Physics 1402: Lecture 7 Today s Agenda


 Roger August Dorsey
 3 years ago
 Views:
Transcription
1 1 Physics 1402: Lecture 7 Tody s gend nnouncements: Lectures posted on: HW ssignments, solutions etc. Homework #2: On Msterphysics tody: due Fridy Go to msteringphysics.com Ls: Begin this week Tody s Topic : End Chpter 24: Definition of Cpcitnce Exmple Clcultions (1) Prllel Plte Cpcitor (2) Cylindricl Cpcitor (3) Isolted Sphere Energy stored in cpcitors Dielectrics Cpcitors in Circuits
2 2 Definitions & Exmples L d Cpcitnce cpcitor is device whose purpose is to store electricl energy which cn then e relesed in controlled mnner during short period of time. cpcitor consists of 2 sptilly seprted conductors which cn e chrged to Q nd Q respectively. The cpcitnce is defined s the rtio of the chrge on one conductor of the cpcitor to the potentil difference etween the conductors.
3 3 Exmple 1: Prllel Plte Cpcitor Clculte the cpcitnce. We ssume σ, σ chrge densities on ech plte with potentil difference V: d Need Q: Need V: from defn: Use Guss Lw to find E Recll: Two Infinite Sheets (into screen) Field outside the sheets is zero Gussin surfce encloses zero net chrge Field inside sheets is not zero: Gussin surfce encloses nonzero net chrge σ σ E=0 E=0 E
4 4 Exmple 1: Prllel Plte Cpcitor Clculte the cpcitnce: ssume Q,Q on pltes with potentil difference V. d s hoped for, the cpcitnce of this cpcitor depends only on its geometry (,d). Dimensions of cpcitnce C = Q/V => [C] = F(rd) = C/V = [Q/V] Exmple: Two pltes, = 10cm x 10cm d = 1cm prt => C = ε 0 /d = = 0.01m 2 /0.01m * 8.852e12 C 2 /Jm = 8.852e12 F
5 5 Lecture 7 CT 1 Suppose the cpcitor shown here is chrged to Q nd then the ttery disconnected. Now suppose I pull the pltes further prt so tht the finl seprtion is d 1. d 1 > d d 1 d If the initil cpcitnce is C 0 nd the finl cpcitnce is C 1, is ) C 1 > C 0 B) C 1 = C 0 C) C 1 < C 0 Exmple 2: Cylindricl Cpcitor Clculte the cpcitnce: ssume Q, Q on surfce of cylinders with potentil difference V. r L
6 6 Recll: Cylindricl Symmetry Gussin surfce is cylinder of rdius r nd length L Cylinder hs chrge Q E r E r pply Guss' Lw: Q L Exmple 2: Cylindricl Cpcitor Clculte the cpcitnce: ssume Q, Q on surfce of cylinders with potentil difference V. r σ σ L If we ssume tht inner cylinder hs Q, then the potentil V is positive if we tke the zero of potentil to e defined t r = : gin: depends only on system prmeters (i.e., geometry)
7 7 Lecture 7, CT 2 In ech cse elow, chrge of Q is plced on solid sphericl conductor nd chrge of Q is plced on concentric conducting sphericl shell. Let V 1 e the potentil difference etween the spheres with ( 1, ). Let V 2 e the potentil difference etween the spheres with ( 2, ). Wht is the reltionship etween V 1 nd V 2? Q Q 1 Q Q 2 () V 1 < V 2 () V 1 = V 2 (c) V 1 > V 2 Exmple 3: Isolted Sphere Cn we define the cpcitnce of single isolted sphere? The sphere hs the ility to store certin mount of chrge t given voltge (versus V=0 t infinity) Need ΔV: V = 0 V R = k e Q/R So, C = R/k e
8 8 V Cpcitors in Prllel Q 1 Q 2 V Q Find equivlent cpcitnce C in the sense tht no mesurement t, could distinguish the ove two situtions. Prllel Comintion: => Totl chrge: Q = Q 1 Q 2 Equivlent Cpcitor: C = C 1 C 2 Cpcitors in Series Q Q Q Q Find equivlent cpcitnce C in the sense tht no mesurement t, could distinguish the ove two situtions. The chrge on C 1 must e the sme s the chrge on C 2 since pplying potentil difference cross cnnot produce net chrge on the inner pltes of C 1 nd C 2. RHS: LHS:
9 9 Exmples: Comintions of Cpcitors How do we strt?? Recognize C 3 is in series with the prllel comintion on C 1 nd C 2. i.e. Energy of Cpcitor How much energy is stored in chrged cpcitor? Clculte the work provided (usully y ttery) to chrge cpcitor to / Q: Clculte incrementl work dw needed to dd chrge dq to cpcitor t voltge V: The totl work W to chrge to Q is then given y: In terms of the voltge V:
10 10 Lecture 7 CT 3 The sme cpcitor s lst time. The cpcitor is chrged to Q nd then the ttery disconnected. Then I pull the pltes further prt so tht the finl seprtion is d 1. d 1 > d If the initil energy is U 0 nd the finl cpcitnce is U 1, is d d 1 ) U 1 > U 0 B) U 1 = U 0 C) U 1 < U 0 Summry Suppose the cpcitor shown here is chrged to Q nd then the ttery disconnected. d Now suppose I pull the pltes further prt so tht the finl seprtion is d 1. How do the quntities Q, W, C, V, E chnge? Q: W: C: V: E: remins the sme.. no wy for chrge to leve. increses.. dd energy to system y seprting decreses.. since energy, ut Q remins sme increses.. since C, ut Q remins sme remins the sme.. depends only on chg density How much do these quntities chnge?.. exercise for student!! nswers:
11 11 Where is the Energy Stored? Clim: energy is stored in the Electric field itself. Think of the energy needed to chrge the cpcitor s eing the energy needed to crete the field. To clculte the energy density in the field, first consider the constnt field generted y prllel plte cpcitor: The Electric field is given y: The energy density u in the field is given y: Units: J/m 3 Dielectrics Empiricl oservtion: Inserting nonconducting mteril etween the pltes of cpcitor chnges the VLUE of the cpcitnce. Definition: The dielectric constnt of mteril is the rtio of the cpcitnce when filled with the dielectric to tht without it. i.e. κ vlues re lwys > 1 (e.g., glss = 5.6; wter = 78) They INCRESE the cpcitnce of cpcitor (generlly good, since it is hrd to mke ig cpcitors They permit more energy to e stored on given cpcitor thn otherwise with vcuum (i.e., ir)
12 12 Prllel Plte Exmple Chrge prllel plte cpcitor filled with vcuum (ir) to potentil difference V 0. n mount of chrge Q = C V 0 is deposited on ech plte. Now insert mteril with dielectric constnt κ. Chrge Q remins constnt Voltge decreses from V 0 to Electric field decreses lso: So, C = κ C 0 Lecture 7, CT 3 Two prllel plte cpcitors re identicl (sme, sme d) except tht C 1 hs hlf of the spce etween the pltes filled with mteril of dielectric constnt κ s shown. If oth cpcitors re given the sme mount of chrge Q, wht is the reltion etween E 1, the electric field in the ir of C 1, nd E 2, the electric field in the ir of C 2 κ Q E 1 =? Q Q C 1 E 2 =? C 2 Q () E 1 < E 2 () E 1 = E 2 (c) E 1 > E 2
CAPACITORS 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 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 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 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 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 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 informationExam 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
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
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 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 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 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 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 202, Lecture 10. Basic Circuit Components
Physics 202, Lecture 10 Tody s Topics DC Circuits (Chpter 26) Circuit components Kirchhoff s Rules RC Circuits Bsic Circuit Components Component del ttery, emf Resistor Relistic Bttery (del) wire Cpcitor
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 information200 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 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 informationPhysics Lecture 14: MON 29 SEP
Physics 2113 Physics 2113 Lecture 14: MON 29 SEP CH25: Cpcitnce Von Kleist ws le to store electricity in the jr. Unknowingly, he h ctully invente novel evice to store potentil ifference. The wter in the
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 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 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 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 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 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 informationPotential Changes Around a Circuit. You must be able to calculate potential changes around a closed loop.
Tody s gend: Potentil Chnges Around Circuit. You must e le to clculte potentil chnges round closed loop. Electromotive force (EMF), Terminl Voltge, nd Internl Resistnce. You must e le to incorporte ll
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 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 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 informationI1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3
2 The Prllel Circuit Electric Circuits: Figure 2 elow show ttery nd multiple resistors rrnged in prllel. Ech resistor receives portion of the current from the ttery sed on its resistnce. The split is
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 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 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 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 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 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 informationResistors. Consider a uniform cylinder of material with mediocre to poor to pathetic conductivity ( )
10/25/2005 Resistors.doc 1/7 Resistors Consider uniform cylinder of mteril with mediocre to poor to r. pthetic conductivity ( ) ˆ This cylinder is centered on the xis, nd hs length. The surfce re of the
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 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 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 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 informationUnit 3: Direct current and electric resistance Electric current and movement of charges. Intensity of current and drift speed. Density of current in
Unit 3: Direct current nd electric resistnce Electric current nd movement of chrges. ntensity of current nd drift speed. Density of current in homogeneous currents. Ohm s lw. esistnce of homogeneous conductor
More informationDesigning Information Devices and Systems I Spring 2018 Homework 8
EECS 16A Designing Informtion Devices nd Systems I Spring 2018 Homework 8 This homework is due Mrch 19, 2018, t 23:59. Selfgrdes re due Mrch 22, 2018, t 23:59. Sumission Formt Your homework sumission
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 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 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 informationInterpreting Integrals and the Fundamental Theorem
Interpreting Integrls nd the Fundmentl Theorem Tody, we go further in interpreting the mening of the definite integrl. Using Units to Aid Interprettion We lredy know tht if f(t) is the rte of chnge of
More informationEMF Notes 9; Electromagnetic Induction ELECTROMAGNETIC INDUCTION
EMF Notes 9; Electromgnetic nduction EECTOMAGNETC NDUCTON (Y&F Chpters 3, 3; Ohnin Chpter 3) These notes cover: Motionl emf nd the electric genertor Electromgnetic nduction nd Frdy s w enz s w nduced electric
More informationA, Electromagnetic Fields Final Exam December 14, 2001 Solution
304351, Electrognetic Fiels Finl Ex Deceer 14, 2001 Solution 1. e9.8. In chpter9.proles.extr.two loops, e of thin wire crry equl n opposite currents s shown in the figure elow. The rius of ech loop is
More informationPhysics 1B schedule Winter Instructor: D.N. Basov Ch18: 1,3,5,7,13,17,21,26,31,33,35,
Week 1:Jn 5 : Jn 1 Physics 1B scheule Winter 009. Instructor: D.N. Bsov bsov@ucs.eu Mon We Friy Lecture: the Electric fiel Lecture: Intro, 15.115.3 Lecture: The oulomb lw, Lecture: Electric Flux & Guss
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 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 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 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 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 informationHomework Assignment 6 Solution Set
Homework Assignment 6 Solution Set PHYCS 440 Mrch, 004 Prolem (Griffiths 4.6 One wy to find the energy is to find the E nd D fields everywhere nd then integrte the energy density for those fields. We know
More informationWhat s in Chapter 13?
Are nd volume 13 Wht s in Chpter 13? 13 01 re 13 0 Are of circle 13 03 res of trpeziums, kites nd rhomuses 13 04 surfce re of rectngulr prism 13 05 surfce re of tringulr prism 13 06 surfce re of cylinder
More informationPhysics 1B: Review for Final Exam Solutions
Physics B: eview for Finl Exm s Andrew Forrester June 6, 2008 In this worksheet we review mteril from the following chpters of Young nd Freedmn plus some dditionl concepts): Chpter 3: Periodic Motion Chpter
More informationDensity of Energy Stored in the Electric Field
Density of Energy Stored in the Electric Field Deprtment of Physics, Cornell University c Tomás A. Aris October 14, 01 Figure 1: Digrm of Crtesin vortices from René Descrtes Principi philosophie, published
More informationF is on a moving charged particle. F = 0, if B v. (sin " = 0)
F is on moving chrged prticle. Chpter 29 Mgnetic Fields Ech mgnet hs two poles, north pole nd south pole, regrdless the size nd shpe of the mgnet. Like poles repel ech other, unlike poles ttrct ech other.
More informationLecture 11: Potential Gradient and Capacitor Review:
Lectue 11: Potentil Gdient nd Cpcito Review: Two wys to find t ny point in spce: Sum o Integte ove chges: q 1 1 q 2 2 3 P i 1 q i i dq q 3 P 1 dq xmple of integting ove distiution: line of chge ing of
More informationThe Velocity Factor of an Insulated TwoWire Transmission Line
The Velocity Fctor of n Insulted TwoWire Trnsmission Line Problem Kirk T. McDonld Joseph Henry Lbortories, Princeton University, Princeton, NJ 08544 Mrch 7, 008 Estimte the velocity fctor F = v/c nd the
More information196 Circuit Analysis with PSpice: A Simplified Approach
196 Circuit Anlysis with PSpice: A Simplified Approch i, A v L t, min i SRC 5 μf v C FIGURE P7.3 () the energy stored in the inductor, nd (c) the instntneous power input to the inductor. (Dul of Prolem
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 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 informationProblem 1. Solution: a) The coordinate of a point on the disc is given by r r cos,sin,0. The potential at P is then given by. r z 2 rcos 2 rsin 2
Prolem Consider disc of chrge density r r nd rdius R tht lies within the xyplne. The origin of the coordinte systems is locted t the center of the ring. ) Give the potentil t the point P,,z in terms of,r,
More informationHow do we solve these things, especially when they get complicated? How do we know when a system has a solution, and when is it unique?
XII. LINEAR ALGEBRA: SOLVING SYSTEMS OF EQUATIONS Tody we re going to tlk out solving systems of liner equtions. These re prolems tht give couple of equtions with couple of unknowns, like: 6= x + x 7=
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 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 informationLinear Inequalities. Work Sheet 1
Work Sheet 1 Liner Inequlities RentHep, cr rentl compny,chrges $ 15 per week plus $ 0.0 per mile to rent one of their crs. Suppose you re limited y how much money you cn spend for the week : You cn spend
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 informationPhysics 202, Lecture 14
Physics 202, Lecture 14 Tody s Topics Sources of the Mgnetic Field (Ch. 28) BiotSvrt Lw Ampere s Lw Mgnetism in Mtter Mxwell s Equtions Homework #7: due Tues 3/11 t 11 PM (4th problem optionl) Mgnetic
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 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 informationDesigning Information Devices and Systems I Fall 2016 Babak Ayazifar, Vladimir Stojanovic Homework 6. This homework is due October 11, 2016, at Noon.
EECS 16A Designing Informtion Devices nd Systems I Fll 2016 Bk Ayzifr, Vldimir Stojnovic Homework 6 This homework is due Octoer 11, 2016, t Noon. 1. Homework process nd study group Who else did you work
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 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 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 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 informationPHYS102  Electric Energy  Capacitors
PHYS102  lectric nerg  Cpcitors Dr. Suess Februr 14, 2007 Plcing Chrges on Conuctors................................................. 2 Plcing Chrges on Conuctors II................................................
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 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 informationDate Lesson Text TOPIC Homework. Solving for Obtuse Angles QUIZ ( ) More Trig Word Problems QUIZ ( )
UNIT 5 TRIGONOMETRI RTIOS Dte Lesson Text TOPI Homework pr. 4 5.1 (48) Trigonometry Review WS 5.1 # 3 5, 9 11, (1, 13)doso pr. 6 5. (49) Relted ngles omplete lesson shell & WS 5. pr. 30 5.3 (50) 5.3 5.4
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 informationReview of Gaussian Quadrature method
Review of Gussin Qudrture method Nsser M. Asi Spring 006 compiled on Sundy Decemer 1, 017 t 09:1 PM 1 The prolem To find numericl vlue for the integrl of rel vlued function of rel vrile over specific rnge
More informationMathematics. Area under Curve.
Mthemtics Are under Curve www.testprepkrt.com Tle of Content 1. Introduction.. Procedure of Curve Sketching. 3. Sketching of Some common Curves. 4. Are of Bounded Regions. 5. Sign convention for finding
More informationThe area under the graph of f and above the xaxis between a and b is denoted by. f(x) dx. π O
1 Section 5. The Definite Integrl Suppose tht function f is continuous nd positive over n intervl [, ]. y = f(x) x The re under the grph of f nd ove the xxis etween nd is denoted y f(x) dx nd clled the
More informationELETROSTATICS Part II: BASICS
GROWING WITH ONPTS: Physics LTROSTTIS Prt II: SIS Presence of chrge on ny oject cretes n electrosttic fiel roun it n in turn n electricl potentil is experience roun the oject. This phenomenon hs foun ppliction
More informationPhysics 202, Lecture 13. Today s Topics
Physics 202, Lecture 13 Tody s Topics Sources of the Mgnetic Field (Ch. 30) Clculting the B field due to currents BiotSvrt Lw Emples: ring, stright wire Force between prllel wires Ampere s Lw: infinite
More informationEECS 141 Due 04/19/02, 5pm, in 558 Cory
UIVERSITY OF CALIFORIA College of Engineering Deprtment of Electricl Engineering nd Computer Sciences Lst modified on April 8, 2002 y Tufn Krlr (tufn@eecs.erkeley.edu) Jn M. Rey, Andrei Vldemirescu Homework
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 informationLecture 3. Limits of Functions and Continuity
Lecture 3 Limits of Functions nd Continuity Audrey Terrs April 26, 21 1 Limits of Functions Notes I m skipping the lst section of Chpter 6 of Lng; the section bout open nd closed sets We cn probbly live
More information10/25/2005 Section 5_2 Conductors empty.doc 1/ Conductors. We have been studying the electrostatics of freespace (i.e., a vacuum).
10/25/2005 Section 5_2 Conductors empty.doc 1/3 52 Conductors Reding Assignment: pp. 122132 We hve been studying the electrosttics of freespce (i.e., vcuum). But, the universe is full of stuff! Q: Does
More information5.1 How do we Measure Distance Traveled given Velocity? Student Notes
. How do we Mesure Distnce Trveled given Velocity? Student Notes EX ) The tle contins velocities of moving cr in ft/sec for time t in seconds: time (sec) 3 velocity (ft/sec) 3 A) Lel the xxis & yxis
More informationChapter 4: Techniques of Circuit Analysis. Chapter 4: Techniques of Circuit Analysis
Chpter 4: Techniques of Circuit Anlysis Terminology NodeVoltge Method Introduction Dependent Sources Specil Cses MeshCurrent Method Introduction Dependent Sources Specil Cses Comprison of Methods Source
More informationCHAPTER 20: Second Law of Thermodynamics
CHAER 0: Second Lw of hermodynmics Responses to Questions 3. kg of liquid iron will hve greter entropy, since it is less ordered thn solid iron nd its molecules hve more therml motion. In ddition, het
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 informationf(x) dx, If one of these two conditions is not met, we call the integral improper. Our usual definition for the value for the definite integral
Improper Integrls Every time tht we hve evluted definite integrl such s f(x) dx, we hve mde two implicit ssumptions bout the integrl:. The intervl [, b] is finite, nd. f(x) is continuous on [, b]. If one
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 informationElectric Potential. Electric Potential Video: Section 1 4. Electric Fields and WORK 9/3/2014. IB Physics SL (Year Two) Wednesday, September 3, 2014
9/3/014 lectric Potentil IB Physics SL (Yer Two) Wenesy, Septemer 3, 014 lectric Potentil Vieo: Section 1 4 lectric Fiels n WORK In orer to rin two like chres ner ech other work must e one. In orer to
More informationChapter 3 Single Random Variables and Probability Distributions (Part 2)
Chpter 3 Single Rndom Vriles nd Proilit Distriutions (Prt ) Contents Wht is Rndom Vrile? Proilit Distriution Functions Cumultive Distriution Function Proilit Densit Function Common Rndom Vriles nd their
More information