Size: px
Start display at page:

Download ""

Transcription

1 Page 1 of 6 Physics II Exam points Name Discussion day/time Pat I. Questions points each. Multiple choice: Fo full cedit, cicle only the coect answe. Fo half cedit, cicle the coect answe and one incoect answe. Fo ¼ cedit, cicle the coect answe and two incoect answes. 1. Two small sphees epel one anothe electostatically. Which of the following must be tue? a. Both have the same chage. b. Neithe is chaged. c. Both ae chaged. d. At least one sphee is chaged. e. They ae oppositely chaged. 2. Thee chages q, Q, and Q ae placed at the cones of an equilateal tiangle as shown. The net foce on chage q due to the othe two chages is a. vetically up q b. vetically down. c. zeo. d. hoizontal to the left. e. hoizontal to the ight. Q Q 3. A positive chage is bought close to a fixed neutal conducto that has a cavity. The cavity is neutal; that is, thee is no net chage in the cavity. Which of the figues best epesents the chage distibution on the inne and oute walls of the conducto? 5 e A long box of length l, width w, and height h contains a line of positive chage density λ. The line of chage is oiented paallel to the length of the box, is centeed within the box, and is length l/2. The net electic flux though the box is a. zeo b. positive c. negative d. not enough infomation given e. positive though one end, and negative though the othe

2 Page 2 of 6 5. Fou chages of equal magnitude ae aanged at the cones of a squae. In which aangement is the magnitude of the electic field at point P a maximum? P P P P e. The maximum electic field occus in moe than one of these aangements. 6. Which point in the electic field is at the highest potential? e. 5 4 E 7.A spheical shell of adius b contains at its cente a metal sphee with adius a. The sphee has chage q wheeas the shell has chage q. Which gaph best epesents the potential as a function of adius? Assume the potential is zeo at infinity. e. 5 f q q a b 5 6

3 Page 3 of 6 8. The chage on each capacito in a set of capacitos in paallel is a. diectly popotional to its capacitance. b. invesely popotional to its capacitance. c. independent of its capacitance. d. the same. e. None of these is coect. 9. The capacitance of a capacito a. is defined as the amount of wok equied to move a chage fom one plate to the othe. b. deceases if a dieletic is placed between its plates. c. is independent of the distance between the plates. d. has units of enegy/chage. e. is independent of the chage on the capacito. 10a. (4 points) If a dieletic is inseted between the plates of a paallelplate capacito that is connected to attey, the a. voltage acoss the capacito deceases. b. electic field between the plates deceases. c. electic field between the plates inceases. d. chage on the capacito plates deceases. e. chage on the capacito plates inceases. 10b. (4 points) If a dieletic is inseted between the plates of a paallelplate capacito that is not connected to attey, the a. voltage acoss the capacito deceases. b. electic field between the plates deceases. c. electic field between the plates inceases. d. chage on the capacito plates deceases. e. chage on the capacito plates inceases.

4 Page 4 of 6 Pat II. Shot answe/sketch. Answe questions 1113 as completely as possible. Show you wok to ean patial cedit! 11. (25 points) A positive chage q 1 lies at the oigin, an unknown chage q 2 lies at (d 1,0), and anothe unknown chage q 3 lies at (d 2 cosθ,d 2 sinθ). All thee chages ae fixed in place. The net electic foce on q 1 is in the negative ydiection. y d 1 a. What is the sign of the chage q 2? q 1 d 2 θ q 2 x q 3 b. What is the sign of the chage q 3? c. What is the foce on q 1 due to q 2? Expess you answe in tems of k, θ, q 1, q 2, d 1, and d 2 (all paametes may not apply). d. What is the foce on q 1 due to q 3? Expess you answe in tems of k, θ, q 1, q 3, d 1, and d 2 (all paametes may not apply). e. Suppose that the magnitude of q 3 is 2q 1. What is q 2? Expess you answe in tems of k, θ, q 1, d 1, and d 2 (all paametes may not apply).

5 12. (25 points) A slab of unifom thickness d, fom d/2 to d/2 along the xaxis, extends infinitely in the y and z diections, as shown. The slab has unifom volume chage density ρ. The electic field is zeo in the middle of the slab, at x=0. a. Which of the following statements is tue of the electic field at the suface of one side of the slab? 1. The diection of E is constant, but its magnitude vaies acoss the suface. 2. Both the magnitude and diection of E ae constant acoss the entie suface. 3. The diection of E vaies acoss the suface, but its magnitude is constant. 4. Both the magnitude and diection of E vay acoss the suface. b. The suface nomal points in the x diection on one side of the slab, and in the x diection on the othe. What is the angle θ that the field E makes with espect to the suface nomal? (the answe is the same fo eithe side). c. To calculate E on one of these sufaces, we'll use Gauss' Law. Descibe the location and shape of you choice fo the Gaussian suface. ρ d x=0 d. What is the total enclosed chage within you suface? y x z e. What is E at the suface? f. Sketch the magnitude of the electic field as function of x. E x=d x=0 x=d x Page 5 of 6

6 Page 6 of (25 points) A hollow cylinde o adius and height h has a total chage q unifomly distibuted ove its suface. The axis of the cylinde coincides with the zaxis, and the cylinde is centeed at the oigin. We will calculate the electic potential at the oigin by summing up the individual potentials due to infinitesimally thin ings. a. Conside a thin ing of thickness dz at a distance z above the oigin, as shown. What is the distance fom the oigin to the ing? b. How much chage is contained in the ing? z dz c. What is the potential d at the oigin due to this ing? d = z=0 h d. To obtain the total potential, you need to integate ove d. What ae the lowe and uppe limits of this integal? e. Evaluate. You may find the following useful: da/(a 2 b 2 ) ½ = ln{a/b(1a 2 /b 2 ) ½ } da/(a 2 b 2 ) = 1/b tan 1 (a/b) da/a = ln(a) z = y x f. What is the potential in the limit that h? This can be solved mathematically o conceptually.

(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

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

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

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

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

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

$ 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

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

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::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

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

Physics 313 Practice Test Page 1. University Physics III Practice Test II

Physics 313 Practice Test Page 1. University Physics III Practice Test II Physics 313 Pactice Test Page 1 Univesity Physics III Pactice Test II This pactice test should give you a ough idea of the fomat and oveall level of the Physics 313 exams. The actual exams will have diffeent

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

ev dm e evd 2 m e 1 2 ev2 B) e 2 0 dm e D) m e

ev dm e evd 2 m e 1 2 ev2 B) e 2 0 dm e D) m e . A paallel-plate capacito has sepaation d. The potential diffeence between the plates is V. If an electon with chage e and mass m e is eleased fom est fom the negative plate, its speed when it eaches

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

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

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

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

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

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

Phys102 Second Major-182 Zero Version Monday, March 25, 2019 Page: 1

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

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

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

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

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

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

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

( ) 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

Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 1 -

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

More information

Exam 3, vers Physics Spring, 2003

Exam 3, vers Physics Spring, 2003 1 of 9 Exam 3, ves. 0001 - Physics 1120 - Sping, 2003 NAME Signatue Student ID # TA s Name(Cicle one): Michael Scheffestein, Chis Kelle, Paisa Seelungsawat Stating time of you Tues ecitation (wite time

More information

Physics Electrostatics: Coulomb s Law

Physics Electrostatics: Coulomb s Law A C U L T Y O E D U C A T I O N Depatment of Cuiculum and Pedagogy Physics Electostatics: Coulomb s Law Science and Mathematics Education Reseach Goup Suppoted by UBC Teaching and Leaning Enhancement und

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

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

06 - ROTATIONAL MOTION Page 1 ( Answers at the end of all questions )

06 - ROTATIONAL MOTION Page 1 ( Answers at the end of all questions ) 06 - ROTATIONAL MOTION Page ) A body A of mass M while falling vetically downwads unde gavity beaks into two pats, a body B of mass ( / ) M and a body C of mass ( / ) M. The cente of mass of bodies B and

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

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

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

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

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

B. Spherical Wave Propagation

B. Spherical Wave Propagation 11/8/007 Spheical Wave Popagation notes 1/1 B. Spheical Wave Popagation Evey antenna launches a spheical wave, thus its powe density educes as a function of 1, whee is the distance fom the antenna. We

More information

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

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

1. THINK Ampere is the SI unit for current. An ampere is one coulomb per second.

1. THINK Ampere is the SI unit for current. An ampere is one coulomb per second. Chapte 4 THINK Ampee is the SI unit fo cuent An ampee is one coulomb pe second EXPRESS To calculate the total chage though the cicuit, we note that A C/s and h 6 s ANALYZE (a) Thus, F I HG K J F H G I

More 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

Phys 1215, First Test. September 20, minutes Name:

Phys 1215, First Test. September 20, minutes Name: Phys 115, Fist Test. Septembe 0, 011 50 minutes Name: Show all wok fo maximum cedit. Each poblem is woth 10 points. k =.0 x 10 N m / C ε 0 = 8.85 x 10-1 C / N m e = 1.60 x 10-1 C ρ = 1.68 x 10-8 Ω m fo

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

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

Physics 107 TUTORIAL ASSIGNMENT #8

Physics 107 TUTORIAL ASSIGNMENT #8 Physics 07 TUTORIAL ASSIGNMENT #8 Cutnell & Johnson, 7 th edition Chapte 8: Poblems 5,, 3, 39, 76 Chapte 9: Poblems 9, 0, 4, 5, 6 Chapte 8 5 Inteactive Solution 8.5 povides a model fo solving this type

More information

Physics 235 Chapter 5. Chapter 5 Gravitation

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

More information

Target Boards, JEE Main & Advanced (IIT), NEET Physics Gauss Law. H. O. D. Physics, Concept Bokaro Centre P. K. Bharti

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:

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

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

! 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

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

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

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

Physics 181. Assignment 4

Physics 181. Assignment 4 Physics 181 Assignment 4 Solutions 1. A sphee has within it a gavitational field given by g = g, whee g is constant and is the position vecto of the field point elative to the cente of the sphee. This

More information

Physics 2B Chapter 22 Notes - Magnetic Field Spring 2018

Physics 2B Chapter 22 Notes - Magnetic Field Spring 2018 Physics B Chapte Notes - Magnetic Field Sping 018 Magnetic Field fom a Long Staight Cuent-Caying Wie In Chapte 11 we looked at Isaac Newton s Law of Gavitation, which established that a gavitational field

More information

AP Physics C: Electricity and Magnetism 2003 Scoring Guidelines

AP Physics C: Electricity and Magnetism 2003 Scoring Guidelines AP Physics C: Electicity and Magnetism 3 Scoing Guidelines The mateials included in these files ae intended fo use by AP teaches fo couse and exam pepaation; pemission fo any othe use must be sought fom

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

Electric Forces: Coulomb s Law

Electric Forces: Coulomb s Law Electic Foces: Coulomb s Law All the matte aound you contains chaged paticles, and it is the electic foces between these chaged paticles that detemine the stength of the mateials and the popeties of the

More information

Physics 4A Chapter 8: Dynamics II Motion in a Plane

Physics 4A Chapter 8: Dynamics II Motion in a Plane Physics 4A Chapte 8: Dynamics II Motion in a Plane Conceptual Questions and Example Poblems fom Chapte 8 Conceptual Question 8.5 The figue below shows two balls of equal mass moving in vetical cicles.

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

PY208 Matter & Interactions Final Exam S2005

PY208 Matter & Interactions Final Exam S2005 PY Matte & Inteactions Final Exam S2005 Name (pint) Please cicle you lectue section below: 003 (Ramakishnan 11:20 AM) 004 (Clake 1:30 PM) 005 (Chabay 2:35 PM) When you tun in the test, including the fomula

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

Phys 222 Sp 2009 Exam 1, Wed 18 Feb, 8-9:30pm Closed Book, Calculators allowed Each question is worth one point, answer all questions

Phys 222 Sp 2009 Exam 1, Wed 18 Feb, 8-9:30pm Closed Book, Calculators allowed Each question is worth one point, answer all questions Phys Sp 9 Exam, Wed 8 Feb, 8-9:3pm Closed Book, Calculatos allowed Each question is woth one point, answe all questions Fill in you Last Name, Middle initial, Fist Name You ID is the middle 9 digits on

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

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

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

13.10 Worked Examples

13.10 Worked Examples 13.10 Woked Examples Example 13.11 Wok Done in a Constant Gavitation Field The wok done in a unifom gavitation field is a faily staightfowad calculation when the body moves in the diection of the field.

More information

The Divergence Theorem

The Divergence Theorem 13.8 The ivegence Theoem Back in 13.5 we ewote Geen s Theoem in vecto fom as C F n ds= div F x, y da ( ) whee C is the positively-oiented bounday cuve of the plane egion (in the xy-plane). Notice this

More information

15 B1 1. Figure 1. At what speed would the car have to travel for resonant oscillations to occur? Comment on your answer.

15 B1 1. Figure 1. At what speed would the car have to travel for resonant oscillations to occur? Comment on your answer. Kiangsu-Chekiang College (Shatin) F:EasteHolidaysAssignmentAns.doc Easte Holidays Assignment Answe Fom 6B Subject: Physics. (a) State the conditions fo a body to undego simple hamonic motion. ( mak) (a)

More information

University of Illinois at Chicago Department of Physics. Electricity & Magnetism Qualifying Examination

University of Illinois at Chicago Department of Physics. Electricity & Magnetism Qualifying Examination E&M poblems Univesity of Illinois at Chicago Depatment of Physics Electicity & Magnetism Qualifying Examination Januay 3, 6 9. am : pm Full cedit can be achieved fom completely coect answes to 4 questions.

More information

Magnetic Field. Conference 6. Physics 102 General Physics II

Magnetic Field. Conference 6. Physics 102 General Physics II Physics 102 Confeence 6 Magnetic Field Confeence 6 Physics 102 Geneal Physics II Monday, Mach 3d, 2014 6.1 Quiz Poblem 6.1 Think about the magnetic field associated with an infinite, cuent caying wie.

More information

CHAPTER 10 ELECTRIC POTENTIAL AND CAPACITANCE

CHAPTER 10 ELECTRIC POTENTIAL AND CAPACITANCE CHAPTER 0 ELECTRIC POTENTIAL AND CAPACITANCE ELECTRIC POTENTIAL AND CAPACITANCE 7 0. ELECTRIC POTENTIAL ENERGY Conside a chaged paticle of chage in a egion of an electic field E. This filed exets an electic

More information

20-9 ELECTRIC FIELD LINES 20-9 ELECTRIC POTENTIAL. Answers to the Conceptual Questions. Chapter 20 Electricity 241

20-9 ELECTRIC FIELD LINES 20-9 ELECTRIC POTENTIAL. Answers to the Conceptual Questions. Chapter 20 Electricity 241 Chapte 0 Electicity 41 0-9 ELECTRIC IELD LINES Goals Illustate the concept of electic field lines. Content The electic field can be symbolized by lines of foce thoughout space. The electic field is stonge

More information

21 MAGNETIC FORCES AND MAGNETIC FIELDS

21 MAGNETIC FORCES AND MAGNETIC FIELDS CHAPTER 1 MAGNETIC ORCES AND MAGNETIC IELDS ANSWERS TO OCUS ON CONCEPTS QUESTIONS 1. (d) Right-Hand Rule No. 1 gives the diection of the magnetic foce as x fo both dawings A and. In dawing C, the velocity

More information

7.2. Coulomb s Law. The Electric Force

7.2. Coulomb s Law. The Electric Force Coulomb s aw Recall that chaged objects attact some objects and epel othes at a distance, without making any contact with those objects Electic foce,, o the foce acting between two chaged objects, is somewhat

More information

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department Physics 8.07: Electromagnetism II September 15, 2012 Prof. Alan Guth PROBLEM SET 2

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department Physics 8.07: Electromagnetism II September 15, 2012 Prof. Alan Guth PROBLEM SET 2 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Depatment Physics 8.07: Electomagnetism II Septembe 5, 202 Pof. Alan Guth PROBLEM SET 2 DUE DATE: Monday, Septembe 24, 202. Eithe hand it in at the lectue,

More information

PHYSICS NOTES GRAVITATION

PHYSICS NOTES GRAVITATION GRAVITATION Newton s law of gavitation The law states that evey paticle of matte in the univese attacts evey othe paticle with a foce which is diectly popotional to the poduct of thei masses and invesely

More information

Physics 111 Lecture 5 Circular Motion

Physics 111 Lecture 5 Circular Motion Physics 111 Lectue 5 Cicula Motion D. Ali ÖVGÜN EMU Physics Depatment www.aovgun.com Multiple Objects q A block of mass m1 on a ough, hoizontal suface is connected to a ball of mass m by a lightweight

More information

Math 259 Winter Handout 6: In-class Review for the Cumulative Final Exam

Math 259 Winter Handout 6: In-class Review for the Cumulative Final Exam Math 259 Winte 2009 Handout 6: In-class Review fo the Cumulative Final Exam The topics coveed by the cumulative final exam include the following: Paametic cuves. Finding fomulas fo paametic cuves. Dawing

More information

PHY2061 Enriched Physics 2 Lecture Notes. Gauss Law

PHY2061 Enriched Physics 2 Lecture Notes. Gauss Law PHY61 Eniched Physics Lectue Notes Law Disclaime: These lectue notes ae not meant to eplace the couse textbook. The content may be incomplete. ome topics may be unclea. These notes ae only meant to be

More information

working pages for Paul Richards class notes; do not copy or circulate without permission from PGR 2004/11/3 10:50

working pages for Paul Richards class notes; do not copy or circulate without permission from PGR 2004/11/3 10:50 woking pages fo Paul Richads class notes; do not copy o ciculate without pemission fom PGR 2004/11/3 10:50 CHAPTER7 Solid angle, 3D integals, Gauss s Theoem, and a Delta Function We define the solid angle,

More information

F g. = G mm. m 1. = 7.0 kg m 2. = 5.5 kg r = 0.60 m G = N m 2 kg 2 = = N

F g. = G mm. m 1. = 7.0 kg m 2. = 5.5 kg r = 0.60 m G = N m 2 kg 2 = = N Chapte answes Heinemann Physics 4e Section. Woked example: Ty youself.. GRAVITATIONAL ATTRACTION BETWEEN SMALL OBJECTS Two bowling balls ae sitting next to each othe on a shelf so that the centes of the

More information

On the Sun s Electric-Field

On the Sun s Electric-Field On the Sun s Electic-Field D. E. Scott, Ph.D. (EE) Intoduction Most investigatos who ae sympathetic to the Electic Sun Model have come to agee that the Sun is a body that acts much like a esisto with a

More information

B da = 0. Q E da = ε. E da = E dv

B da = 0. Q E da = ε. E da = E dv lectomagnetic Theo Pof Ruiz, UNC Asheville, doctophs on YouTube Chapte Notes The Maxwell quations in Diffeential Fom 1 The Maxwell quations in Diffeential Fom We will now tansfom the integal fom of the

More information

Math 2263 Solutions for Spring 2003 Final Exam

Math 2263 Solutions for Spring 2003 Final Exam Math 6 Solutions fo Sping Final Exam ) A staightfowad appoach to finding the tangent plane to a suface at a point ( x, y, z ) would be to expess the cuve as an explicit function z = f ( x, y ), calculate

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

SPH4U Unit 6.3 Gravitational Potential Energy Page 1 of 9

SPH4U Unit 6.3 Gravitational Potential Energy Page 1 of 9 SPH4 nit 6.3 Gavitational Potential negy Page of Notes Physics ool box he gavitational potential enegy of a syste of two (spheical) asses is diectly popotional to the poduct of thei asses, and invesely

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

THE LAPLACE EQUATION. The Laplace (or potential) equation is the equation. u = 0. = 2 x 2. x y 2 in R 2

THE LAPLACE EQUATION. The Laplace (or potential) equation is the equation. u = 0. = 2 x 2. x y 2 in R 2 THE LAPLACE EQUATION The Laplace (o potential) equation is the equation whee is the Laplace opeato = 2 x 2 u = 0. in R = 2 x 2 + 2 y 2 in R 2 = 2 x 2 + 2 y 2 + 2 z 2 in R 3 The solutions u of the Laplace

More information

13. The electric field can be calculated by Eq. 21-4a, and that can be solved for the magnitude of the charge N C m 8.

13. The electric field can be calculated by Eq. 21-4a, and that can be solved for the magnitude of the charge N C m 8. CHAPTR : Gauss s Law Solutions to Assigned Poblems Use -b fo the electic flux of a unifom field Note that the suface aea vecto points adially outwad, and the electic field vecto points adially inwad Thus

More information

Collaborative ASSIGNMENT Assignment 3: Sources of magnetic fields Solution

Collaborative ASSIGNMENT Assignment 3: Sources of magnetic fields Solution Electicity and Magnetism: PHY-04. 11 Novembe, 014 Collaboative ASSIGNMENT Assignment 3: Souces of magnetic fields Solution 1. a A conducto in the shape of a squae loop of edge length l m caies a cuent

More information

3.6 Applied Optimization

3.6 Applied Optimization .6 Applied Optimization Section.6 Notes Page In this section we will be looking at wod poblems whee it asks us to maimize o minimize something. Fo all the poblems in this section you will be taking the

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

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

Motion along curved path *

Motion along curved path * OpenStax-CNX module: m14091 1 Motion along cuved path * Sunil Kuma Singh This wok is poduced by OpenStax-CNX and licensed unde the Ceative Commons Attibution License 2.0 We all expeience motion along a

More information

MAGNETIC FIELD INTRODUCTION

MAGNETIC FIELD INTRODUCTION MAGNETIC FIELD INTRODUCTION It was found when a magnet suspended fom its cente, it tends to line itself up in a noth-south diection (the compass needle). The noth end is called the Noth Pole (N-pole),

More information