevatve foces may depend only

More information

Test 1 phy What mass of a material with density ρ is required to make a hollow spherical shell having inner radius r i and outer radius r o?

Test 1 phy What mass of a material with density ρ is required to make a hollow spherical shell having inner radius r i and outer radius r o? Test 1 phy 0 1. a) What s the pupose of measuement? b) Wte all fou condtons, whch must be satsfed by a scala poduct. (Use dffeent symbols to dstngush opeatons on ectos fom opeatons on numbes.) c) What

More information

Physics 202, Lecture 2. Announcements

Physics 202, Lecture 2. Announcements Physcs 202, Lectue 2 Today s Topcs Announcements Electc Felds Moe on the Electc Foce (Coulomb s Law The Electc Feld Moton of Chaged Patcles n an Electc Feld Announcements Homewok Assgnment #1: WebAssgn

More information

PHYS Week 5. Reading Journals today from tables. WebAssign due Wed nite

PHYS Week 5. Reading Journals today from tables. WebAssign due Wed nite PHYS 015 -- Week 5 Readng Jounals today fom tables WebAssgn due Wed nte Fo exclusve use n PHYS 015. Not fo e-dstbuton. Some mateals Copyght Unvesty of Coloado, Cengage,, Peason J. Maps. Fundamental Tools

More information

Integral Vector Operations and Related Theorems Applications in Mechanics and E&M

Integral Vector Operations and Related Theorems Applications in Mechanics and E&M Dola Bagayoko (0) Integal Vecto Opeatons and elated Theoems Applcatons n Mechancs and E&M Ι Basc Defnton Please efe to you calculus evewed below. Ι, ΙΙ, andιιι notes and textbooks fo detals on the concepts

More information

Dynamics of Rigid Bodies

Dynamics of Rigid Bodies Dynamcs of Rgd Bodes A gd body s one n whch the dstances between consttuent patcles s constant thoughout the moton of the body,.e. t keeps ts shape. Thee ae two knds of gd body moton: 1. Tanslatonal Rectlnea

More information

THE MAGNETIC FIELD. This handout covers: The magnetic force between two moving charges. The magnetic field, B, and magnetic field lines

THE MAGNETIC FIELD. This handout covers: The magnetic force between two moving charges. The magnetic field, B, and magnetic field lines EM 005 Handout 7: The Magnetic ield 1 This handout coes: THE MAGNETIC IELD The magnetic foce between two moing chages The magnetic field,, and magnetic field lines Magnetic flux and Gauss s Law fo Motion

More information

TEST-03 TOPIC: MAGNETISM AND MAGNETIC EFFECT OF CURRENT Q.1 Find the magnetic field intensity due to a thin wire carrying current I in the Fig.

TEST-03 TOPIC: MAGNETISM AND MAGNETIC EFFECT OF CURRENT Q.1 Find the magnetic field intensity due to a thin wire carrying current I in the Fig. TEST-03 TPC: MAGNETSM AND MAGNETC EFFECT F CURRENT Q. Fnd the magnetc feld ntensty due to a thn we cayng cuent n the Fg. - R 0 ( + tan) R () 0 ( ) R 0 ( + ) R 0 ( + tan ) R Q. Electons emtted wth neglgble

More information

Remember: When an object falls due to gravity its potential energy decreases.

Remember: When an object falls due to gravity its potential energy decreases. Chapte 5: lectc Potental As mentoned seveal tmes dung the uate Newton s law o gavty and Coulomb s law ae dentcal n the mathematcal om. So, most thngs that ae tue o gavty ae also tue o electostatcs! Hee

More information

1. Starting with the local version of the first law of thermodynamics q. derive the statement of the first law of thermodynamics for a control volume

1. Starting with the local version of the first law of thermodynamics q. derive the statement of the first law of thermodynamics for a control volume EN10: Contnuum Mechancs Homewok 5: Alcaton of contnuum mechancs to fluds Due 1:00 noon Fda Febua 4th chool of Engneeng Bown Unvest 1. tatng wth the local veson of the fst law of themodnamcs q jdj q t and

More information

Scalars and Vectors Scalar

Scalars and Vectors Scalar Scalas and ectos Scala A phscal quantt that s completel chaacteed b a eal numbe (o b ts numecal value) s called a scala. In othe wods a scala possesses onl a magntude. Mass denst volume tempeatue tme eneg

More information

COMPLEMENTARY ENERGY METHOD FOR CURVED COMPOSITE BEAMS

COMPLEMENTARY ENERGY METHOD FOR CURVED COMPOSITE BEAMS ultscence - XXX. mcocd Intenatonal ultdscplnay Scentfc Confeence Unvesty of skolc Hungay - pl 06 ISBN 978-963-358-3- COPLEENTRY ENERGY ETHOD FOR CURVED COPOSITE BES Ákos József Lengyel István Ecsed ssstant

More information

V. Principles of Irreversible Thermodynamics. s = S - S 0 (7.3) s = = - g i, k. "Flux": = da i. "Force": = -Â g a ik k = X i. Â J i X i (7.

V. Principles of Irreversible Thermodynamics. s = S - S 0 (7.3) s = = - g i, k. Flux: = da i. Force: = -Â g a ik k = X i. Â J i X i (7. Themodynamcs and Knetcs of Solds 71 V. Pncples of Ievesble Themodynamcs 5. Onsage s Teatment s = S - S 0 = s( a 1, a 2,...) a n = A g - A n (7.6) Equlbum themodynamcs detemnes the paametes of an equlbum

More information

4.4 Continuum Thermomechanics

4.4 Continuum Thermomechanics 4.4 Contnuum Themomechancs The classcal themodynamcs s now extended to the themomechancs of a contnuum. The state aables ae allowed to ay thoughout a mateal and pocesses ae allowed to be eesble and moe

More information

Stellar Astrophysics. dt dr. GM r. The current model for treating convection in stellar interiors is called mixing length theory:

Stellar Astrophysics. dt dr. GM r. The current model for treating convection in stellar interiors is called mixing length theory: Stella Astophyscs Ovevew of last lectue: We connected the mean molecula weght to the mass factons X, Y and Z: 1 1 1 = X + Y + μ 1 4 n 1 (1 + 1) = X μ 1 1 A n Z (1 + ) + Y + 4 1+ z A Z We ntoduced the pessue

More information

2. Electrostatics. Dr. Rakhesh Singh Kshetrimayum 8/11/ Electromagnetic Field Theory by R. S. Kshetrimayum

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

More information

Rigid Bodies: Equivalent Systems of Forces

Rigid Bodies: Equivalent Systems of Forces Engneeng Statcs, ENGR 2301 Chapte 3 Rgd Bodes: Equvalent Sstems of oces Intoducton Teatment of a bod as a sngle patcle s not alwas possble. In geneal, the se of the bod and the specfc ponts of applcaton

More information

Today s Plan. Electric Dipoles. More on Gauss Law. Comment on PDF copies of Lectures. Final iclicker roll-call

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

More information

Chapter 13 - Universal Gravitation

Chapter 13 - Universal Gravitation Chapte 3 - Unesal Gataton In Chapte 5 we studed Newton s thee laws of moton. In addton to these laws, Newton fomulated the law of unesal gataton. Ths law states that two masses ae attacted by a foce gen

More information

Chapter Fifiteen. Surfaces Revisited

Chapter Fifiteen. Surfaces Revisited Chapte Ffteen ufaces Revsted 15.1 Vecto Descpton of ufaces We look now at the vey specal case of functons : D R 3, whee D R s a nce subset of the plane. We suppose s a nce functon. As the pont ( s, t)

More information

VEKTORANALYS FLUX INTEGRAL LINE INTEGRAL. and. Kursvecka 2. Kapitel 4 5. Sidor 29 50

VEKTORANALYS FLUX INTEGRAL LINE INTEGRAL. and. Kursvecka 2. Kapitel 4 5. Sidor 29 50 VEKTORANAYS Ksecka INE INTEGRA and UX INTEGRA Kaptel 4 5 Sdo 9 5 A wnd TARGET PROBEM We want to psh a mne cat along a path fom A to B. Bt the wnd s blowng. How mch enegy s needed? (.e. how mch s the wok?

More information

TUTORIAL 9. Static magnetic field

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

More information

ELECTROSTATICS::BHSEC MCQ 1. A. B. C. D.

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

More information

Objects usually are charged up through the transfer of electrons from one object to the other.

Objects 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 information

8 Baire Category Theorem and Uniform Boundedness

8 Baire Category Theorem and Uniform Boundedness 8 Bae Categoy Theoem and Unfom Boundedness Pncple 8.1 Bae s Categoy Theoem Valdty of many esults n analyss depends on the completeness popety. Ths popety addesses the nadequacy of the system of atonal

More information

Electric field generated by an electric dipole

Electric 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 information

Chapter 12 Equilibrium and Elasticity

Chapter 12 Equilibrium and Elasticity Chapte 12 Equlbum and Elastcty In ths chapte we wll defne equlbum and fnd the condtons needed so that an object s at equlbum. We wll then apply these condtons to a vaety of pactcal engneeng poblems of

More information

Set of square-integrable function 2 L : function space F

Set of square-integrable function 2 L : function space F Set of squae-ntegable functon L : functon space F Motvaton: In ou pevous dscussons we have seen that fo fee patcles wave equatons (Helmholt o Schödnge) can be expessed n tems of egenvalue equatons. H E,

More information

Review for Midterm-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

More information

Electrostatics (Electric Charges and Field) #2 2010

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

More information

Gauss Law. Physics 231 Lecture 2-1

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 information

EM-2. 1 Coulomb s law, electric field, potential field, superposition q. Electric field of a point charge (1)

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

More information

Physics Exam 3

Physics Exam 3 Physcs 114 1 Exam 3 The numbe of ponts fo each secton s noted n backets, []. Choose a total of 35 ponts that wll be gaded that s you may dop (not answe) a total of 5 ponts. Clealy mak on the cove of you

More information

UNIVERSITÀ DI PISA. Math thbackground

UNIVERSITÀ DI PISA. Math thbackground UNIVERSITÀ DI ISA Electomagnetc Radatons and Bologcal l Inteactons Lauea Magstale n Bomedcal Engneeng Fst semeste (6 cedts), academc ea 2011/12 of. aolo Nepa p.nepa@et.unp.t Math thbackgound Edted b D.

More information

Objectives: After finishing this unit you should be able to:

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

More information

Hopefully Helpful Hints for Gauss s Law

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

More information

(Sample 3) Exam 1 - Physics Patel SPRING 1998 FORM CODE - A (solution key at end of exam)

(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 information

Engineering Mechanics. Force resultants, Torques, Scalar Products, Equivalent Force systems

Engineering Mechanics. Force resultants, Torques, Scalar Products, Equivalent Force systems Engneeng echancs oce esultants, Toques, Scala oducts, Equvalent oce sstems Tata cgaw-hll Companes, 008 Resultant of Two oces foce: acton of one bod on anothe; chaacteed b ts pont of applcaton, magntude,

More information

PHYS 1444 Lecture #5

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

More information

CMSC 425: Lecture 5 More on Geometry and Geometric Programming

CMSC 425: Lecture 5 More on Geometry and Geometric Programming CMSC 425: Lectue 5 Moe on Geomety and Geometic Pogamming Moe Geometic Pogamming: In this lectue we continue the discussion of basic geometic ogamming fom the eious lectue. We will discuss coodinate systems

More information

Q. Obtain the Hamiltonian for a one electron atom in the presence of an external magnetic field.

Q. Obtain the Hamiltonian for a one electron atom in the presence of an external magnetic field. Syed Ashad Hussain Lectue Deatment of Physics Tiua Univesity www.sahussaintu.wodess.com Q. Obtain the Hamiltonian fo a one electon atom in the esence of an extenal magnetic field. To have an idea about

More information

Physics Exam II Chapters 25-29

Physics Exam II Chapters 25-29 Physcs 114 1 Exam II Chaptes 5-9 Answe 8 of the followng 9 questons o poblems. Each one s weghted equally. Clealy mak on you blue book whch numbe you do not want gaded. If you ae not sue whch one you do

More information

Chapter I Matrices, Vectors, & Vector Calculus 1-1, 1-9, 1-10, 1-11, 1-17, 1-18, 1-25, 1-27, 1-36, 1-37, 1-41.

Chapter I Matrices, Vectors, & Vector Calculus 1-1, 1-9, 1-10, 1-11, 1-17, 1-18, 1-25, 1-27, 1-36, 1-37, 1-41. Chapte I Matces, Vectos, & Vecto Calculus -, -9, -0, -, -7, -8, -5, -7, -36, -37, -4. . Concept of a Scala Consde the aa of patcles shown n the fgue. he mass of the patcle at (,) can be epessed as. M (,

More information

Rotational Kinematics. Rigid Object about a Fixed Axis Western HS AP Physics 1

Rotational Kinematics. Rigid Object about a Fixed Axis Western HS AP Physics 1 Rotatonal Knematcs Rgd Object about a Fxed Axs Westen HS AP Physcs 1 Leanng Objectes What we know Unfom Ccula Moton q s Centpetal Acceleaton : Centpetal Foce: Non-unfom a F c c m F F F t m ma t What we

More information

Review of Vector Algebra and Vector Calculus Operations

Review of Vector Algebra and Vector Calculus Operations Revew of Vecto Algeba and Vecto Calculus Opeatons Tpes of vaables n Flud Mechancs Repesentaton of vectos Dffeent coodnate sstems Base vecto elatons Scala and vecto poducts Stess Newton s law of vscost

More information

2 E. on each of these two surfaces. r r r r. Q E E ε. 2 2 Qencl encl right left 0

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

More information

Chapter 22 The Electric Field II: Continuous Charge Distributions

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

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

$ 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 information

Magnetostatics. Magnetic Forces. = qu. Biot-Savart Law H = Gauss s Law for Magnetism. Ampere s Law. Magnetic Properties of Materials. Inductance M.

Magnetostatics. Magnetic Forces. = qu. Biot-Savart Law H = Gauss s Law for Magnetism. Ampere s Law. Magnetic Properties of Materials. Inductance M. Magnetic Foces Biot-Savat Law Gauss s Law fo Magnetism Ampee s Law Magnetic Popeties of Mateials nductance F m qu d B d R 4 R B B µ 0 J Magnetostatics M. Magnetic Foces The electic field E at a point in

More information

Physical & Interfacial Electrochemistry 2013

Physical & Interfacial Electrochemistry 2013 Physcal & Intefacal Electochemsty 013 Lectue 3. Ion-on nteactons n electolyte solutons. Module JS CH3304 MoleculaThemodynamcs and Knetcs Ion-Ion Inteactons The themodynamc popetes of electolyte solutons

More information

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!

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,

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.

? 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 information

( ) Make-up Tests. From Last Time. Electric Field Flux. o The Electric Field Flux through a bit of area is

( ) 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 information

PHYS 2421 Fields and Waves

PHYS 2421 Fields and Waves PHYS 242 Felds nd Wves Instucto: Joge A. López Offce: PSCI 29 A, Phone: 747-7528 Textook: Unvesty Physcs e, Young nd Feedmn 23. Electc potentl enegy 23.2 Electc potentl 23.3 Clcultng electc potentl 23.4

More information

Quadrupole terms in the Maxwell equations: Born energy, partial molar volume and entropy of ions. Debye-Hückel theory in a quadrupolarizable medium

Quadrupole terms in the Maxwell equations: Born energy, partial molar volume and entropy of ions. Debye-Hückel theory in a quadrupolarizable medium 5 uaduole tems n the Maxwell equatons: Bon enegy, atal mola volume and entoy of ons. ebye-hückel theoy n a quaduolazable medum Radom I. Slavchov,* a Tzanko I. Ivanov b a eatment of Physcal Chemsty, Faculty

More information

EE 5337 Computational Electromagnetics (CEM)

EE 5337 Computational Electromagnetics (CEM) 7//28 Instucto D. Raymond Rumpf (95) 747 6958 cumpf@utep.edu EE 5337 Computatonal Electomagnetcs (CEM) Lectue #6 TMM Extas Lectue 6These notes may contan copyghted mateal obtaned unde fa use ules. Dstbuton

More information

Physics 1501 Lecture 19

Physics 1501 Lecture 19 Physcs 1501 ectue 19 Physcs 1501: ectue 19 Today s Agenda Announceents HW#7: due Oct. 1 Mdte 1: aveage 45 % Topcs otatonal Kneatcs otatonal Enegy Moents of Ineta Physcs 1501: ectue 19, Pg 1 Suay (wth copason

More information

PHYS 1444 Section 501 Lecture #7

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

More information

17.1 Electric Potential Energy. Equipotential Lines. PE = energy associated with an arrangement of objects that exert forces on each other

17.1 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 information

Unit 7: Sources of magnetic field

Unit 7: Sources of magnetic field Unit 7: Souces of magnetic field Oested s expeiment. iot and Savat s law. Magnetic field ceated by a cicula loop Ampèe s law (A.L.). Applications of A.L. Magnetic field ceated by a: Staight cuent-caying

More information

Electric Field. y s +q. Point charge: Uniformly charged sphere: Dipole: for r>>s :! ! E = 1. q 1 r 2 ˆr. E sphere. at <0,r,0> at <0,0,r>

Electric Field. y s +q. Point charge: Uniformly charged sphere: Dipole: for r>>s :! ! E = 1. q 1 r 2 ˆr. E sphere. at <0,r,0> at <0,0,r> Electic Field Point chage: E " ˆ Unifomly chaged sphee: E sphee E sphee " Q ˆ fo >R (outside) fo >s : E " s 3,, at z y s + x Dipole moment: p s E E s "#,, 3 s "#,, 3 at

More information

Faraday s Law. Faraday s Law. Faraday s Experiments. Faraday s Experiments. Magnetic Flux. Chapter 31. Law of Induction (emf( emf) Faraday s Law

Faraday s Law. Faraday s Law. Faraday s Experiments. Faraday s Experiments. Magnetic Flux. Chapter 31. Law of Induction (emf( emf) Faraday s Law Faaday s Law Faaday s Epeiments Chapte 3 Law of nduction (emf( emf) Faaday s Law Magnetic Flu Lenz s Law Geneatos nduced Electic fields Michael Faaday discoeed induction in 83 Moing the magnet induces

More information

Chapter 21: Gauss s Law

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

More information

1. A body will remain in a state of rest, or of uniform motion in a straight line unless it

1. A body will remain in a state of rest, or of uniform motion in a straight line unless it Pncples of Dnamcs: Newton's Laws of moton. : Foce Analss 1. A bod wll eman n a state of est, o of unfom moton n a staght lne unless t s acted b etenal foces to change ts state.. The ate of change of momentum

More information

Basic Electrohydrodynamics (Electrostatics) of the Floating Water Bridge

Basic Electrohydrodynamics (Electrostatics) of the Floating Water Bridge Basc lectohyoynamcs lectostatcs) o the loatng Wate Bge Wate has a emanent electc ole moment ue to ts molecula conguaton To scuss a ole, let us assume two ont chages, one wth chage +q an one wth chage q,

More information

Review. Electrostatic. Dr. Ray Kwok SJSU

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

More information

Module 18: Outline. Magnetic Dipoles Magnetic Torques

Module 18: Outline. Magnetic Dipoles Magnetic Torques Module 18: Magnetic Dipoles 1 Module 18: Outline Magnetic Dipoles Magnetic Toques 2 IA nˆ I A Magnetic Dipole Moment μ 3 Toque on a Cuent Loop in a Unifom Magnetic Field 4 Poblem: Cuent Loop Place ectangula

More information

8.022 (E&M) - Lecture 2

8.022 (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 information

F = net force on the system (newton) F,F and F. = different forces working. E = Electric field strength (volt / meter)

F = 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 information

Physics 207 Lecture 16

Physics 207 Lecture 16 Physcs 07 Lectue 6 Goals: Lectue 6 Chapte Extend the patcle odel to gd-bodes Undestand the equlbu of an extended object. Analyze ollng oton Undestand otaton about a fxed axs. Eploy consevaton of angula

More information

Evaluation of Various Types of Wall Boundary Conditions for the Boltzmann Equation

Evaluation of Various Types of Wall Boundary Conditions for the Boltzmann Equation Ealuaton o Vaous Types o Wall Bounday Condtons o the Boltzmann Equaton Chstophe D. Wlson a, Ramesh K. Agawal a, and Felx G. Tcheemssne b a Depatment o Mechancal Engneeng and Mateals Scence Washngton Unesty

More information

! E da = 4πkQ enc, has E under the integral sign, so it is not ordinarily an

! 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 information

Concept of Game Equilibrium. Game theory. Normal- Form Representation. Game definition. Lecture Notes II-1 Static Games of Complete Information

Concept of Game Equilibrium. Game theory. Normal- Form Representation. Game definition. Lecture Notes II-1 Static Games of Complete Information Game theoy he study of multeson decsons Fou tyes of games Statc games of comlete nfomaton ynamc games of comlete nfomaton Statc games of ncomlete nfomaton ynamc games of ncomlete nfomaton Statc v. dynamc

More information

CHAPTER 25 ELECTRIC POTENTIAL

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

More information

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 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 information

Multipole Radiation. March 17, 2014

Multipole Radiation. March 17, 2014 Multpole Radaton Mach 7, 04 Zones We wll see that the poblem of hamonc adaton dvdes nto thee appoxmate egons, dependng on the elatve magntudes of the dstance of the obsevaton pont,, and the wavelength,

More information

Unit 6 Practice Test. Which vector diagram correctly shows the change in velocity Δv of the mass during this time? (1) (1) A. Energy KE.

Unit 6 Practice Test. Which vector diagram correctly shows the change in velocity Δv of the mass during this time? (1) (1) A. Energy KE. Unit 6 actice Test 1. Which one of the following gaphs best epesents the aiation of the kinetic enegy, KE, and of the gaitational potential enegy, GE, of an obiting satellite with its distance fom the

More information

ECE 3318 Applied Electricity and Magnetism. Spring Prof. David R. Jackson Dept. Of ECE. Notes 20 Dielectrics

ECE 3318 Applied Electricity and Magnetism. Spring Prof. David R. Jackson Dept. Of ECE. Notes 20 Dielectrics ECE 3318 Applied Electicity and Magnetism Sping 218 Pof. David R. Jackson Dept. Of ECE Notes 2 Dielectics 1 Dielectics Single H 2 O molecule: H H Wate ε= εε O 2 Dielectics (cont.) H H Wate ε= εε O Vecto

More information

Φ E = E A E A = p212c22: 1

Φ 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 information

Phys-272 Lecture 17. Motional Electromotive Force (emf) Induced Electric Fields Displacement Currents Maxwell s Equations

Phys-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 information

Force and Work: Reminder

Force and Work: Reminder Electic Potential Foce and Wok: Reminde Displacement d a: initial point b: final point Reminde fom Mechanics: Foce F if thee is a foce acting on an object (e.g. electic foce), this foce may do some wok

More information

Some Approximate Analytical Steady-State Solutions for Cylindrical Fin

Some Approximate Analytical Steady-State Solutions for Cylindrical Fin Some Appoxmate Analytcal Steady-State Solutons fo Cylndcal Fn ANITA BRUVERE ANDRIS BUIIS Insttute of Mathematcs and Compute Scence Unvesty of Latva Rana ulv 9 Rga LV459 LATVIA Astact: - In ths pape we

More information

Contact, information, consultations

Contact, information, consultations ontact, nfomaton, consultatons hemsty A Bldg; oom 07 phone: 058-347-769 cellula: 664 66 97 E-mal: wojtek_c@pg.gda.pl Offce hous: Fday, 9-0 a.m. A quote of the week (o camel of the week): hee s no expedence

More information

Chapter 23: GAUSS LAW 343

Chapter 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

Groupoid and Topological Quotient Group

Groupoid and Topological Quotient Group lobal Jounal of Pue and Appled Mathematcs SSN 0973-768 Volume 3 Numbe 7 07 pp 373-39 Reseach nda Publcatons http://wwwpublcatoncom oupod and Topolocal Quotent oup Mohammad Qasm Manna Depatment of Mathematcs

More information

From last times. MTE1 results. Quiz 1. GAUSS LAW for any closed surface. What is the Electric Flux? How to calculate Electric Flux?

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

More information

9/12/2013. Microelectronics Circuit Analysis and Design. Modes of Operation. Cross Section of Integrated Circuit npn Transistor

9/12/2013. Microelectronics Circuit Analysis and Design. Modes of Operation. Cross Section of Integrated Circuit npn Transistor Mcoelectoncs Ccut Analyss and Desgn Donald A. Neamen Chapte 5 The pola Juncton Tanssto In ths chapte, we wll: Dscuss the physcal stuctue and opeaton of the bpola juncton tanssto. Undestand the dc analyss

More information

19 The Born-Oppenheimer Approximation

19 The Born-Oppenheimer Approximation 9 The Bon-Oppenheme Appoxmaton The full nonelatvstc Hamltonan fo a molecule s gven by (n a.u.) Ĥ = A M A A A, Z A + A + >j j (883) Lets ewte the Hamltonan to emphasze the goal as Ĥ = + A A A, >j j M A

More information

Complex atoms and the Periodic System of the elements

Complex atoms and the Periodic System of the elements Complex atoms and the Peodc System of the elements Non-cental foces due to electon epulson Cental feld appoxmaton electonc obtals lft degeneacy of l E n l = R( hc) ( n δ ) l Aufbau pncple Lectue Notes

More information

p = q s Previously.Electric Fields Point charge: Lecture 3 Uniformly charged sphere: Chapter 14. Matter & Electric Fields Dipole: for r>>s : 1 E = y

p = q s Previously.Electric Fields Point charge: Lecture 3 Uniformly charged sphere: Chapter 14. Matter & Electric Fields Dipole: for r>>s : 1 E = y Peviously.lectic ields Point chage: Diole: fo >>s : y z s + Diole moment: x s Unifomly chaged shee: Q shee fo >R (outside) fo

More information

anubhavclasses.wordpress.com CBSE Solved Test Papers PHYSICS Class XII Chapter : Electrostatics

anubhavclasses.wordpress.com CBSE Solved Test Papers PHYSICS Class XII Chapter : Electrostatics CBS Solved Test Papes PHYSICS Class XII Chapte : lectostatics CBS TST PAPR-01 CLASS - XII PHYSICS (Unit lectostatics) 1. Show does the foce between two point chages change if the dielectic constant of

More information

Chapter IV Vector and Tensor Analysis IV.2 Vector and Tensor Analysis September 23,

Chapter IV Vector and Tensor Analysis IV.2 Vector and Tensor Analysis September 23, hapte I ecto and Tenso Analyss I. ecto and Tenso Analyss eptembe, 07 47 hapte I ecto and Tenso Analyss I. ecto and Tenso Analyss eptembe, 07 48 I. ETOR AND TENOR ANALYI I... Tenso functon th Let A n n

More information

Physics 11 Chapter 20: Electric Fields and Forces

Physics 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 information