Exam 1 Solutions (1) C, D, A, B (2) C, A, D, B (3) C, B, D, A (4) A, C, D, B (5) D, C, A, B


 Job Warner
 4 years ago
 Views:
Transcription
1 PHY 249, Fll 216 Exm 1 Solutions nswer 1 is correct for ll problems. 1. Two uniformly chrged spheres, nd B, re plced t lrge distnce from ech other, with their centers on the x xis. The chrge on sphere is q, wheres tht on sphere B is 2q. If the electrosttic force on sphere is Fî, tht on sphere B is (1) Fî (2) Fî (3) 2Fî (4) 2Fî (5) 1 2 Fî Recll Newton s third lw. 2. In ech of the four configurtions lbeled, B, C, D in the figure, five chrges re eqully spced long the x xis. ll chrges hve the sme mgnitude, e, but some of them re +e nd some e. Rnk the mgnitude of the force on the middle chrge for the different configurtions, with the lrgest first nd the smllest lst. B C D (1) C, D,, B (2) C,, D, B (3) C, B, D, (4), C, D, B (5) D, C,, B In C, the forces by the four chrges dd up, wheres they completely cncel out in B. Therefore, C is the first, nd B the lst. Of the remining two configurtions, D comes before, becuse the two outermost chrges do not contribute to the net force in D, wheres in they compete with the forces by the two inner chrges. 3. prticle with positive chrge Q is on the y xis distnce from the origin, nd prticle with positive chrge q is on the x xis distnce d from the origin. Wht is the vlue of d for which the x component of the electrosttic force on the second prticle is the lrgest? (1) / 2 (2) (3) 2 (4) 2 (5) 2 2 For convenience, let s cll the second distnce x insted of d. The mgnitude of the force is F = kqq/( 2 +x 2 ). The similrityofthetwotringles,onedefinedbythetwoprticlesndtheoriginndthe otherdefinedbytheforcevectornd its x nd y components, leds to F x = Fx/( 2 +x 2 ) 1/2 for the x component of the force. Hence F x = kqqx/( 2 +x 2 ) 3/2. To mximize this, set df x /dx =, which gives 1/( 2 +x 2 ) 3/2 3 2 x(2x)/(2 +x 2 ) 5/2 =. Solve this for x. 4. Three prticles, ech chrged with 1. nc, re plced on three corners of squre of edge lengths = 1. m, s shown. Wht is the mgnitude of the electric field t the empty corner, lbeled? (1) 17 N/C (2) 27 N/C (3) 12 N/C (4) 24 N/C (5) 31 N/C Find the x nd y components of ech force, then dd the components of the three forces seprtely to obtin F x nd F y of the net force F. Finlly, find F by computing (F 2 x +F 2 y) 1/2. lterntively, notice tht the sum of the forces by the two nerest chrges, 2(kq 2 / 2 ), is in exctly the sme direction s the force by the third chrge on the digonl corner, kq 2 /(2 2 ). So just dd the two expressions nd plug in numbers.
2 5. line of chrge of length L nd chrge per unit length, λ, is locted on the x xis, s shown in the figure. Which expression below gives the x component of the electric field, E x, t distnce D from the left end of the line? D x x= x=l (1) L kxλ (x 2 +D 2 ) 3/2dx (2) L kdλ (x 2 +D 2 ) 3/2dx (3) L kxλ x 2 +D 2dx (4) L kdλ x 2 +D 2dx (5) L kλ x 2 +D 2dx The mgnitude of the electric field due to n infinitesiml line element dx locted t x is de = k(λdx)/(x 2 +D 2 ). Use the similrity of two norml tringles, s ws done in the solution to Problem 3, to find tht the x component of this force is given by de x = dex/(x 2 +D 2 ) 1/2. Integrte this from x = to x = L. 6. glss rod forms semicircle of rdius r = 5 cm with chrge of +q distributed uniformly in the upper qudrnt nd q distributed uniformly in the lower qudrnt. Wht is the direction of the electric field t the center P of the semicircle? (1) ĵ (2) ĵ (3) î (4) î (5) The electric field is zero. +q q r y P x The electric field due to the positively chrged prt of the rod points in the î ĵ direction, wheres the negtively chrged prt produces n electric field pointing in the î ĵ direction. Since the mgnitudes of the two fields re exctly the sme, their x components will cncel out, leving only the component in the ĵ direction. 7. Two thin concentric sphericl shells mde of copper hve net chrges of q 1 = 46 nc, q 2 = 69 nc nd rdii of r 1 = 15 cm, r 2 = 34 cm s shown in the figure. Wht is the surfce chrge density on the inner surfce of the smller shell, with rdius r 1, in units of C/m 2? q 2 q 1 r 2 r 1 (1) (2) (3) (4) (5) t equilibrium, no chrge will pper on the inner surfce of conductor unless the cvity contins chrged body. lterntively, in the present geometry, you my drw sphericl, concentric Gussin surfce whose rdius is slightly lrger thn the inner rdius of the inner shell. Since the electric field in conductor is zero t equilibrium, the field on the Gussin surfce will be zero. Guss theorem tells tht the enclosed chrge, nmely the chrge on the inner surfce, is zero. 8. Three very lrge prllel plnes re seprted by distnces d nd 2d. They crry chrges, whose densities re +σ, 2σ, nd +3σ, s shown in the figure. Wht is the mgnitude of the electric field t point in the middle between the second nd third pltes? (Hint: Electric fields re vectors tht dd s such.) +σ 2σ +3σ (1) 2σ ǫ (2) σ ǫ (3) σ 2ǫ (4) 3σ 2ǫ d 2d (5) 3σ ǫ The mgnitudes of the fields produced by the three pltes re σ/(2ǫ ), 2σ/(2ǫ ), nd 3σ/(2ǫ ). The first one points to the right, wheres the other two point to the left. So the mgnitude of the net field is ( 1+2+3)σ/(2ǫ ),
3 9. The figure shows four solid spheres,, B, C, D, ech with chrge Q uniformly distributed throughout its volume. For ll spheres, point P is t the sme distnce from the center of the sphere, s shown. Rnk the spheres ccording to the mgnitude of the electric field they produce t point P, gretest first. (1) nd B, C, D (2) The field is eqully strong in ll of the cses. (3) B,, C nd D (with C nd D equl) (4) B,, C, D (5) D, C, nd B (with nd B equl) P P P P B C D round the center of ech sphere, drw concentric sphericl Gussin surfce tht goes through point P. Since the res of these surfces re identicl, the electric field t P depends only on the mount of the enclosed chrge, not on the re of the Gussin surfce. The Gussin surfces for nd B completely enclose Q, so these spheres produce the strongest field. The Gussin surfce for C encloses lrger frction of Q thn does the Gussin surfce for D. So sphere C comes second, nd sphere D the lst. 1. smll bll, with chrge of 4 µc on it, is plced in sphericl cvity inside sphericl conductor, s illustrted in the figure. The net chrge on the conductor is 3 µc. Wht is the mount of chrge on the outer surfce of the conductor? + (1) 1 µc (2) 7 µc (3) (4) 3 µc (5) 4 µc The 4 µc chrge on the bll ttrcts chrge of 4 µc to the inner surfce of the conductor. s result, 3 ( 4) µc will pper on the outer surfce so tht the net chrge on the conductor will remin 3 µc. 11. solid sphericl conductor is given net positive chrge. The electrosttic potentil of the conductor is (1) constnt throughout the volume. (2) lrgest t the center. (3) lrgest on the surfce. (4) lrgest somewhere between the center nd surfce. (5) zero t the center. t equilibrium, the electric field inside conductor is lwys zero nd, consequently, the electrosttic potentil is constnt throughout. 12. Two conducting spheres re plced fr prt from ech other. The smller of the two crries totl chrge Q. The lrger one, whose rdius is three times tht of the smller one, crries no net chrge. fter the two spheres re connected by thin conducting wire, the mounts of chrge on the smller nd lrger spheres re, respectively: (1) Q/4 nd 3Q/4 (2) Q/1 nd 9Q/1 (3) Q/3 nd 2Q/3 (4) Q/2 nd Q/2 (5) Q nd 2Q Some of the Q will move to the lrger sphere so tht the electrosttic potentils V of the two sphere will be equl. Since V of given sphere is proportionl to the chrge on it nd inversely proportionl to its rdius, the chrges on the two spheres must be in the rtio of 1 to 3, the rtio of the two rdii. The smller sphere gets Q/4 nd the lrger sphere gets 3Q/4.
4 13. Eight prticles re plced on squre of side length, s shown in the figure. Ech prticle is chrged with n mount indicted. Wht is the electric potentil t the center of the squre, if V = t infinity? +q +2q 3q +q q 3q 2q +q (1) 4 2kq/ (2) 5kq/ (3) 3kq/ (4) kq/( 5) (5) kq/( 2) The electrosttic potentils produced by the four prticles on the edges will cncel out t the center. dding the potentils produced by the four prticles t the corners gives kq/(/ 2) k(3q)/(/ 2)+kq/(/ 2) k(3q)/(/ 2). 14. n electron is moving rightwrd between two prllel chrged pltes seprted by distnce d = 1. cm, s shown in the figure. The plte potentils re V 1 = 3 V nd V 2 = 2 V. If the initil speed of the electron t the left plte is 1. km/s, wht is its speed just s it reches the right plte? d V 1 V 2 (1) 1,9 km/s (2) 23 km/s (3) 64 km/s (4) 7.6 km/s (5) The electron will never rech the right plte. Since the electron is negtively chrged wheres the potentil of the right plte is higher thn tht of the left plte, the electron will rech the right plte. Let V be the potentil difference, 1 V. ccording to the conservtion of energy, 1 2 mv2 f 1 2 mv2 i = ev, where v f nd v i re the finl nd initil speeds of the electron. fter plugging in numbers, you will immeditely find tht the second term on the left side is much smller thn the right side of the eqution. So just solve the simplified, pproximte eqution 1 2 mv2 f = ev for v f. slower, errorprone wy of solving this problem is to first find the electric field E = V/d, then the ccelertion = ee/m. Next find the trvelling time t of the electron by solving the kinetic eqution, which is qudrtic (yikes), nd compute v f = v i +t. 15. prllelplte cpcitor hs plte seprtion d nd cpcitnce C. If slb of metl of thickness d/3 is inserted in the middle of the gp between the two pltes, s shown, wht will be the cpcitnce between the pltes? d d/3 (1) 3C/2 (2) 2C (3) C (4) C/2 (5) The originl cpcitnce is given by C = ǫ /d, where is the re of ech plte. fter the insertion of the slb, let us chrge the cpcitor with chrge q +q on the top plte nd q on the bottom plte. Then q will pper on the top surfce of the slb nd +q on the bottom surfce, ttrcted to the chrges on the pltes. This mens tht the rrngement is equivlent to two cpcitors, ech with plte seprtion of d/3, in series. Ech of these cpcitors hs cpcitnce of ǫ /(d/3), which is 3C. Two such cpcitnces in series mke 3C/2. lterntively, compre the originl cpcitor with the finl cpcitor, both chrged with q, nd notice tht the electric field in the gp(s) is the sme for the two. Since the totl gp size for the second cpcitor is 2/3 of the first one, the potentil difference cross it is lso 2/3 of tht of the first one. (Note tht the potentil difference cross the slb is zero.) The sme q but 2/3 of V this mens tht its cpcitnce, C = q/v, is 3/2 of the originl cpcitnce.
5 16. In the figure, potentil difference of V = 24 V is pplied cross the rrngement of cpcitors with cpcitnces C 1 = C 2 = 4. µf nd C 3 = 1. µf. Wht is the chrge on one of the pltes of cpcitor C 1? C 1 (1) 48 µc V (2) 96 µc (3) 72 µc (4) 12 µc (5) 6. µc C 2 C 3 The equivlent cpcitnce of C 1 nd C 2 in series is 2. µf. The equivlent cpcitor will therefore hve chrge of 24 V 2. µf = 48 µc. Peek inside the equivlent cpcitor nd find tht this mount of chrge ppers on C 1, s well s C 2 for tht mtter. 17. Wht is the equivlent cpcitnce, in µf, of the circuit shown if ech cpcitor hs cpcitnce of 1 µf? C 1 C 2 C3 C 4 (1) 6/11 (2) 11/6 (3) 5/6 (4) 6 (5) 1/6 V C 5 C 6 The circuit consists of three groups of cpcitors, in series. The first group comprises C 1 lone, the second group three cpcitors in prllel, nd the third group two cpcitors in prllel. Therefore, the equivlent cpcitnce is tht of 1 µf, 3 µf, nd 2 µf in series 6/11 µf becuse 1+1/3+1/2 = 11/ Wires C nd D re mde of different mterils nd hve length L C = L D = 1. m. The resistivity nd rdius of wire C re Ωm nd 1. mm, nd those of wire D re Ωm nd.3 mm. The wires re joined s shown, nd current of 2. is pssed through the combo. Wht is the rte t which energy is dissipted in wire C? C D L C L D (1) 5 W (2) 1 W (3) 3 W (4) 14 W (5) 21 W The resistnce of wire C is R = ( )(1.)/[π( ) 2 ] = 4.π Ω. The rte t which energy is dissipted is the power, P = i 2 R, which is bout 5 W V bttery is connected to resistive strip consisting of three sections with the sme crosssectionl re but different conductivities. The figure gives the electric potentil V versus position x long the strip. The conductivity of section 3 is (Ωm) 1. Wht is the conductivity of section 1, in 1 7 (Ωm) 1? (1) 6. (2) 3. (3) 1.5 (4) 4.5 (5) V 1 x 2 3 Recll E = ρj, where the three symbols re the electric field, conductivity, nd current density. Since the crosssectionl res of the three sections re the sme, J is the sme throughout. Therefore, the E of ech section is proportionl to ρ, inversely proportionl to its conductivity. Noting tht E is the slope of the curve of V versus x, find tht the E in section 1 is one hlf the E in section 3. This mens tht the conductivity of section 1 is twice the conductivity of section 3. lterntively, solve V = ir = i(ρl/) = il(σ) for conductivity σ to find σ = il/(v). Since i nd re constnt throughout, σ is proportionl to L/V, which is twice s lrge in section 1 s in section 3 ccording to the grph.
6 2. resistor dissiptes.5 W when potentil difference of 3. V is pplied. When the potentil difference is chnged to 1. V, wht is the power dissipted in this resistor? (1).56 W (2) 4.5 W (3) 1.5 W (4).5 W (5).17 W P = V 2 /R. s V is decresed by fctor of 3, P will decrese by fctor of 9.
200 points 5 Problems on 4 Pages and 20 Multiple Choice/Short Answer Questions on 5 pages 1 hour, 48 minutes
PHYSICS 132 Smple Finl 200 points 5 Problems on 4 Pges nd 20 Multiple Choice/Short Answer Questions on 5 pges 1 hour, 48 minutes Student Nme: Recittion Instructor (circle one): nme1 nme2 nme3 nme4 Write
More informationSample Exam 5  Skip Problems 13
Smple Exm 5  Skip Problems 13 Physics 121 Common Exm 2: Fll 2010 Nme (Print): 4 igit I: Section: Honors Code Pledge: As n NJIT student I, pledge to comply with the provisions of the NJIT Acdemic Honor
More informationPhysics 2135 Exam 1 February 14, 2017
Exm Totl / 200 Physics 215 Exm 1 Ferury 14, 2017 Printed Nme: Rec. Sec. Letter: Five multiple choice questions, 8 points ech. Choose the est or most nerly correct nswer. 1. Two chrges 1 nd 2 re seprted
More informationragsdale (zdr82) HW2 ditmire (58335) 1
rgsdle (zdr82) HW2 ditmire (58335) This printout should hve 22 questions. Multiplechoice questions my continue on the next column or pge find ll choices before nswering. 00 0.0 points A chrge of 8. µc
More informationLecture 13  Linking E, ϕ, and ρ
Lecture 13  Linking E, ϕ, nd ρ A Puzzle... InnerSurfce Chrge Density A positive point chrge q is locted offcenter inside neutrl conducting sphericl shell. We know from Guss s lw tht the totl chrge on
More informationPhysics 24 Exam 1 February 18, 2014
Exm Totl / 200 Physics 24 Exm 1 Februry 18, 2014 Printed Nme: Rec. Sec. Letter: Five multiple choice questions, 8 points ech. Choose the best or most nerly correct nswer. 1. The totl electric flux pssing
More informationInstructor(s): Acosta/Woodard PHYSICS DEPARTMENT PHY 2049, Fall 2015 Midterm 1 September 29, 2015
Instructor(s): Acost/Woodrd PHYSICS DEPATMENT PHY 049, Fll 015 Midterm 1 September 9, 015 Nme (print): Signture: On m honor, I hve neither given nor received unuthorized id on this emintion. YOU TEST NUMBE
More informationVersion 001 Exam 1 shih (57480) 1
Version 001 Exm 1 shih 57480) 1 This printout should hve 6 questions. Multiplechoice questions my continue on the next column or pge find ll choices before nswering. Holt SF 17Rev 1 001 prt 1 of ) 10.0
More informationIMPORTANT. Read these directions carefully:
Physics 208: Electricity nd Mgnetism Finl Exm, Secs. 506 510. 7 My. 2004 Instructor: Dr. George R. Welch, 415 EngineeringPhysics, 8457737 Print your nme netly: Lst nme: First nme: Sign your nme: Plese
More informationPhysics 1402: Lecture 7 Today s Agenda
1 Physics 1402: Lecture 7 Tody s gend nnouncements: Lectures posted on: www.phys.uconn.edu/~rcote/ HW ssignments, solutions etc. Homework #2: On Msterphysics tody: due Fridy Go to msteringphysics.com Ls:
More informationCAPACITORS AND DIELECTRICS
Importnt Definitions nd Units Cpcitnce: CAPACITORS AND DIELECTRICS The property of system of electricl conductors nd insultors which enbles it to store electric chrge when potentil difference exists between
More informationProf. Anchordoqui. Problems set # 4 Physics 169 March 3, 2015
Prof. Anchordoui Problems set # 4 Physics 169 Mrch 3, 15 1. (i) Eight eul chrges re locted t corners of cube of side s, s shown in Fig. 1. Find electric potentil t one corner, tking zero potentil to be
More informationPhysics 121 Sample Common Exam 1 NOTE: ANSWERS ARE ON PAGE 8. Instructions:
Physics 121 Smple Common Exm 1 NOTE: ANSWERS ARE ON PAGE 8 Nme (Print): 4 Digit ID: Section: Instructions: Answer ll questions. uestions 1 through 16 re multiple choice questions worth 5 points ech. You
More informationPhysics 9 Fall 2011 Homework 2  Solutions Friday September 2, 2011
Physics 9 Fll 0 Homework  s Fridy September, 0 Mke sure your nme is on your homework, nd plese box your finl nswer. Becuse we will be giving prtil credit, be sure to ttempt ll the problems, even if you
More informationPhysics Jonathan Dowling. Lecture 9 FIRST MIDTERM REVIEW
Physics 10 Jonthn Dowling Physics 10 ecture 9 FIRST MIDTERM REVIEW A few concepts: electric force, field nd potentil Electric force: Wht is the force on chrge produced by other chrges? Wht is the force
More informationUniversity of Alabama Department of Physics and Astronomy. PH126: Exam 1
University of Albm Deprtment of Physics nd Astronomy PH 16 LeClir Fll 011 Instructions: PH16: Exm 1 1. Answer four of the five questions below. All problems hve equl weight.. You must show your work for
More informationReading from Young & Freedman: For this topic, read the introduction to chapter 24 and sections 24.1 to 24.5.
PHY1 Electricity Topic 5 (Lectures 7 & 8) pcitors nd Dielectrics In this topic, we will cover: 1) pcitors nd pcitnce ) omintions of pcitors Series nd Prllel 3) The energy stored in cpcitor 4) Dielectrics
More informationProblems for HW X. C. Gwinn. November 30, 2009
Problems for HW X C. Gwinn November 30, 2009 These problems will not be grded. 1 HWX Problem 1 Suppose thn n object is composed of liner dielectric mteril, with constnt reltive permittivity ɛ r. The object
More informationHomework Assignment 3 Solution Set
Homework Assignment 3 Solution Set PHYCS 44 6 Ferury, 4 Prolem 1 (Griffiths.5(c The potentil due to ny continuous chrge distriution is the sum of the contriutions from ech infinitesiml chrge in the distriution.
More informationDIRECT CURRENT CIRCUITS
DRECT CURRENT CUTS ELECTRC POWER Consider the circuit shown in the Figure where bttery is connected to resistor R. A positive chrge dq will gin potentil energy s it moves from point to point b through
More informationwest (mrw3223) HW 24 lyle (16001) 1
west (mrw3223) HW 24 lyle (16001) 1 This printout should hve 30 questions. Multiplechoice questions my continue on the next column or pge find ll choices before nswering. Reding ssignment: Hecht, sections
More informationJackson 2.26 Homework Problem Solution Dr. Christopher S. Baird University of Massachusetts Lowell
Jckson 2.26 Homework Problem Solution Dr. Christopher S. Bird University of Msschusetts Lowell PROBLEM: The twodimensionl region, ρ, φ β, is bounded by conducting surfces t φ =, ρ =, nd φ = β held t zero
More informationConducting Ellipsoid and Circular Disk
1 Problem Conducting Ellipsoid nd Circulr Disk Kirk T. McDonld Joseph Henry Lbortories, Princeton University, Princeton, NJ 08544 (September 1, 00) Show tht the surfce chrge density σ on conducting ellipsoid,
More information 5  TEST 2. This test is on the final sections of this session's syllabus and. should be attempted by all students.
 5  TEST 2 This test is on the finl sections of this session's syllbus nd should be ttempted by ll students. Anything written here will not be mrked.  6  QUESTION 1 [Mrks 22] A thin nonconducting
More informationPhysics Honors. Final Exam Review Free Response Problems
Physics Honors inl Exm Review ree Response Problems m t m h 1. A 40 kg mss is pulled cross frictionless tble by string which goes over the pulley nd is connected to 20 kg mss.. Drw free body digrm, indicting
More informationMath 0230 Calculus 2 Lectures
Mth Clculus Lectures Chpter 7 Applictions of Integrtion Numertion of sections corresponds to the text Jmes Stewrt, Essentil Clculus, Erly Trnscendentls, Second edition. Section 7. Ares Between Curves Two
More informationMath 8 Winter 2015 Applications of Integration
Mth 8 Winter 205 Applictions of Integrtion Here re few importnt pplictions of integrtion. The pplictions you my see on n exm in this course include only the Net Chnge Theorem (which is relly just the Fundmentl
More informationDesigning Information Devices and Systems I Discussion 8B
Lst Updted: 20181017 19:40 1 EECS 16A Fll 2018 Designing Informtion Devices nd Systems I Discussion 8B 1. Why Bother With Thévenin Anywy? () Find Thévenin eqiuvlent for the circuit shown elow. 2kΩ 5V
More informationThat reminds me must download the test prep HW. adapted from (nz118.jpg)
Tht reminds me must downlod the test prep HW. dpted from http://www.neringzero.net (nz118.jpg) Em 1: Tuesdy, Feb 14, 5:006:00 PM Test rooms: Instructor Sections Room Dr. Hle F, H 104 Physics Dr. Kurter
More informationChapter 6 Electrostatic Boundary Value Problems. Dr. Talal Skaik
Chpter 6 Electrosttic Boundry lue Problems Dr. Tll Skik 1 1 Introduction In previous chpters, E ws determined by coulombs lw or Guss lw when chrge distribution is known, or potentil is known throughout
More informationLecture 1: Electrostatic Fields
Lecture 1: Electrosttic Fields Instructor: Dr. Vhid Nyyeri Contct: nyyeri@iust.c.ir Clss web site: http://webpges.iust.c. ir/nyyeri/courses/bee 1.1. Coulomb s Lw Something known from the ncient time (here
More informationPhysics 3323, Fall 2016 Problem Set 7 due Oct 14, 2016
Physics 333, Fll 16 Problem Set 7 due Oct 14, 16 Reding: Griffiths 4.1 through 4.4.1 1. Electric dipole An electric dipole with p = p ẑ is locted t the origin nd is sitting in n otherwise uniform electric
More informationPhysics Graduate Prelim exam
Physics Grdute Prelim exm Fll 2008 Instructions: This exm hs 3 sections: Mechnics, EM nd Quntum. There re 3 problems in ech section You re required to solve 2 from ech section. Show ll work. This exm is
More informationName Solutions to Test 3 November 8, 2017
Nme Solutions to Test 3 November 8, 07 This test consists of three prts. Plese note tht in prts II nd III, you cn skip one question of those offered. Some possibly useful formuls cn be found below. Brrier
More informationElectricity and Magnetism
PHY472 Dt Provided: Formul sheet nd physicl constnts Dt Provided: A formul sheet nd tble of physicl constnts is ttched to this pper. DEPARTMENT OF PHYSICS & Autumn Semester 20092010 ASTRONOMY DEPARTMENT
More informationSolutions to Physics: Principles with Applications, 5/E, Giancoli Chapter 16 CHAPTER 16
CHAPTER 16 1. The number of electrons is N = Q/e = ( 30.0 10 6 C)/( 1.60 10 19 C/electrons) = 1.88 10 14 electrons.. The mgnitude of the Coulomb force is Q /r. If we divide the epressions for the two forces,
More information#6A&B Magnetic Field Mapping
#6A& Mgnetic Field Mpping Gol y performing this lb experiment, you will: 1. use mgnetic field mesurement technique bsed on Frdy s Lw (see the previous experiment),. study the mgnetic fields generted by
More informationProblem Set 3 Solutions
Msschusetts Institute of Technology Deprtment of Physics Physics 8.07 Fll 2005 Problem Set 3 Solutions Problem 1: Cylindricl Cpcitor Griffiths Problems 2.39: Let the totl chrge per unit length on the inner
More informationAP Physics C: Electricity & Magnetism 1999 FreeResponse Questions
AP Physics C: Electricity & Mgnetism 1999 Freeesponse Questions The mterils included in these files re intended for noncommercil use by AP techers for course nd exm preprtion; permission for ny other
More informationPhys 6321 Final Exam  Solutions May 3, 2013
Phys 6321 Finl Exm  Solutions My 3, 2013 You my NOT use ny book or notes other thn tht supplied with this test. You will hve 3 hours to finish. DO YOUR OWN WORK. Express your nswers clerly nd concisely
More informationLast Time emphasis on Efield. Potential of spherical conductor. Quick quiz. Connected spheres. Varying Efields on conductor.
Lst Time emphsis on Efiel Electric flux through surfce Guss lw: Totl electric flux through close surfce proportionl to chrge enclose Q " E = E = 4$k e Q % o Chrge istribution on conuctors Chrge ccumultes
More informationProblem Set 4: Mostly Magnetic
University of Albm Deprtment of Physics nd Astronomy PH 102 / LeClir Summer 2012 nstructions: Problem Set 4: Mostly Mgnetic 1. Answer ll questions below. Show your work for full credit. 2. All problems
More informationExam 1 September 21, 2012 Instructor: Timothy Martin
PHY 232 Exm 1 Sept 21, 212 Exm 1 September 21, 212 Instructor: Timothy Mrtin Stuent Informtion Nme n section: UK Stuent ID: Set #: Instructions Answer the questions in the spce provie. On the long form
More informationJackson 2.7 Homework Problem Solution Dr. Christopher S. Baird University of Massachusetts Lowell
Jckson.7 Homework Problem Solution Dr. Christopher S. Bird University of Msschusetts Lowell PROBLEM: Consider potentil problem in the hlfspce defined by, with Dirichlet boundry conditions on the plne
More informationLecture 5 Capacitance Ch. 25
Lecture 5 pcitnce h. 5 rtoon  pcitnce definition nd exmples. Opening Demo  Dischrge cpcitor Wrmup prolem Physlet Topics pcitnce Prllel Plte pcitor Dielectrics nd induced dipoles oxil cle, oncentric
More informationPART 1 MULTIPLE CHOICE Circle the appropriate response to each of the questions below. Each question has a value of 1 point.
PART MULTIPLE CHOICE Circle the pproprite response to ech of the questions below. Ech question hs vlue of point.. If in sequence the second level difference is constnt, thn the sequence is:. rithmetic
More informationToday in Physics 122: work, energy and potential in electrostatics
Tody in Physics 1: work, energy nd potentil in electrosttics Leftovers Perfect conductors Fields from chrges distriuted on perfect conductors Guss s lw for grvity Work nd energy Electrosttic potentil energy,
More informationPhys102 General Physics II
Phys1 Generl Physics II pcitnce pcitnce pcitnce definition nd exmples. Dischrge cpcitor irculr prllel plte cpcitior ylindricl cpcitor oncentric sphericl cpcitor Dielectric Sls 1 pcitnce Definition of cpcitnce
More informationARITHMETIC OPERATIONS. The real numbers have the following properties: a b c ab ac
REVIEW OF ALGEBRA Here we review the bsic rules nd procedures of lgebr tht you need to know in order to be successful in clculus. ARITHMETIC OPERATIONS The rel numbers hve the following properties: b b
More informationElectric Potential. Concepts and Principles. An Alternative Approach. A Gravitational Analogy
. Electric Potentil Concepts nd Principles An Alterntive Approch The electric field surrounding electric chrges nd the mgnetic field surrounding moving electric chrges cn both be conceptulized s informtion
More informationPhys 201 Midterm 1 S. Nergiz, E.Oğuz, C. Saçlıoğlu T. Turgut Fall '01 No :. Name :. Total Grade :. Grade :. y=a. x=a +q. x=a q +q. +Q r.
Phs 0 Miterm S. Nergiz, E.ğuz, C. Sçlıoğlu T. Turgut Fll '0 No :. Nme :. Totl Gre :. Gre :. Question : Three point chrges re plce s shown in figure. ) Clculte the coulom force on ech chrge. ) Fin the electrosttic
More informationSummary of equations chapters 7. To make current flow you have to push on the charges. For most materials:
Summry of equtions chpters 7. To mke current flow you hve to push on the chrges. For most mterils: J E E [] The resistivity is prmeter tht vries more thn 4 orders of mgnitude between silver (.6E8 Ohm.m)
More informationProblem Solving 7: Faraday s Law Solution
MASSACHUSETTS NSTTUTE OF TECHNOLOGY Deprtment of Physics: 8.02 Prolem Solving 7: Frdy s Lw Solution Ojectives 1. To explore prticulr sitution tht cn led to chnging mgnetic flux through the open surfce
More informationInClass Problems 2 and 3: Projectile Motion Solutions. InClass Problem 2: Throwing a Stone Down a Hill
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Deprtment of Physics Physics 8T Fll Term 4 InClss Problems nd 3: Projectile Motion Solutions We would like ech group to pply the problem solving strtegy with the
More information13.4 Work done by Constant Forces
13.4 Work done by Constnt Forces We will begin our discussion of the concept of work by nlyzing the motion of n object in one dimension cted on by constnt forces. Let s consider the following exmple: push
More informationPhysics 2135 Exam 1 September 23, 2014
Exm Totl Physics 2135 Exm 1 September 23, 2014 Key Printe Nme: 200 / 200 N/A Rec. Sec. Letter: Five multiple choice questions, 8 points ech. Choose the best or most nerly correct nswer. B 1. Object A hs
More informationPHYSICS 211 MIDTERM I 21 April 2004
PHYSICS MIDERM I April 004 Exm is closed book, closed notes. Use only your formul sheet. Write ll work nd nswers in exm booklets. he bcks of pges will not be grded unless you so request on the front of
More informationMath 426: Probability Final Exam Practice
Mth 46: Probbility Finl Exm Prctice. Computtionl problems 4. Let T k (n) denote the number of prtitions of the set {,..., n} into k nonempty subsets, where k n. Argue tht T k (n) kt k (n ) + T k (n ) by
More informationSUMMER KNOWHOW STUDY AND LEARNING CENTRE
SUMMER KNOWHOW STUDY AND LEARNING CENTRE Indices & Logrithms 2 Contents Indices.2 Frctionl Indices.4 Logrithms 6 Exponentil equtions. Simplifying Surds 13 Opertions on Surds..16 Scientific Nottion..18
More informationHints for Exercise 1 on: Current and Resistance
Hints for Exercise 1 on: Current nd Resistnce Review the concepts of: electric current, conventionl current flow direction, current density, crrier drift velocity, crrier numer density, Ohm s lw, electric
More informationConsolidation Worksheet
Cmbridge Essentils Mthemtics Core 8 NConsolidtion Worksheet N Consolidtion Worksheet Work these out. 8 b 7 + 0 c 6 + 7 5 Use the number line to help. 2 Remember + 2 2 +2 2 2 + 2 Adding negtive number is
More informationPhysics 241 Exam 1 February 19, 2004
Phsics 241 Em 1 Februr 19, 24 One (both sides) 8 1/2 11 crib sheet is llowed. It must be of our own cretion. k = 1 = 9 1 9 N m2 4p 2 2 = 8.85 112 N m 2 e =1.62 119 c = 2.99792458 1 8 m/s (speed of light)
More informationIntro to Nuclear and Particle Physics (5110)
Intro to Nucler nd Prticle Physics (5110) Feb, 009 The Nucler Mss Spectrum The Liquid Drop Model //009 1 E(MeV) n n(n1)/ E/[ n(n1)/] (MeV/pir) 1 C 16 O 0 Ne 4 Mg 7.7 14.44 19.17 8.48 4 5 6 6 10 15.4.41
More information7.1 Integral as Net Change and 7.2 Areas in the Plane Calculus
7.1 Integrl s Net Chnge nd 7. Ares in the Plne Clculus 7.1 INTEGRAL AS NET CHANGE Notecrds from 7.1: Displcement vs Totl Distnce, Integrl s Net Chnge We hve lredy seen how the position of n oject cn e
More informationELECTROSTATIC ENERGY AND CAPACITORS
ELETROSTATI ENERGY AND APAITORS EXERISES Section. Electrosttic Energy. INTERPRET We re to find the work required to ssemble liner sequence of chrges. DEVELOP We use the technique described for ssembling
More information5.2 Volumes: Disks and Washers
4 pplictions of definite integrls 5. Volumes: Disks nd Wshers In the previous section, we computed volumes of solids for which we could determine the re of crosssection or slice. In this section, we restrict
More informationAPPLICATIONS OF THE DEFINITE INTEGRAL
APPLICATIONS OF THE DEFINITE INTEGRAL. Volume: Slicing, disks nd wshers.. Volumes by Slicing. Suppose solid object hs boundries extending from x =, to x = b, nd tht its crosssection in plne pssing through
More informationName Class Date. Match each phrase with the correct term or terms. Terms may be used more than once.
Exercises 341 Flow of Chrge (pge 681) potentil difference 1 Chrge flows when there is between the ends of conductor 2 Explin wht would hppen if Vn de Grff genertor chrged to high potentil ws connected
More informationChapter 7 Steady Magnetic Field. september 2016 Microwave Laboratory Sogang University
Chpter 7 Stedy Mgnetic Field september 2016 Microwve Lbortory Sogng University Teching point Wht is the mgnetic field? BiotSvrt s lw: Coulomb s lw of Mgnetic field Stedy current: current flow is independent
More informationPH 102 Exam I Solutions
PH 102 Exm I Solutions 1. Three ienticl chrges of = 5.0 µc lie long circle of rius 2.0 m t ngles of 30, 150, n 270 s shown below. Wht is the resultnt electric fiel t the center of the circle? By symmetry,
More informationHung problem # 3 April 10, 2011 () [4 pts.] The electric field points rdilly inwrd [1 pt.]. Since the chrge distribution is cylindriclly symmetric, we pick cylinder of rdius r for our Gussin surfce S.
More informationPHYSICS ASSIGNMENT9
MPS/PHYXII11/A9 PHYSICS ASSIGNMENT9 *********************************************************************************************************** 1. A wire kept long the northsouth direction is llowed
More informationPhysics 712 Electricity and Magnetism Solutions to Final Exam, Spring 2016
Physics 7 Electricity nd Mgnetism Solutions to Finl Em, Spring 6 Plese note tht some possibly helpful formuls pper on the second pge The number of points on ech problem nd prt is mrked in squre brckets
More informationReference. Vector Analysis Chapter 2
Reference Vector nlsis Chpter Sttic Electric Fields (3 Weeks) Chpter 3.3 Coulomb s Lw Chpter 3.4 Guss s Lw nd pplictions Chpter 3.5 Electric Potentil Chpter 3.6 Mteril Medi in Sttic Electric Field Chpter
More informationScientific notation is a way of expressing really big numbers or really small numbers.
Scientific Nottion (Stndrd form) Scientific nottion is wy of expressing relly big numbers or relly smll numbers. It is most often used in scientific clcultions where the nlysis must be very precise. Scientific
More informationLog1 Contest Round 3 Theta Individual. 4 points each 1 What is the sum of the first 5 Fibonacci numbers if the first two are 1, 1?
008 009 Log1 Contest Round Thet Individul Nme: points ech 1 Wht is the sum of the first Fiboncci numbers if the first two re 1, 1? If two crds re drwn from stndrd crd deck, wht is the probbility of drwing
More informationPhysics 102. Final Examination. Spring Semester ( ) P M. Fundamental constants. n = 10P
ε µ0 N mp M G T Kuwit University hysics Deprtment hysics 0 Finl Exmintin Spring Semester (00) My, 0 Time: 5:00 M :00 M Nme.Student N Sectin N nstructrs: Drs. bdelkrim, frsheh, Dvis, Kkj, Ljk, Mrfi, ichler,
More informationMultiple Integrals. Review of Single Integrals. Planar Area. Volume of Solid of Revolution
Multiple Integrls eview of Single Integrls eding Trim 7.1 eview Appliction of Integrls: Are 7. eview Appliction of Integrls: Volumes 7.3 eview Appliction of Integrls: Lengths of Curves Assignment web pge
More informationMATH 253 WORKSHEET 24 MORE INTEGRATION IN POLAR COORDINATES. r dr = = 4 = Here we used: (1) The halfangle formula cos 2 θ = 1 2
MATH 53 WORKSHEET MORE INTEGRATION IN POLAR COORDINATES ) Find the volume of the solid lying bove the xyplne, below the prboloid x + y nd inside the cylinder x ) + y. ) We found lst time the set of points
More informationHomework Assignment 5 Solution Set
Homework Assignment 5 Solution Set PHYCS 44 3 Februry, 4 Problem Griffiths 3.8 The first imge chrge gurntees potentil of zero on the surfce. The secon imge chrge won t chnge the contribution to the potentil
More informationMath 113 Exam 2 Practice
Mth 3 Exm Prctice Februry 8, 03 Exm will cover 7.4, 7.5, 7.7, 7.8, 8.3 nd 8.5. Plese note tht integrtion skills lerned in erlier sections will still be needed for the mteril in 7.5, 7.8 nd chpter 8. This
More informationPhys 4321 Final Exam December 14, 2009
Phys 4321 Finl Exm December 14, 2009 You my NOT use the text book or notes to complete this exm. You nd my not receive ny id from nyone other tht the instructor. You will hve 3 hours to finish. DO YOUR
More informationSection 4.8. D v(t j 1 ) t. (4.8.1) j=1
Difference Equtions to Differentil Equtions Section.8 Distnce, Position, nd the Length of Curves Although we motivted the definition of the definite integrl with the notion of re, there re mny pplictions
More informationSOLUTIONS FOR ADMISSIONS TEST IN MATHEMATICS, COMPUTER SCIENCE AND JOINT SCHOOLS WEDNESDAY 5 NOVEMBER 2014
SOLUTIONS FOR ADMISSIONS TEST IN MATHEMATICS, COMPUTER SCIENCE AND JOINT SCHOOLS WEDNESDAY 5 NOVEMBER 014 Mrk Scheme: Ech prt of Question 1 is worth four mrks which re wrded solely for the correct nswer.
More information( ) as a fraction. Determine location of the highest
AB Clculus Exm Review Sheet  Solutions A. Preclculus Type prolems A1 A2 A3 A4 A5 A6 A7 This is wht you think of doing Find the zeros of f ( x). Set function equl to 0. Fctor or use qudrtic eqution if
More informationCandidates must show on each answer book the type of calculator used.
UNIVERSITY OF EAST ANGLIA School of Mthemtics My/June UG Exmintion 2007 2008 ELECTRICITY AND MAGNETISM Time llowed: 3 hours Attempt FIVE questions. Cndidtes must show on ech nswer book the type of clcultor
More informationPhysicsAndMathsTutor.com
1. A uniform circulr disc hs mss m, centre O nd rdius. It is free to rotte bout fixed smooth horizontl xis L which lies in the sme plne s the disc nd which is tngentil to the disc t the point A. The disc
More informationChapter E  Problems
Chpter E  Prolems Blinn College  Physics 2426  Terry Honn Prolem E.1 A wire with dimeter d feeds current to cpcitor. The chrge on the cpcitor vries with time s QHtL = Q 0 sin w t. Wht re the current
More informationThe Wave Equation I. MA 436 Kurt Bryan
1 Introduction The Wve Eqution I MA 436 Kurt Bryn Consider string stretching long the x xis, of indeterminte (or even infinite!) length. We wnt to derive n eqution which models the motion of the string
More information( ) where f ( x ) is a. AB Calculus Exam Review Sheet. A. Precalculus Type problems. Find the zeros of f ( x).
AB Clculus Exm Review Sheet A. Preclculus Type prolems A1 Find the zeros of f ( x). This is wht you think of doing A2 A3 Find the intersection of f ( x) nd g( x). Show tht f ( x) is even. A4 Show tht f
More informationthan 1. It means in particular that the function is decreasing and approaching the x
6 Preclculus Review Grph the functions ) (/) ) log y = b y = Solution () The function y = is n eponentil function with bse smller thn It mens in prticulr tht the function is decresing nd pproching the
More informationEnergy creation in a moving solenoid? Abstract
Energy cretion in moving solenoid? Nelson R. F. Brg nd Rnieri V. Nery Instituto de Físic, Universidde Federl do Rio de Jneiro, Cix Postl 68528, RJ 21941972 Brzil Abstrct The electromgnetic energy U em
More informationDesigning Information Devices and Systems I Spring 2018 Homework 7
EECS 16A Designing Informtion Devices nd Systems I Spring 2018 omework 7 This homework is due Mrch 12, 2018, t 23:59. Selfgrdes re due Mrch 15, 2018, t 23:59. Sumission Formt Your homework sumission should
More informationThis final is a three hour open book, open notes exam. Do all four problems.
Physics 55 Fll 27 Finl Exm Solutions This finl is three hour open book, open notes exm. Do ll four problems. [25 pts] 1. A point electric dipole with dipole moment p is locted in vcuum pointing wy from
More informationImproper Integrals, and Differential Equations
Improper Integrls, nd Differentil Equtions October 22, 204 5.3 Improper Integrls Previously, we discussed how integrls correspond to res. More specificlly, we sid tht for function f(x), the region creted
More informationMagnetic forces on a moving charge. EE Lecture 26. Lorentz Force Law and forces on currents. Laws of magnetostatics
Mgnetic forces on moving chrge o fr we ve studied electric forces between chrges t rest, nd the currents tht cn result in conducting medium 1. Mgnetic forces on chrge 2. Lws of mgnetosttics 3. Mgnetic
More informationMORE FUNCTION GRAPHING; OPTIMIZATION. (Last edited October 28, 2013 at 11:09pm.)
MORE FUNCTION GRAPHING; OPTIMIZATION FRI, OCT 25, 203 (Lst edited October 28, 203 t :09pm.) Exercise. Let n be n rbitrry positive integer. Give n exmple of function with exctly n verticl symptotes. Give
More information4.4 Areas, Integrals and Antiderivatives
. res, integrls nd ntiderivtives 333. Ares, Integrls nd Antiderivtives This section explores properties of functions defined s res nd exmines some connections mong res, integrls nd ntiderivtives. In order
More informationImproper Integrals. Type I Improper Integrals How do we evaluate an integral such as
Improper Integrls Two different types of integrls cn qulify s improper. The first type of improper integrl (which we will refer to s Type I) involves evluting n integrl over n infinite region. In the grph
More informationTheoretische Physik 2: Elektrodynamik (Prof. A.S. Smith) Home assignment 4
WiSe 1 8.1.1 Prof. Dr. A.S. Smith Dipl.Phys. Ellen Fischermeier Dipl.Phys. Mtthis Sb m Lehrstuhl für Theoretische Physik I Deprtment für Physik FriedrichAlexnderUniversität ErlngenNürnberg Theoretische
More information