PHY132 Lecture 6 02/05/2010. Lecture 6 1

Size: px
Start display at page:

Download "PHY132 Lecture 6 02/05/2010. Lecture 6 1"

Transcription

1 Claical Phyic II PHY3 Lectue 6 The lectic Potential ti - II /5/ Lectue 6

2 Wok by a Vaying Foce Wok i a cala quantity, an we can thu a little piece of wok togethe, i.e. um a eie of ot-pouct of the foce F( i) with mall pat i of the total tajectoy F j F i θ j θ i θ k /5/ Thu, the geneal efinition of Wok: W lim F F( ) ie i.e. fo F() contant: n i i = n i = ( ) W= F () = F = F = F Δ = FΔcoθ Lectue 6 F k F,

3 /5/ (lectic) Potential negy an Potential When the lectic foce oe net wok W F l (eithe poitive o negative) on a chage, the eult i a change in it kinetic enegy: F net = ma W net F net l =ΔK =Δ(½mv ) The electic foce i a conevative foce, o we may aociate an LCTRIC POTNTIAL NRGY with the foce (a fo ANY conevative foce!): W = ΔU: ΔU = U f U i = W,i f i f F l A we i fo the electic fiel, we can now make the enegy INDPNDNT of the value of the chage by efining a POTNTIAL V() a the Potential-negy-pe- unit--chage: f f ΔU i f Δ V V( ) ( ) i = f f V i = = q q F i i Lectue 6 3

4 If the electic fiel i zeo eveywhee, the potential A. i zeo eveywhee B. i contant an the ame eveywhee C. vaie a you go along /5/ Lectue 6 4

5 Potential negy fo a Point Chage Conie a point chage : the Wok on chage q, by electic foce F moving q fom to i then: q q θ /5/ q coθ W = = ( ) = = F 4 U() q q = U U U = Δ = U ( ) = q q (, ) πε ( ) q ( ) V = fo Point Chage; o outie a Spheically Symmetic chage Note, with thi choice: U (= ) =, V (= ) = U q an again: F = = V = = Lectue 6 5

6 The Potential of a Point Chage The POTNTIAL i the Potential ti negy ivie i by q the chage : V ( ) U ( ) fo a point chage, o fo a = = q pheically ymmetic chage Fo ANY geneal lectic Fiel: ΔV a b = V b V a = a b eg e.g. fo contant: = (σ/ε )i: ΔV = = (σ/ε ) ( b a ) Conequence & Note: Potential V i a SCALAR (NON-vecto) quantity! The zeo-point of V i abitay: what ht count i the DIFFRNC ΔV! Check the ign of ΔV uing common ene! The fiel i minu the GRADINT of V: = V/, y = V/y, z = V/z INSID a conucto the POTNTIAL IS CONSTANT (becaue =!) Unit fo potential: VOLTS = V = J/C = Nm/C /5/ Lectue 6 6

7 Fo a unifom fiel = i,, the potential A. i contant too B. inceae with C. eceae with /5/ Lectue 6 7

8 Paallel Plate Two lage paallel l plate with unifom chage enitie +σ an σ, epaate by itance. i plate : σ σ Fiel ( ) = n = (in between the plane; zeo outie!) ε ε Potential Diff.: ΔV ( ) = V () V ( ) = W ( ) q = W( ) q /5/ V=σ/ε +σ σ O V() () Note: the potential V gow going upteam to the fiel σ/ε = F q = σ σ σ = q q = = ε ε ε V= [ ] σ V () = ε ( ) plane of chage + choice: V ( = ) = ( ) choice: ( ) = Δ V = V( = ) V( = ) = σ σ Note: = V = ( ) =+ ε ε σ an between the plate Lectue 6 8 σ

9 Two Coaial Cyline Single cyline aiu R, chage enity λ: λ ( ) = (pointing out!) Aume > >R; πε thu we epect ΔV> λ ΔV( ) = V( ) V( ) = W( ) q = W( ) q λ λ λ = = = = ln > > πε πε πε λ R λ R λ R = ln ln V () = ln πε πε πε Two long coaial conucting cyline, aii a an b>a, with linea chage enitie +λ (inne) an λ (oute cyline) : + λ+ ( λ) long unifom cyline; > R b: ( ) = =, ( V( ) = contant) πε b +λ = bin bin λ λ λ a < b : in ( ), = = = πε V () ln πε πε πε b : ( ), ( ) ln in λ b in < a = V = Note: V ln πε a πε /5/ () ( if ) thu V( )! an V(=R)= λ () λ b in +λ between Lectue 6 the cyl' 9 b in = = =+ πε a λ

10 Chage Sphee Single conucting phee aiu R an chage : ( ) = ( fo R, ele = ; ( = ) =! aume: > ) ΔV( ) = V ( ) V ( ) = W( ) q = W( ) q move //, q i.e. out- = k q = k = k k = wa! V ( R) = k ; V ( < R) = k R V ( ) = k Two concentic conucting phee with ih R, an R >R, : + k( + ) k( + ) R : ( ) = k : V( ) = V( R ) = R V() k R < R : () = : Δ V() = V() V( R ) = k < R R < R : ( ) =, Δ V ( ) = V ( ) = V ( R ) /5/ < R Note: = V = V( ) V( R ) = k =+ R between contant R Lectue 6 R the ph'

11 The value of the potential at a cetain point A. eally oen t matte; it i the potential iffeence between two poition that oe matte B., if the point i at infinity, i alway zeo C. oe matte, an i a funamental quantity /5/ Lectue 6

Honors Classical Physics I

Honors Classical Physics I Hono Claical Phyic I PHY141 Lectue 9 Newton Law of Gavity Pleae et you Clicke Channel to 1 9/15/014 Lectue 9 1 Newton Law of Gavity Gavitational attaction i the foce that act between object that have a

More information

4. Compare the electric force holding the electron in orbit ( r = 0.53

4. Compare the electric force holding the electron in orbit ( r = 0.53 Electostatics WS Electic Foce an Fiel. Calculate the magnitue of the foce between two 3.60-µ C point chages 9.3 cm apat.. How many electons make up a chage of 30.0 µ C? 3. Two chage ust paticles exet a

More information

Lecture 6: Electrostatic Potential

Lecture 6: Electrostatic Potential Lectue 6: Electostatic Potential Last lectue eview: Electostatic potential enegy U = F el l efeence point Fo two chages Q an q: U = qe Q l = qq 1 4πε 0 U U ++ o -- +- o -+ The electostatic potential enegy

More information

Electric Potential. Outline. Potential Energy per Unit Charge. Potential Difference. Potential Energy Difference. Quiz Thursday on Chapters 23, 24.

Electric Potential. Outline. Potential Energy per Unit Charge. Potential Difference. Potential Energy Difference. Quiz Thursday on Chapters 23, 24. lectic otential Quiz Thusay on Chaptes 3, 4. Outline otential as enegy pe unit chage. Thi fom of Coulomb s Law. elations between fiel an potential. otential negy pe Unit Chage Just as the fiel is efine

More information

Electric Potential and Gauss s Law, Configuration Energy Challenge Problem Solutions

Electric Potential and Gauss s Law, Configuration Energy Challenge Problem Solutions Poblem 1: Electic Potential an Gauss s Law, Configuation Enegy Challenge Poblem Solutions Consie a vey long o, aius an chage to a unifom linea chage ensity λ a) Calculate the electic fiel eveywhee outsie

More information

Static Electric Fields. Coulomb s Law Ε = 4πε. Gauss s Law. Electric Potential. Electrical Properties of Materials. Dielectrics. Capacitance E.

Static Electric Fields. Coulomb s Law Ε = 4πε. Gauss s Law. Electric Potential. Electrical Properties of Materials. Dielectrics. Capacitance E. Coulomb Law Ε Gau Law Electic Potential E Electical Popetie of Mateial Conducto J σe ielectic Capacitance Rˆ V q 4πε R ρ v 2 Static Electic Field εe E.1 Intoduction Example: Electic field due to a chage

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

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

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

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

Module 05: Gauss s s Law a

Module 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 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

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

SPH4UI 28/02/2011. Total energy = K + U is constant! Electric Potential Mr. Burns. GMm

SPH4UI 28/02/2011. Total energy = K + U is constant! Electric Potential Mr. Burns. GMm 8//11 Electicity has Enegy SPH4I Electic Potential M. Buns To sepaate negative an positive chages fom each othe, wok must be one against the foce of attaction. Theefoe sepeate chages ae in a higheenegy

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

Welcome to Physics 272

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)

More information

Homework Set 4 Physics 319 Classical Mechanics. m m k. x, x, x, x T U x x x x l 2. x x x x. x x x x

Homework Set 4 Physics 319 Classical Mechanics. m m k. x, x, x, x T U x x x x l 2. x x x x. x x x x Poble 78 a) The agangian i Hoewok Set 4 Phyic 319 Claical Mechanic k b) In te of the cente of a cooinate an x x1 x x1 x xc x x x x x1 xc x xc x x x x x1 xc x xc x, x, x, x T U x x x x l 1 1 1 1 1 1 1 1

More information

Algebra-based Physics II

Algebra-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 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

The Law of Biot-Savart & RHR P θ

The Law of Biot-Savart & RHR P θ The Law of iot-savat & RHR P R dx x Jean-aptiste iot élix Savat Phys 122 Lectue 19 G. Rybka Recall: Potential Enegy of Dipole Wok equied to otate a cuentcaying loop in a magnetic field Potential enegy

More information

( )( )( ) ( ) + ( ) ( ) ( )

( )( )( ) ( ) + ( ) ( ) ( ) 3.7. Moel: The magnetic fiel is that of a moving chage paticle. Please efe to Figue Ex3.7. Solve: Using the iot-savat law, 7 19 7 ( ) + ( ) qvsinθ 1 T m/a 1.6 1 C. 1 m/s sin135 1. 1 m 1. 1 m 15 = = = 1.13

More information

An o5en- confusing point:

An o5en- confusing point: An o5en- confusing point: Recall this example fom last lectue: E due to a unifom spheical suface chage, density = σ. Let s calculate the pessue on the suface. Due to the epulsive foces, thee is an outwad

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

Chapter 19 Webassign Help Problems

Chapter 19 Webassign Help Problems Chapte 9 Webaign Help Poblem 4 5 6 7 8 9 0 Poblem 4: The pictue fo thi poblem i a bit mileading. They eally jut give you the pictue fo Pat b. So let fix that. Hee i the pictue fo Pat (a): Pat (a) imply

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.

(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 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

( ) 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

That is, the acceleration of the electron is larger than the acceleration of the proton by the same factor the electron is lighter than the proton.

That is, the acceleration of the electron is larger than the acceleration of the proton by the same factor the electron is lighter than the proton. PHY 8 Test Pactice Solutions Sping Q: [] A poton an an electon attact each othe electically so, when elease fom est, they will acceleate towa each othe. Which paticle will have a lage acceleation? (Neglect

More information

Chapter 25 Electric Potential

Chapter 25 Electric Potential Chpte 5 lectic Potentil consevtive foces -> potentil enegy - Wht is consevtive foce? lectic potentil = U / : the potentil enegy U pe unit chge is function of the position in spce Gol:. estblish the eltionship

More information

Gauss s Law Simulation Activities

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

More information

[Griffiths Ch.1-3] 2008/11/18, 10:10am 12:00am, 1. (6%, 7%, 7%) Suppose the potential at the surface of a hollow hemisphere is specified, as shown

[Griffiths Ch.1-3] 2008/11/18, 10:10am 12:00am, 1. (6%, 7%, 7%) Suppose the potential at the surface of a hollow hemisphere is specified, as shown [Giffiths Ch.-] 8//8, :am :am, Useful fomulas V ˆ ˆ V V V = + θ+ φ ˆ and v = ( v ) + (sin θvθ ) + v θ sinθ φ sinθ θ sinθ φ φ. (6%, 7%, 7%) Suppose the potential at the suface of a hollow hemisphee is specified,

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

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

Electrostatics. 3) positive object: lack of electrons negative object: excess of electrons

Electrostatics. 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 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

DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS

DEVIL 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 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

Physics 2212 GH Quiz #2 Solutions Spring 2016

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

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

Voltage ( = Electric Potential )

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

More information

Your Comments. Conductors and Insulators with Gauss's law please...so basically everything!

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

More information

Look 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

Look 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 information

Electric Potential. and Equipotentials

Electric Potential. and Equipotentials Electic Potentil nd Euipotentils U Electicl Potentil Review: W wok done y foce in going fom to long pth. l d E dl F W dl F θ Δ l d E W U U U Δ Δ l d E W U U U U potentil enegy electic potentil Potentil

More information

DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS

DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS LSN 10-: MOTION IN A GRAVITATIONAL FIELD Questions Fom Reading Activity? Gavity Waves? Essential Idea: Simila appoaches can be taken in analyzing electical

More information

Physics 122, Fall December 2012

Physics 122, Fall December 2012 Physics 1, Fall 01 6 Decembe 01 Toay in Physics 1: Examples in eview By class vote: Poblem -40: offcente chage cylines Poblem 8-39: B along axis of spinning, chage isk Poblem 30-74: selfinuctance of a

More information

Electromagnetism Physics 15b

Electromagnetism Physics 15b lectomagnetism Physics 15b Lectue #20 Dielectics lectic Dipoles Pucell 10.1 10.6 What We Did Last Time Plane wave solutions of Maxwell s equations = 0 sin(k ωt) B = B 0 sin(k ωt) ω = kc, 0 = B, 0 ˆk =

More information

Electric Field, Potential Energy, & Voltage

Electric Field, Potential Energy, & Voltage Slide 1 / 66 lectic Field, Potential negy, & oltage Wok Slide 2 / 66 Q+ Q+ The foce changes as chages move towads each othe since the foce depends on the distance between the chages. s these two chages

More information

PHYS 2135 Exam I February 13, 2018

PHYS 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 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

Solutions. V in = ρ 0. r 2 + a r 2 + b, where a and b are constants. The potential at the center of the atom has to be finite, so a = 0. r 2 + b.

Solutions. V in = ρ 0. r 2 + a r 2 + b, where a and b are constants. The potential at the center of the atom has to be finite, so a = 0. r 2 + b. Solutions. Plum Pudding Model (a) Find the coesponding electostatic potential inside and outside the atom. Fo R The solution can be found by integating twice, 2 V in = ρ 0 ε 0. V in = ρ 0 6ε 0 2 + a 2

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

GRAVITATION. Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., New Delhi -18 PG 1

GRAVITATION. Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., New Delhi -18 PG 1 Einstein Classes, Unit No. 0, 0, Vahman Ring Roa Plaza, Vikas Pui Extn., New Delhi -8 Ph. : 96905, 857, E-mail einsteinclasses00@gmail.com, PG GRAVITATION Einstein Classes, Unit No. 0, 0, Vahman Ring Roa

More information

Review: Electrostatics and Magnetostatics

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

More information

Flux. Area Vector. Flux of Electric Field. Gauss s Law

Flux. 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 information

Page 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 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

(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

FI 2201 Electromagnetism

FI 2201 Electromagnetism FI Electomagnetim Aleande A. Ikanda, Ph.D. Phyic of Magnetim and Photonic Reeach Goup ecto Analyi CURILINEAR COORDINAES, DIRAC DELA FUNCION AND HEORY OF ECOR FIELDS Cuvilinea Coodinate Sytem Cateian coodinate:

More information

Faraday s Law (continued)

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

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

PHY 213. General Physics II Test 2.

PHY 213. General Physics II Test 2. Univesity of Kentucky Depatment of Physics an Astonomy PHY 3. Geneal Physics Test. Date: July, 6 Time: 9:-: Answe all questions. Name: Signatue: Section: Do not flip this page until you ae tol to o so.

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

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

3.8.1 Electric Potential Due to a System of Two Charges. Figure Electric dipole

3.8.1 Electric Potential Due to a System of Two Charges. Figure Electric dipole 3.8 Solved Poblems 3.8.1 Electic Potential Due to a System o Two Chages Conside a system o two chages shown in Figue 3.8.1. Figue 3.8.1 Electic dipole Find the electic potential at an abitay point on the

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

Electromagnetic Theory 1

Electromagnetic 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 information

18.1 Origin of Electricity 18.2 Charged Objects and Electric Force

18.1 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 information

Exam 1. Exam 1 is on Tuesday, February 14, from 5:00-6:00 PM.

Exam 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 information

JURONG JUNIOR COLLEGE Physics Department Tutorial: Electric Fields (solutions)

JURONG JUNIOR COLLEGE Physics Department Tutorial: Electric Fields (solutions) JJ 5 H Physics (646) Electic Fields_tutsoln JURONG JUNIOR COLLEGE Physics Depatment Tutoial: Electic Fields (solutions) No Solution LO Electic field stength at a point in an electic field is defined as

More information

Lecture 8 - Gauss s Law

Lecture 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 information

Today in Physics 122: getting V from E

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

More information

PH126 Exam I Solutions

PH126 Exam I Solutions PH6 Exam I Solutions q Q Q q. Fou positively chage boies, two with chage Q an two with chage q, ae connecte by fou unstetchable stings of equal length. In the absence of extenal foces they assume the equilibium

More information

Physics 107 HOMEWORK ASSIGNMENT #15

Physics 107 HOMEWORK ASSIGNMENT #15 Physics 7 HOMEWORK SSIGNMENT #5 Cutnell & Johnson, 7 th eition Chapte 8: Poblem 4 Chapte 9: Poblems,, 5, 54 **4 small plastic with a mass of 6.5 x - kg an with a chage of.5 µc is suspene fom an insulating

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

Quantum Mechanics I - Session 5

Quantum Mechanics I - Session 5 Quantum Mechanics I - Session 5 Apil 7, 015 1 Commuting opeatos - an example Remine: You saw in class that Â, ˆB ae commuting opeatos iff they have a complete set of commuting obsevables. In aition you

More information

Physics 122, Fall September 2012

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

More information

Electrostatics. 1. Show does the force between two point charges change if the dielectric constant of the medium in which they are kept increase?

Electrostatics. 1. Show does the force between two point charges change if the dielectric constant of the medium in which they are kept increase? Electostatics 1. Show does the foce between two point chages change if the dielectic constant of the medium in which they ae kept incease? 2. A chaged od P attacts od R whee as P epels anothe chaged od

More information

LECTURE 14. m 1 m 2 b) Based on the second law of Newton Figure 1 similarly F21 m2 c) Based on the third law of Newton F 12

LECTURE 14. m 1 m 2 b) Based on the second law of Newton Figure 1 similarly F21 m2 c) Based on the third law of Newton F 12 CTU 4 ] NWTON W O GVITY -The gavity law i foulated fo two point paticle with ae and at a ditance between the. Hee ae the fou tep that bing to univeal law of gavitation dicoveed by NWTON. a Baed on expeiental

More information

That is, the acceleration of the electron is larger than the acceleration of the proton by the same factor the electron is lighter than the proton.

That is, the acceleration of the electron is larger than the acceleration of the proton by the same factor the electron is lighter than the proton. PHYS 55 Pactice Test Solutions Fall 8 Q: [] poton an an electon attact each othe electicall so, when elease fom est, the will acceleate towa each othe Which paticle will have a lage acceleation? (Neglect

More information

FI 2201 Electromagnetism

FI 2201 Electromagnetism FI 2201 Electomagnetism Alexande A. Iskanda, Ph.D. Physics of Magnetism and Photonics Reseach Goup Electodynamics ELETROMOTIVE FORE AND FARADAY S LAW 1 Ohm s Law To make a cuent flow, we have to push the

More information

Physics 1502: Lecture 4 Today s Agenda

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

More information

Kinetic energy, work, and potential energy. Work, the transfer of energy: force acting through distance: or or

Kinetic 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 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

Sensors and Actuators Introduction to sensors

Sensors and Actuators Introduction to sensors Sensos an ctuatos Intouction to sensos Sane Stuijk (s.stuijk@tue.nl) Depatment of Electical Engineeing Electonic Systems PITIE SENSORS (hapte 3., 7., 9.,.6, 3., 3.) 3 Senso classification type / quantity

More information

PHYS 1441 Section 002. Lecture #3

PHYS 1441 Section 002. Lecture #3 PHYS 1441 Section 00 Chapte 1 Lectue #3 Wednesday, Sept. 6, 017 Coulomb s Law The Electic Field & Field Lines Electic Fields and Conductos Motion of a Chaged Paticle in an Electic Field Electic Dipoles

More information

Aaa Hal ARC 103 Haq Mou Hill 114 Mug Seh PHY LH Sen Zzz SEC 111

Aaa Hal ARC 103 Haq Mou Hill 114 Mug Seh PHY LH Sen Zzz SEC 111 The Fist Midtem!!! The fist common hou midtem exam will be held on Thusday Octobe 5, 9:50 to 11:10 PM (at night) on the Busch campus. You should go to the oom coesponding to the fist 3 lettes of you last

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

TRAVELING WAVES. Chapter Simple Wave Motion. Waves in which the disturbance is parallel to the direction of propagation are called the

TRAVELING WAVES. Chapter Simple Wave Motion. Waves in which the disturbance is parallel to the direction of propagation are called the Chapte 15 RAVELING WAVES 15.1 Simple Wave Motion Wave in which the ditubance i pependicula to the diection of popagation ae called the tanvee wave. Wave in which the ditubance i paallel to the diection

More information

( ) rad ( 2.0 s) = 168 rad

( ) rad ( 2.0 s) = 168 rad .) α 0.450 ω o 0 and ω 8.00 ω αt + ω o o t ω ω o α HO 9 Solution 8.00 0 0.450 7.8 b.) ω ω o + αδθ o Δθ ω 8.00 0 ω o α 0.450 7. o Δθ 7. ev.3 ev π.) ω o.50, α 0.300, Δθ 3.50 ev π 7π ev ω ω o + αδθ o ω ω

More information

Fields and Waves I Spring 2005 Homework 4. Due 8 March 2005

Fields and Waves I Spring 2005 Homework 4. Due 8 March 2005 Homewok 4 Due 8 Mach 005. Inceasing the Beakdown Voltage: This fist question is a mini design poject. You fist step is to find a commecial cable (coaxial o two wie line) fo which you have the following

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

Solutions to Problems : Chapter 19 Problems appeared on the end of chapter 19 of the Textbook

Solutions to Problems : Chapter 19 Problems appeared on the end of chapter 19 of the Textbook Solutions to Poblems Chapte 9 Poblems appeae on the en of chapte 9 of the Textbook 8. Pictue the Poblem Two point chages exet an electostatic foce on each othe. Stategy Solve Coulomb s law (equation 9-5)

More information

Review of Potential Energy. The Electric Potential. Plotting Fields and Potentials. Electric Potential of a Point Charge

Review 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 information

Chapter 22: Electric Fields. 22-1: What is physics? General physics II (22102) Dr. Iyad SAADEDDIN. 22-2: The Electric Field (E)

Chapter 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 information

Rotational Motion: Statics and Dynamics

Rotational Motion: Statics and Dynamics Physics 07 Lectue 17 Goals: Lectue 17 Chapte 1 Define cente of mass Analyze olling motion Intoduce and analyze toque Undestand the equilibium dynamics of an extended object in esponse to foces Employ consevation

More information

Chapter 13: Gravitation

Chapter 13: Gravitation v m m F G Chapte 13: Gavitation The foce that makes an apple fall is the same foce that holds moon in obit. Newton s law of gavitation: Evey paticle attacts any othe paticle with a gavitation foce given

More information

Physics 2102 Lecture: 07 TUE 09 FEB

Physics 2102 Lecture: 07 TUE 09 FEB Physics 2102 Jonathan Dowling Physics 2102 Lectue: 07 TUE 09 FEB Electic Potential II PHYS2102 FIRST MIDTERM EXAM 6 7PM THU 11 FEB 2009 Dowling s Sec. 4 in??? YOU MUST BRING YOUR STUDENT ID YOU MUST WRITE

More information

AP Physics Electric Potential Energy

AP 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 information

Physics C Rotational Motion Name: ANSWER KEY_ AP Review Packet

Physics C Rotational Motion Name: ANSWER KEY_ AP Review Packet Linea and angula analogs Linea Rotation x position x displacement v velocity a T tangential acceleation Vectos in otational motion Use the ight hand ule to detemine diection of the vecto! Don t foget centipetal

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

University Physics (PHY 2326)

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

More information