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.

Size: px
Start display at page:

Download "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."

Transcription

1 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 gavitational attaction.) a) The acceleations ae the same since the Coulomb foces ae equal. b) The electon since it is lighte. c) The poton since it is heavie. ) The paticles won t acceleate since the foces cancel each othe out. Solution: b The chages act upon each othe with foces which in the spiit of Newton s 3 law fom action-eaction pais. So, the poton an the electon will attact each othe with foces with same magnitue. Hence, in confomity with Newton s n law, thei acceleations will epen on thei elative masses: a m e p F F meae mpap ae ap a m p e That is, the acceleation of the electon is lage than the acceleation of the poton by the same facto the electon is lighte than the poton. Q: [] Two chages ae epesente in the figue with some electic fiel lines. Base on the patten, which chage is lage an by how much? a) The positive chage, thee times. b) The negative chage, thee times. c) The chages ae equal. ) The positive chage, two times. Solution: a The numbe of electic fiel lines is popotional to the intensity of the electic fiel so the positive chage is lage since it has moe lines suouning it. Also, the fiel of a chage n times lage than anothe chage shoul be epesente by n times moe fiel lines. So, since in ou case thee ae lines exiting the positive chage but only of them en on the negative chage, the positive chage must be 3 times lage. Q3: [] A poton entes with hoizontal velocity v in the vacuume space between the hoizontal plates of a chage paallel-plate capacito. Which of the fou paths epicte on the iagam will be most likely followe by the poton? a) A (staight line) b) B (ac of cicle) c) C (ellipse) ) D (paabola) A B C D v y x Solution: The electic fiel between the plates is unifom, so the foce acting on the poton is constant, so its acceleation is constant. Since the poton caies a positive chage, the foce is in the iection of the fiel, vetically upwa in the positive y-iection. Consequently, only the y-component of the paticle s motion is acceleate wheeas the x-component is not. Hence, the time epenence of the cooinates is given by Fe e y at t E t m an x vt. (Alas, PHY 7 bites us fom behin ) m Substituting the time between the two equations, we get a quaatic epenency between y an x, that is, the path is paabolic: e x ee y E y x m v mv. Q: [] An electon is place in the inteio of an imaginay sphee one thi the aius fom the ight hemispheic suface. Then the electic flux though the suface of the sphee is -e

2 PHY 8 Test Pactice Solutions Sping a) e b) e 3 c) e ) e 9 Solution: a The sphee can be chosen as a Gaussian. Then, by Gauss s law, the flux though its close suface is popotional to the chage within iespective of its position: e Q5: [] Which of the ajacent cuves most likely epesents the electic potential of a chage metallic sphee in electostatic equilibium as a function of the istance fom the cente of the sphee. R is the aius of the sphee. a) A b) B c) C ) D Solution: Thee is no net chage insie a metal, so the inne fiel is zeo. Theefoe, the potential must be constant thoughout the inteio of the conucto an it thee is no iscontinuity at the suface as on gaph D. A B R R C D R R Q6: [] Thee point chages with the same magnitue q =.6 μc ae locate in the -q cones of an equilateal tiangle of sie =.56 mm. What is the wok one on the positive chage to bing it to its cone fom infinity? q a) 89 J b) 56 J -q c) 8 J ) J Solution: a The wok one by the two negative chages to bing the positive chage fom infinity to the cone of the tiangle is given by the iffeence of potential between the two positions multiplie by the tanspote chage. The positive chage moves though the potential ceate by the two negative point chages. Theefoe we get q q q W q q q 8 J. Q7: [] The figue epesents the electic potential of a ipole. A positive test chage is elease in vicinity with an initial velocity oiente as in the figue. Which of the inicate tajectoies will be most likely followe by the test chage? a) A b) B c) C ) D Solution: The positive test chage spontaneously moves in the iection of the electic fiel pointing own the gaient of potential towa egions with lowe electic potentials, so it will ten to fall into the potential well coesponing to the negative chage of the ipole. Since the test chage has an initial velocity, it will fall own into the sink along a spial tajectoy much like the motion of a mass own a whilpool. C v D B A

3 PHY 8 Test Pactice Solutions Sping Q8: [] Suppose that you want to buil a paallel plate capacito with capacity of. F. You esign inclues cicula metallic plates sepaate by. cm of vacuum. What shoul be the aius of one of these plates? a) 5. m b) m c).5 m ) m Solution: b The capacitance of a capacito is given by its geomety an the mateial in between the plates. Thus, fo the paallel plate capacito with cicula plates of aius A C C km. So, you can see why we sai in class that Faa is a athe lage unit. Q9: [] Consie two paallel plate capacitos, with capacitances C lage than C, but the same plate sepaations =. If each of the capacitos is chage with the same amount of chage, which capacito has a lage electic fiel in between the plates? a) Capacito C. b) Capacito C. c) The electic fiel is the same. ) Depens on the plate aeas. Solution: b Capacitance C is lage than C, but they hol the same chage, so the potential iffeence acoss C must be lage: C C Q Q. Theefoe, since the potential iffeence is popotional to the constant fiel in between the plate by = E, we get E E E E. Q: [] Two ai-fille capacitos ae connecte in paallel an chage. A ielectic is insete in between the plates of one of them. What happens with the chage stoe on the othe one? a) Stays the same. b) Inceases. c) Deceases. ) Becomes zeo. Solution: c The effect of the ielectic is to incease the capacitance of the espective capacito an thus its ability to hol moe chage with a smalle potential. Since the total chage on the combination must stay the same with o without the ielectic (it cannot go anywhee), the voltage will ecease. But a smalle voltage acoss the capacito without the ielectic means that it looses chage (it goes onto the othe one). Using pime symbols fo the chages afte the ielectic is insete, we can show systematically how the chage changes on the secon capacito, as following: C KC Qnet Q Q Q Q Q Q Q Q C C since the voltage is the same, so Q /C = Q /C C KC Q C C Q Q Q Q C C Q KC C C C KC C 3

4 PHY 8 Test Pactice Solutions Sping P: Thee point chages = 6. μc an = 3. μc ae fixe in the cones of a vetical equilateal tiangle of sie = cm, as in the figue. A test chage q =.6 μc of mass m is place in point A whee it floats in static equilibium at height h = / cm above the chages Q. a) [] Use vecto aows to epesent the electic fiels,, an ceate by the thee chages in point A. The fiel exists in point A inepenent of the pesence of the test chage. The souce chages ae positive, such that the espective fiels ae aows pointing aially away fom each chage. b) [7] Split the vectos in x an y-components an fin a symbolical expession fo the magnitue of the net electic fiel in point A. It shoul epen on,, an constants. Then epesent the vecto net fiel on the figue an calculate the magnitue numeically. Note that the x-components of the fiels ceate by the bottom chages cancel each othe out, so we emain only with thei y-components which ae equal. Theefoe, the net fiel is given by Q Q E Esin E k k, whee an ae the istances between the espective chages an point A. Fom the geomety of the aangement, Theefoe. 3, h 3 Q Q k Q E k k Q 3 3 The negative sign means that the net fiel is oiente ownwa. Q 7. m. α = 5 Q / q A y α / B / Q x c) [3] Repesent the electic foce acting on chage q. Then use equilibium to calculate the mass m of the test chage. The test chage is negative such that the foce will be vetically upwa (against the fiel). Since the chage is in equilibium F mg qe mg m q E g.39 kg. e ) [] Suppose that the uppe chage is emove. Calculate the iffeence of electic potential ceate by the emaining chages between points A an B. Both chages contibute to the potentials equally. Theefoe Q Q Q 5 B A k k k.8. e) [] The test chage q is elease fom est an moves ownwa. Calculate its spee in point B. Since the test chage falls fom est its balance of final an initial potential enegies gives us the final kinetic enegy mg qa qb mv mv mg q B A.3 J, such that the spee is v.3.39 m s. m s. y a P: A cylinical wie of aius a is electically chage with unifom linea ensity λ = 3. - C/m. Consie the cyline infinitely long L P (,) x

5 PHY 8 Test Pactice Solutions Sping an aligne with y-axis, as in the figue. The questions below will lea you though the most common calculation of the electic fiel an potential in point P(,), at a istance =. cm fom the axis of the cyline. a) [] Sketch a cylinical Gaussian of aius an abitay height L aoun the wie epesente on the figue. Denote q the chage enclose by this suface an wite it own in tems of λ an L. q L b) [5] Use Gauss s Law to povie a symbolical expession fo the magnitue of the electic fiel E in point P in tems of, λ an ε. Then calculate it numeically. Inicate on the figue the iection of the vecto E in point P. Since the electic fiel must espect the aial symmety of the chage, the electic flux though the Gaussian must be nonzeo only though the cuve suface (so no flux though the top an bottom). Moeove, by symmety, the magnitue of the fiel must be constant on these cuve sufaces. Consequently, by Gauss s Law, we get E E A E L q E L L E by Gauss's Law Gaussian Since the chage on the wie is negative, the fiel vecto points aially insie as inicate by the expession fo the component E which is negative. Numeically, the fiel magnitue is E.8 m c) [5] Use the expession fo the electic fiel to fin a symbolical expession fo the iffeence of electic potential between point P an a point outsie the wie at istance fom P, locate on the x-axis. Fo any consevative fiel with aial symmety, we have the elationship between the fiel stength an the potential: E ˆ ; Hence, we get E E ln, whee the pime is a customay way to mak a ummy vaiable since is a limit of integation. The goun o suface of zeo potential can be taken on the suface of the wie, = a, an then this is an expession fo the potential at istance. ) [6] Now suppose that a poton is launche in point P moving to the ight along x-axis with initial spee v = 5 m/s. What istance oes the poton tavel befoe it stops? We can use consevation of enegy. Since thee is no nonconsevative foce acting on the poton, the consevation of enegy between the initial configuation (point P) an the point at position x whee it stops (since the poton is attacte by the negative chage on the wie) is given by: mv e e. C x Hence, we can calculate the istance = x tavele by the poton e mv ex ln mv mv mv e e ln e e.5 mm e P3: A capacitive cicuit is connecte to a battey with a potential iffeence =, as in the figue. The capacitances ae C =. nf, C =. nf, C 3 = 5.6 nf, C = nf. b a) [] Use the space below to euce the cicuit to simple foms an calculate the equivalent capacitance C of the cicuit. C 3 C 3 C C C 5 a c

6 PHY 8 Test Pactice Solutions Sping b c a c b) [] Calculate the net C 3 C chage Q stoe on the combination. The use it to C C calculate the potential iffeence ab between points a-b on the cicuit. a Q C nc Since the equivalent capacito C, which is connecte acoss points a-b, contibutes to the net capacitance C in a seies cicuit (see the secon cicuit iagam above), the chage Q on C is equal to the net chage Q. Theefoe, applying the efinition of capacitance to the equivalent capacito C, we get Q abc Q ab Q C. b c) [3] Now let s look close at the paallel-plate ai-fille capacitos C an C. Knowing that the aeas A of thei plates is the same, an the sepaation between the plates of C is =. mm, what is the sepaation between the plates of C? Using the epenency of capacitance on the pemittivity an geomety, we have C C C A an C A. Hence, iviing the expession to get i of the unknown aea, we obtain C C C C. mm a ) [3] Calculate the magnitues of the electic fiel E, in between the plates of the espective capacitos. Since the plate sepaations ae iffeent, the same potential iffeence ab will ceate iffeent electic fiels insie each of the two capacitos: E ab. N C an E ab. N C e) [] Calculate the chages Q, on the espective capacitos. Then, fin a way to calculate the aea A of the plates of the two capacitos (Hint: use fo instance Q an E. How can you wite E in tems of Q?) Applying the efinition of capacitance, we get Q abc 8. nc an Q abc 6 nc Notice that, inee, Q Q = Q = Q. Recall that the constant fiel between the plates is given by the chage ensity σ. Fo instance, using C, since Q A E Q A A Q E.5 m f) [] Compute the electostatic foces between the plates of each of the two capacitos. The electic foce appeas because each plate is in the constant fiel of the othe one. Because the net fiel is twice the fiel pouce by each plate, we obtain 5 F Q E 8. N 5 an F Q E 3 N 6

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

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

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

Physics Courseware Physics II Electric Field and Force

Physics Courseware Physics II Electric Field and Force Physics Cousewae Physics II lectic iel an oce Coulomb s law, whee k Nm /C test Definition of electic fiel. This is a vecto. test Q lectic fiel fo a point chage. This is a vecto. Poblem.- chage of µc is

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

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

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

Chapter 28: Magnetic Field and Magnetic Force. Chapter 28: Magnetic Field and Magnetic Force. Chapter 28: Magnetic fields. Chapter 28: Magnetic fields

Chapter 28: Magnetic Field and Magnetic Force. Chapter 28: Magnetic Field and Magnetic Force. Chapter 28: Magnetic fields. Chapter 28: Magnetic fields Chapte 8: Magnetic fiels Histoically, people iscoe a stone (e 3 O 4 ) that attact pieces of ion these stone was calle magnets. two ba magnets can attact o epel epening on thei oientation this is ue to

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

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 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

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

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

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

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

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

$ 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

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

General Relativity Homework 5

General Relativity Homework 5 Geneal Relativity Homewok 5. In the pesence of a cosmological constant, Einstein s Equation is (a) Calculate the gavitational potential point souce with = M 3 (). R µ Rg µ + g µ =GT µ. in the Newtonian

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

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

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

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

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

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

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

(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

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

Physics C: Electricity and Magnetism

Physics C: Electricity and Magnetism Physics C: Electicity an Magnetism TABLE OF INFORMATION FOR CONSTANTS AND CONVERSION FACTORS - unifie atomic mass unit, u =. 66 7 kg = 93 MeV/ c Poton mass, m p = 67. 7 kg Neuton mass, m n = 67. 7 kg Electon

More information

Section 5: Magnetostatics

Section 5: Magnetostatics ection 5: Magnetostatics In electostatics, electic fiels constant in time ae pouce by stationay chages. In magnetostatics magnetic fiels constant in time ae pouces by steay cuents. Electic cuents The electic

More information

Basic oces an Keple s Laws 1. Two ientical sphees of gol ae in contact with each othe. The gavitational foce of attaction between them is Diectly popotional to the squae of thei aius ) Diectly popotional

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

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

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

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

15. SIMPLE MHD EQUILIBRIA

15. SIMPLE MHD EQUILIBRIA 15. SIMPLE MHD EQUILIBRIA In this Section we will examine some simple examples of MHD equilibium configuations. These will all be in cylinical geomety. They fom the basis fo moe the complicate equilibium

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

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

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

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

Calculate the electric potential at B d2=4 m Calculate the electric potential at A d1=3 m 3 m 3 m

Calculate the electric potential at B d2=4 m Calculate the electric potential at A d1=3 m 3 m 3 m MTE : Ch 13 5:3-7pm on Oct 31 ltenate Exams: Wed Ch 13 6:3pm-8:pm (people attending the altenate exam will not be allowed to go out of the oom while othes fom pevious exam ae still aound) Thu @ 9:-1:3

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

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

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

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

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

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

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

4.[1pt] Two small spheres with charges -4 C and -9 C are held 9.5 m apart. Find the magnitude of the force between them.

4.[1pt] Two small spheres with charges -4 C and -9 C are held 9.5 m apart. Find the magnitude of the force between them. . [pt] A peson scuffing he feet on a wool ug on a y ay accumulates a net chage of - 4.uC. How many ecess electons oes this peson get? Coect, compute gets:.63e+4. [pt] By how much oes he mass incease? Coect,

More information

MAGNETICS EFFECTS OF ELECTRIC CURRENT

MAGNETICS EFFECTS OF ELECTRIC CURRENT Lesson- MAGNETCS EFFECTS F ELECTC CUENT este in 8 by obseving the eflection of compass neele when it is bought nea a cuent caying conucto iscovee that a cuent caying conucto pouces magnetic fiel in space

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

1 2 U CV. K dq I dt J nqv d J V IR P VI

1 2 U CV. K dq I dt J nqv d J V IR P VI o 5 o T C T F 9 T K T o C 7.5 L L T V VT Q mct nct Q F V ml F V dq A H k TH TC dt L pv nt Kt nt CV ideal monatomic gas 5 CV ideal diatomic gas w/o vibation V W pdv V U Q W W Q e Q Q e Canot H C T T S C

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

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 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

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

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

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

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

Equilibria of a cylindrical plasma

Equilibria of a cylindrical plasma // Miscellaneous Execises Cylinical equilibia Equilibia of a cylinical plasma Consie a infinitely long cyline of plasma with a stong axial magnetic fiel (a geat fusion evice) Plasma pessue will cause the

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

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

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

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

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

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

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

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

5. ELECTROSTATICS. Synopsis :

5. ELECTROSTATICS. Synopsis : 5. ELECTROSTATICS Synopsis :. Stuy of stationay electic chages at est is known as electostatics.. Electic Chage : i) It is a funamental popety of matte an neve foun fee. ii) Thee ae two kins of chages

More information

Chapter 25. Electric Potential

Chapter 25. Electric Potential Chapte 25 Electic Potential C H P T E R O U T L I N E 251 Potential Diffeence and Electic Potential 252 Potential Diffeences in a Unifom Electic Field 253 Electic Potential and Potential Enegy Due to Point

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

11) A thin, uniform rod of mass M is supported by two vertical strings, as shown below.

11) A thin, uniform rod of mass M is supported by two vertical strings, as shown below. Fall 2007 Qualifie Pat II 12 minute questions 11) A thin, unifom od of mass M is suppoted by two vetical stings, as shown below. Find the tension in the emaining sting immediately afte one of the stings

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

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

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

? 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

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

! 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

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

SAMPLE PAPER I. Time Allowed : 3 hours Maximum Marks : 70

SAMPLE PAPER I. Time Allowed : 3 hours Maximum Marks : 70 SAMPL PAPR I Time Allowed : 3 hous Maximum Maks : 70 Note : Attempt All questions. Maks allotted to each question ae indicated against it. 1. The magnetic field lines fom closed cuves. Why? 1 2. What is

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

16.1 Permanent magnets

16.1 Permanent magnets Unit 16 Magnetism 161 Pemanent magnets 16 The magnetic foce on moving chage 163 The motion of chaged paticles in a magnetic field 164 The magnetic foce exeted on a cuent-caying wie 165 Cuent loops and

More information

Chapter 13 Gravitation

Chapter 13 Gravitation Chapte 13 Gavitation In this chapte we will exploe the following topics: -Newton s law of gavitation, which descibes the attactive foce between two point masses and its application to extended objects

More 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

The Millikan Experiment: Determining the Elementary Charge

The Millikan Experiment: Determining the Elementary Charge LAB EXERCISE 7.5.1 7.5 The Elementay Chage (p. 374) Can you think of a method that could be used to suggest that an elementay chage exists? Figue 1 Robet Millikan (1868 1953) m + q V b The Millikan Expeiment:

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

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

Mark answers in spaces on the answer sheet

Mark answers in spaces on the answer sheet Mak answes in spaces 31-43 on the answe sheet PHYSICS 1 Summe 005 EXAM 3: July 5 005 9:50pm 10:50pm Name (pinted): ID Numbe: Section Numbe: INSTRUCTIONS: Some questions ae one point, othes ae two points,

More information

10. Force is inversely proportional to distance between the centers squared. R 4 = F 16 E 11.

10. Force is inversely proportional to distance between the centers squared. R 4 = F 16 E 11. NSWRS - P Physics Multiple hoice Pactice Gavitation Solution nswe 1. m mv Obital speed is found fom setting which gives v whee M is the object being obited. Notice that satellite mass does not affect obital

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

6. A bus is moving with a velocity of 0 m/s on a staight oa. A scooteist wishes to ovetake the bus in 00 secons. If the bus is at a istance of km fom the scooteist, at what velocity shoul the scooteist

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

ELECTROMAGNETISM (CP2)

ELECTROMAGNETISM (CP2) Revision Lectue on ELECTROMAGNETISM (CP) Electostatics Magnetostatics Induction EM Waves based on pevious yeas Pelims questions State Coulomb s Law. Show how E field may be defined. What is meant by E

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

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

OSCILLATIONS AND GRAVITATION

OSCILLATIONS AND GRAVITATION 1. SIMPLE HARMONIC MOTION Simple hamonic motion is any motion that is equivalent to a single component of unifom cicula motion. In this situation the velocity is always geatest in the middle of the motion,

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

Current, Resistance and

Current, Resistance and Cuent, Resistance and Electomotive Foce Chapte 25 Octobe 2, 2012 Octobe 2, 2012 Physics 208 1 Leaning Goals The meaning of electic cuent, and how chages move in a conducto. What is meant by esistivity

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 122, Fall October 2012

Physics 122, Fall October 2012 Today in Physics 1: electostatics eview David Blaine takes the pactical potion of his electostatics midtem (Gawke). 11 Octobe 01 Physics 1, Fall 01 1 Electostatics As you have pobably noticed, electostatics

More information