Chapter 22 : Electric potential


 Vivien Francis
 4 years ago
 Views:
Transcription
1 Chapter 22 : Electric potential What is electric potential? How does it relate to potential energy? How does it relate to electric field? Some simple applications
2 What does it mean when it says 1.5 Volts on the battery? The electric potential difference between the ends is 1.5 Volts
3 230 V 1.5 V 100,000 V So what is a volt?
4 The electric potential difference VV in volts between two points is the work in Joules needed to move 1 C of charge between those points WW = qq VV W = work done [in J] q = charge [in C] V = potential difference [in V] VV is measured in volts [V] : 1 V = 1 J/C
5 The electric potential difference VV in volts between two points is the work in Joules needed to move 1 C of charge between those points WW = qq VV The 1.5 V battery does 1.5 J of work for every 1 C of charge flowing round the circuit
6 Potential energy What is this thing called potential? Potential energy crops up everywhere in physics
7 Potential energy Potential energy U is the energy stored in a system (when work is done against a force) e.g. force of gravity FF = mmmm Work = Force x Distance FF h WW = FF h = mmmmm UU = mmmmm
8 Potential energy Potential energy may be released and converted into other forms (such as kinetic energy) Work is done, increasing the potential energy
9 Potential energy Potential energy difference is the only thing that matters not the reference (or zero) level For example, applying conservation of energy to a mechanics problem: Final energy = Initial energy KKKK ffffffffff + PPPP ffffffffff = KKKK iiiiiiiiiiiiii + PPPP iiiiiiiiiiiiii KKKK ffffffffff = KKKK iiiiiiiiiiiiii + (PPPP iiiiiiiiiiiiii PPPP ffffffffff ) Difference in potential energy
10 Potential energy Potential energy difference doesn t depend on the path only on the two points A and B
11 Potential energy Potential energy U is the energy stored in a system second example e.g. stretching a spring FF FF = kkkk Work = Force x Distance Force is varying with distance! WW = kkkk dddd = 1 2 kkxx2 xx UU = 1 2 kkxx2
12 e.g. moving a charge through an electric field EE qq xx FF FF = qqqq (minus sign because the force is opposite to E) Work = Force x Distance WW = FF xx = qqqq xx Potential difference VV is work needed to move 1C of charge: WW = qq VV Equate: qq VV = qqqq xx EE = VV xx
13 Electric field is the gradient of potential EE = VV High V EE Low V VV xx Positive charges feel a force from high to low potential xx xx Negative charges feel a force from low to high potential
14 Two parallel plates have equal and opposite charge. Rank the indicated positions from highest to lowest electric potential A B D C A=C, B=D 2. A, B, C, D 3. C, D=B, A 4. A, B=D, C 0% 0% 0% 0%
15 Analogy with gravitational potential Gravitational potential difference exerts force on mass Electric potential difference exerts force on charge VV qq xx
16 Electric field is the gradient of potential EE = VV High V EE Low V xx The dashed lines are called equipotentials (lines of constant V) Electric field lines are perpendicular to equipotentials It takes no work to move a charge along an equipotential (work done = dddd = FF. dddd = qqee. dddd = 0)
17 Summary for two plates at potential difference V EE Electric field is the potential gradient EE = VV dd Work W to move charge q from ve to +ve plate dd WW = qq VV
18 Link to potential energy The electric potential difference VV between two points is the work needed to move 1 C of charge between those points WW = qq VV This work is also equal to the potential energy difference UU between those points UU = qq VV Potential V = potential energy per unit charge U/q
19 An electron is placed at X on the negative plate of a pair of charged parallel plates. For the maximum work to be done on it, which point should it be moved to? 1. A 2. B 3. C 4. D 5. A or C 6. C or D X B A D C % 0% 0% 0% 0% 0%
20 What is the electric potential near a charge +Q? Work = Force x Distance FF = kk QQ qq +q xx 2 Force is varying with distance, need integral! rr rr kk QQ qq WW = FF dddd = xx 2 dddd = kk QQ qq rr xx +Q Potential energy UU = kk QQ qq rr Electric potential VV = UU qq = kk QQ rr
21 What is the electric potential near a charge +Q? +q rr +Q Electric potential VV = kk QQ rr
22 Exercise: a potential difference of 200 V is applied across a pair of parallel plates m apart. (a) calculate E and draw its direction between the plates. The electric field is the gradient in potential EE = VV xx = = VV mm 1 [oooo NN CC 1 ] VV = 200 VV = 0 EE +ve plate ve plate
23 Exercise: a potential difference of 200 V is applied across a pair of parallel plates m apart. (b) an electron is placed between the plates, next to the negative plate. Calculate the force on the electron, the acceleration of the electron, and the time it takes to reach the other plate. Force FF = qqqq = ( ) ( ) = NN FF = mmmm Acceleration aa = FF mm EE ee +ve plate ve plate = = mm ss 2 dd = 1 2 aatt2 Time tt = 2dd aa tt = = ss e = 1.6 x C; m e = 9.1 x kg
24 Exercise: a potential difference of 200 V is applied across a pair of parallel plates m apart. (c) calculate the work done on the electron as it travels between the plates. The potential difference is the work done on 1C charge Work WW = qqqq = = JJ EE ee +ve plate ve plate e = 1.6 x C; m e = 9.1 x kg
25 Chapter 22 summary Electric potential difference V is the work done when moving unit charge: WW = qqqq The electric potential energy is therefore also given by: UU = qqqq The electric field is the gradient of the potential: EE = VV/ xx Charges feel a force from high electric potential to low potential
Revision : Thermodynamics
Revision : Thermodynamics Formula sheet Formula sheet Formula sheet Thermodynamics key facts (1/9) Heat is an energy [measured in JJ] which flows from high to low temperature When two bodies are in thermal
More informationHeat, Work, and the First Law of Thermodynamics. Chapter 18 of Essential University Physics, Richard Wolfson, 3 rd Edition
Heat, Work, and the First Law of Thermodynamics Chapter 18 of Essential University Physics, Richard Wolfson, 3 rd Edition 1 Different ways to increase the internal energy of system: 2 Joule s apparatus
More informationWork, Energy, and Power. Chapter 6 of Essential University Physics, Richard Wolfson, 3 rd Edition
Work, Energy, and Power Chapter 6 of Essential University Physics, Richard Wolfson, 3 rd Edition 1 With the knowledge we got so far, we can handle the situation on the left but not the one on the right.
More informationWorksheets for GCSE Mathematics. Quadratics. mrmathematics.com Maths Resources for Teachers. Algebra
Worksheets for GCSE Mathematics Quadratics mrmathematics.com Maths Resources for Teachers Algebra Quadratics Worksheets Contents Differentiated Independent Learning Worksheets Solving x + bx + c by factorisation
More informationLecture 3 Transport in Semiconductors
EE 471: Transport Phenomena in Solid State Devices Spring 2018 Lecture 3 Transport in Semiconductors Bryan Ackland Department of Electrical and Computer Engineering Stevens Institute of Technology Hoboken,
More informationSecondary 3H Unit = 1 = 7. Lesson 3.3 Worksheet. Simplify: Lesson 3.6 Worksheet
Secondary H Unit Lesson Worksheet Simplify: mm + 2 mm 2 4 mm+6 mm + 2 mm 2 mm 20 mm+4 5 2 9+20 2 0+25 4 +2 2 + 2 8 2 6 5. 2 yy 2 + yy 6. +2 + 5 2 2 2 0 Lesson 6 Worksheet List all asymptotes, holes and
More informationWorksheets for GCSE Mathematics. Algebraic Expressions. Mr Black 's Maths Resources for Teachers GCSE 19. Algebra
Worksheets for GCSE Mathematics Algebraic Expressions Mr Black 's Maths Resources for Teachers GCSE 19 Algebra Algebraic Expressions Worksheets Contents Differentiated Independent Learning Worksheets
More informationSECTION 4: ULTRACAPACITORS. ESE 471 Energy Storage Systems
SECTION 4: ULTRACAPACITORS ESE 471 Energy Storage Systems 2 Introduction Ultracapacitors 3 Capacitors are electrical energy storage devices Energy is stored in an electric field Advantages of capacitors
More informationMathematics Ext 2. HSC 2014 Solutions. Suite 403, 410 Elizabeth St, Surry Hills NSW 2010 keystoneeducation.com.
Mathematics Ext HSC 4 Solutions Suite 43, 4 Elizabeth St, Surry Hills NSW info@keystoneeducation.com.au keystoneeducation.com.au Mathematics Extension : HSC 4 Solutions Contents Multiple Choice... 3 Question...
More informationRotational Motion. Chapter 10 of Essential University Physics, Richard Wolfson, 3 rd Edition
Rotational Motion Chapter 10 of Essential University Physics, Richard Wolfson, 3 rd Edition 1 We ll look for a way to describe the combined (rotational) motion 2 Angle Measurements θθ ss rr rrrrrrrrrrrrrr
More informationExam 2 Fall 2015
1 95.144 Exam 2 Fall 2015 Section instructor Section number Last/First name Last 3 Digits of Student ID Number: Show all work. Show all formulas used for each problem prior to substitution of numbers.
More informationMath 171 Spring 2017 Final Exam. Problem Worth
Math 171 Spring 2017 Final Exam Problem 1 2 3 4 5 6 7 8 9 10 11 Worth 9 6 6 5 9 8 5 8 8 8 10 12 13 14 15 16 17 18 19 20 21 22 Total 8 5 5 6 6 8 6 6 6 6 6 150 Last Name: First Name: Student ID: Section:
More informationGravitation. Chapter 8 of Essential University Physics, Richard Wolfson, 3 rd Edition
Gravitation Chapter 8 of Essential University Physics, Richard Wolfson, 3 rd Edition 1 What you are about to learn: Newton's law of universal gravitation About motion in circular and other orbits How to
More informationCoulomb s Law and Coulomb s Constant
PreLab Quiz / PHYS 224 Coulomb s Law and Coulomb s Constant Your Name: Lab Section: 1. What will you investigate in this lab? 2. Consider a capacitor created when two identical conducting plates are placed
More informationElectrostatics Notes 2 Electric Field on a Single Charge
Electrostatics Notes 2 Electric Field on a Single Charge There are many similarities between gravitational and electrostatic forces. One such similarity is that both forces can be exerted on objects that
More informationElectric Field and Electric Potential (A)
PreLab Quiz / PHYS 224 Electric Field and Electric Potential (A) Your Name Lab Section 1. What do you investigate in this lab? 2. In a uniform electric field between two parallel plates, a potential probe
More informationElectrostatics Notes 1 Charges and Coulomb s Law
Electrostatics Notes 1 Charges and Coulomb s Law Matter is made of particles which are or charged. The unit of charge is the ( ) Charges are, meaning that they cannot be It is thought that the total charge
More informationElectric Potential Energy
Electric Potential Energy the electric potential energy of two charges depends on the distance between the charges when two like charges are an infinite distance apart, the potential energy is zero An
More information10.1 Three Dimensional Space
Math 172 Chapter 10A notes Page 1 of 12 10.1 Three Dimensional Space 2D space 0 xx.. xx, 0 yy yy, PP(xx, yy) [Fig. 1] Point PP represented by (xx, yy), an ordered pair of real nos. Set of all ordered
More information1. The graph of a function f is given above. Answer the question: a. Find the value(s) of x where f is not differentiable. Ans: x = 4, x = 3, x = 2,
1. The graph of a function f is given above. Answer the question: a. Find the value(s) of x where f is not differentiable. x = 4, x = 3, x = 2, x = 1, x = 1, x = 2, x = 3, x = 4, x = 5 b. Find the value(s)
More informationThermodynamic Cycles
Thermodynamic Cycles Content Thermodynamic Cycles Carnot Cycle Otto Cycle Rankine Cycle Refrigeration Cycle Thermodynamic Cycles Carnot Cycle Derivation of the Carnot Cycle Efficiency Otto Cycle Otto Cycle
More informationSemester 2 Physics (SF 026) Lecture: BP 3 by Yew Sze Fiona Website:
Semester 2 Physics (SF 026) Lecture: BP 3 by Yew Sze Ling @ Fiona Website: http://yslphysics.weebly.com/ Chapter 1: Electrostatics The study of electric charges at rest, the forces between them and the
More informationSupport Vector Machines. CSE 4309 Machine Learning Vassilis Athitsos Computer Science and Engineering Department University of Texas at Arlington
Support Vector Machines CSE 4309 Machine Learning Vassilis Athitsos Computer Science and Engineering Department University of Texas at Arlington 1 A Linearly Separable Problem Consider the binary classification
More information10.4 The Cross Product
Math 172 Chapter 10B notes Page 1 of 9 10.4 The Cross Product The cross product, or vector product, is defined in 3 dimensions only. Let aa = aa 1, aa 2, aa 3 bb = bb 1, bb 2, bb 3 then aa bb = aa 2 bb
More informationExam Programme VWO Mathematics A
Exam Programme VWO Mathematics A The exam. The exam programme recognizes the following domains: Domain A Domain B Domain C Domain D Domain E Mathematical skills Algebra and systematic counting Relationships
More informationPhysics 1051 Lecture 14. Electric Potential. Physics General Physics II Oscillations, Waves and Magnetism
Physics 1051 Lecture 14 Electric Potential Lecture 14  Contents 20.0 Describing Electric Phenomenon using Electric Potential 20.1 Electric Potential Difference and Electric Potential 20.2 Potential Difference
More informationGrover s algorithm. We want to find aa. Search in an unordered database. QC oracle (as usual) Usual trick
Grover s algorithm Search in an unordered database Example: phonebook, need to find a person from a phone number Actually, something else, like hard (e.g., NPcomplete) problem 0, xx aa Black box ff xx
More informationL.2 Formulas and Applications
43 L. Formulas and Applications In the previous section, we studied how to solve linear equations. Those skills are often helpful in problem solving. However, the process of solving an application problem
More information1. The diagram shows the electric field lines produced by an electrostatic focussing device.
1. The diagram shows the electric field lines produced by an electrostatic focussing device. Which one of the following diagrams best shows the corresponding equipotential lines? The electric field lines
More informationRational Expressions and Functions
Rational Expressions and Functions In the previous two chapters we discussed algebraic expressions, equations, and functions related to polynomials. In this chapter, we will examine a broader category
More informationRecall Gravitational Potential Energy
Electric Potential Recall Gravitational Potential Energy How can you increase the gravitational potential energy of an object? Raise it above the surface of the earth. The amount of work done against earth
More informationQuiz 3 Info. Average 6.40 St. Dev Quiz 3 Scores. 2/25/2014 Physics 132 1
Quiz 3 Info Quiz 3 Scores Average 6.40 St. Dev 2.62 35 30 25 20 15 10 5 0 0 1 2 3 4 5 6 7 8 9 10 2/25/2014 Physics 132 1 1. (3 pts) A particular reaction has a negative enthalpy change AND a negative entropy
More informationQuestion 20.1a Electric Potential Energy I
Question 20.1a Electric Potential Energy I A proton and an electron are in a constant electric field created by oppositely charged plates. You release the proton from the positive side and the electron
More informationChapter 19 Electric Potential and Electric Field
Chapter 19 Electric Potential and Electric Field The electrostatic force is a conservative force. Therefore, it is possible to define an electrical potential energy function with this force. Work done
More informationMathematics Paper 2 Grade 12 Preliminary Examination 2017
Mathematics Paper 2 Grade 12 Preliminary Examination 2017 DURATION: 180 min EXAMINER: R. Obermeyer MARKS: 150 MODERATOR: A. Janisch Date: 15 September 2017 External Moderator: I. Atteridge INSTRUCTIONS:
More informationUnit WorkBook 4 Level 4 ENG U8 Mechanical Principles 2018 UniCourse Ltd. All Rights Reserved. Sample
2018 UniCourse Ltd. A Rights Reserved. Pearson BTEC Levels 4 Higher Nationals in Engineering (RQF) Unit 8: Mechanical Principles Unit Workbook 4 in a series of 4 for this unit Learning Outcome 4 Translational
More informationModel answers for the 2012 Electricity Revision booklet:
Model answers for the 0 Electricity Revision booklet: SAMPLE ASSESSMENT SCHEDULE Physics 973 (.6): Demonstrate understanding of electricity and electromagnetism Assessment Criteria Achievement Achievement
More informationPHY103A: Lecture # 4
Semester II, 201718 Department of Physics, IIT Kanpur PHY103A: Lecture # 4 (Text Book: Intro to Electrodynamics by Griffiths, 3 rd Ed.) Anand Kumar Jha 10Jan2018 Notes The Solutions to HW # 1 have been
More informationSECTION 5: CAPACITANCE & INDUCTANCE. ENGR 201 Electrical Fundamentals I
SECTION 5: CAPACITANCE & INDUCTANCE ENGR 201 Electrical Fundamentals I 2 Fluid Capacitor Fluid Capacitor 3 Consider the following device: Two rigid hemispherical shells Separated by an impermeable elastic
More informationLecture 2: Plasma particles with E and B fields
Lecture 2: Plasma particles with E and B fields Today s Menu Magnetized plasma & Larmor radius Plasma s diamagnetism Charged particle in a multitude of EM fields: drift motion ExB drift, gradient drift,
More informationSECTION 7: STEADYSTATE ERROR. ESE 499 Feedback Control Systems
SECTION 7: STEADYSTATE ERROR ESE 499 Feedback Control Systems 2 Introduction SteadyState Error Introduction 3 Consider a simple unityfeedback system The error is the difference between the reference
More information(1) Correspondence of the density matrix to traditional method
(1) Correspondence of the density matrix to traditional method New method (with the density matrix) Traditional method (from thermal physics courses) ZZ = TTTT ρρ = EE ρρ EE = dddd xx ρρ xx ii FF = UU
More informationHaar Basis Wavelets and Morlet Wavelets
Haar Basis Wavelets and Morlet Wavelets September 9 th, 05 Professor Davi Geiger. The Haar transform, which is one of the earliest transform functions proposed, was proposed in 90 by a Hungarian mathematician
More informationEndofChapter Exercises
EndofChapter Exercises Exercises 1 12 are primarily conceptual questions designed to see whether you understand the main concepts of the chapter. 1. (a) If the electric field at a particular point is
More informationModule 7 (Lecture 25) RETAINING WALLS
Module 7 (Lecture 25) RETAINING WALLS Topics Check for Bearing Capacity Failure Example Factor of Safety Against Overturning Factor of Safety Against Sliding Factor of Safety Against Bearing Capacity Failure
More informationAcceleration due to Gravity
1. Object Acceleration due to Gravity To determine the acceleration due to gravity by different methods. 2. Apparatus Balance, ball bearing, clamps, electric timers, meter stick, paper strips, precision
More informationThe Bose Einstein quantum statistics
Page 1 The Bose Einstein quantum statistics 1. Introduction Quantized lattice vibrations Thermal lattice vibrations in a solid are sorted in classical mechanics in normal modes, special oscillation patterns
More informationC = V Q. To find the capacitance of two conductors:
Capacitance Capacitance is a measure of the ability of two conductors to store charge when a given potential difference is established between them. Two conductors, on one of which is charge +Q and on
More informationQuantum Mechanics. An essential theory to understand properties of matter and light. Chemical Electronic Magnetic Thermal Optical Etc.
Quantum Mechanics An essential theory to understand properties of matter and light. Chemical Electronic Magnetic Thermal Optical Etc. Fall 2018 Prof. Sergio B. Mendes 1 CHAPTER 3 Experimental Basis of
More informationUnit 2. Current, Voltage and Resistance
Strand G. Electricity Unit 2. Current, Voltage and Resistance Contents Page Current 2 Potential Difference, Electromotive Force and Power 5 Resistance and Ohm s Law 9 G.2.1. Current In a metallic conductor
More informationStrand H Unit 3: Electromagnetic induction. Text Answers. Exercise H.3.1 Answers. a force of F = N. Since F = Bev,
Exercise H.3.1 Answers 1. The magnetic field B = 0.6T and the electron of charge 1.6 1019 C experiences a force of F = 2.88 1015 N. Since F = Bev, vv = FF BBBB = 2.88 10 15 NN 1.6 10 19 CC 0.6TT = 30000mmss
More informationPhysics 141 Second MidTerm Examination Spring 2015 March 31, 2015
Physics 141 Second MidTerm Examination Spring 2015 March 31, 2015 Your Number Solutions LAST Name (print) FIRST Name (print) Signature: UIN #: Your Section: Barkan 9 am Barkan 11 am Goeckner 3 pm PROBLEM
More informationUnit WorkBook 2 Level 4 ENG U13 Fundamentals of Thermodynamics and Heat Engines UniCourse LTD. All Rights Reserved. Sample
Pearson BTEC Levels 4 Higher Nationals in Engineering (RQF) Unit 13: Fundamentals of Thermodynamics and Heat Engines Unit Workbook 2 in a series of 4 for this unit Learning Outcome 2 Plant Equipment Page
More information3. Mathematical Modelling
3. Mathematical Modelling 3.1 Modelling principles 3.1.1 Model types 3.1.2 Model construction 3.1.3 Modelling from first principles 3.2 Models for technical systems 3.2.1 Electrical systems 3.2.2 Mechanical
More informationChapter 2. Electric Fields Field Intensity Due to a Point Charge
Chapter 2 Electric Fields An electric field exists in a region if electrical forces are exerted on charged bodies in that region. The direction of an electric field at a point is the direction in which
More informationIntroduction to Electrical Theory and DC Circuits
Introduction to Electrical Theory and DC Circuits For Engineers of All Disciplines by James Doane, PhD, PE Contents 1.0 Course Overview... 4 2.0 Fundamental Concepts... 4 2.1 Electric Charges... 4 2.1.1
More informationPHYSICS 12 NAME: Electrostatics Review
NAME: Electrostatics Review 1. The diagram below shows two positive charges of magnitude Q and 2Q. Which vector best represents the direction of the electric field at point P, which is equidistant from
More informationChapter 6. Work and Energy
Chapter 6 Work and Energy 6.1 Work Done by a Constant Force W = Fs 1 N m = 1 joule ( J) 6.1 Work Done by a Constant Force W = ( F cosθ )s cos0 = 1 cos90 = 0 cos180 = 1 6.1 Work Done by a Constant Force
More informationLos Altos Physics Honors. Electrostatics: Electric Fields, Electric Forces, Electric Potentials and. Electric Potential Energy.
Los Altos Physics Honors Electrostatics: Electric Fields, Electric Forces, Electric Potentials and Electric Potential Energy Workbook adam.randall@mvla.net www.laphysics.com dls.mvla.net/los_altos Spring
More informationElectric potential energy The concept of electric potential and potential difference Motion of charges in electric field
In this chapter, you will learn: Electric potential energy The concept of electric potential and potential difference Motion of charges in electric field 2.1 Electric potential energy When a charged particle
More informationEquation Sheet, Phys 1321 (Exam II), University of Houston, Fall 2016 Instructor: Dr. W. P. Su
vv (tt) = ddrr (tt) dddd vv aaaaaa = Δrr Δtt aa (tt) = ddvv (tt) dddd aa aaaaaa = Δvv Δtt Equation Sheet, Phys 1321 (Exam II), University of Houston, Fall 2016 Instructor: Dr. W. P. Su AAAAAA. ssssssssss
More informationElectric Potential Energy Chapter 16
Electric Potential Energy Chapter 16 Electric Energy and Capacitance Sections: 1, 2, 4, 6, 7, 8, 9 The electrostatic force is a conservative force It is possible to define an electrical potential energy
More informationTerms of Use. Copyright Embark on the Journey
Terms of Use All rights reserved. No part of this packet may be reproduced, stored in a retrieval system, or transmitted in any form by any means  electronic, mechanical, photocopies, recording, or otherwise
More informationBHASVIC MαTHS. Skills 1
PART A: Integrate the following functions with respect to x: (a) cos 2 2xx (b) tan 2 xx (c) (d) 2 PART B: Find: (a) (b) (c) xx 1 2 cosec 2 2xx 2 cot 2xx (d) 2cccccccccc2 2xx 2 ccccccccc 5 dddd Skills 1
More informationBig Bang Planck Era. This theory: cosmological model of the universe that is best supported by several aspects of scientific evidence and observation
Big Bang Planck Era Source: http://www.crystalinks.com/bigbang.html Source: http://www.odec.ca/index.htm This theory: cosmological model of the universe that is best supported by several aspects of scientific
More informationFACULTY OF EDUCATION. Department of Curriculum and Pedagogy. Physics Momentum. Science and Mathematics Education Research Group
FACULTY OF EDUCATION Department of Curriculum and Pedagogy Physics Momentum Science and Mathematics Education Research Group Supported by UBC Teaching and Learning Enhancement Fund 20122015 Question MomentumTitle
More informationWorksheets for GCSE Mathematics. Solving Equations. Mr Black's Maths Resources for Teachers GCSE 19. Algebra
Worksheets for GCSE Mathematics Solving Equations Mr Black's Maths Resources for Teachers GCSE 19 Algebra Equations Worksheets Contents Differentiated Independent Learning Worksheets Solving Equations
More informationLecture No. 1 Introduction to Method of Weighted Residuals. Solve the differential equation L (u) = p(x) in V where L is a differential operator
Lecture No. 1 Introduction to Method of Weighted Residuals Solve the differential equation L (u) = p(x) in V where L is a differential operator with boundary conditions S(u) = g(x) on Γ where S is a differential
More informationPHYSICS 12 NAME: Electrostatics Review
NAME: Electrostatics Review 1. The diagram below shows two positive charges of magnitude Q and 2Q. Which vector best represents the direction of the electric field at point P, which is equidistant from
More informationPHL424: Feynman diagrams
PHL424: Feynman diagrams In 1940s, R. Feynman developed a diagram technique to describe particle interactions in spacetime. Feynman diagram example Richard Feynman time Particles are represented by lines
More informationSECTION 8: ROOTLOCUS ANALYSIS. ESE 499 Feedback Control Systems
SECTION 8: ROOTLOCUS ANALYSIS ESE 499 Feedback Control Systems 2 Introduction Introduction 3 Consider a general feedback system: Closedloop transfer function is KKKK ss TT ss = 1 + KKKK ss HH ss GG ss
More informationLecture No. 5. For all weighted residual methods. For all (Bubnov) Galerkin methods. Summary of Conventional Galerkin Method
Lecture No. 5 LL(uu) pp(xx) = 0 in ΩΩ SS EE (uu) = gg EE on ΓΓ EE SS NN (uu) = gg NN on ΓΓ NN For all weighted residual methods NN uu aaaaaa = uu BB + αα ii φφ ii For all (Bubnov) Galerkin methods ii=1
More informationExam 1PHYS 102S14
Class: Date: Exam 1PHYS 102S14 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The magnitude of the charge on an electron is approximately: a. 1023
More informationChapter 16 Electrical Energy Capacitance. HW: 1, 2, 3, 5, 7, 12, 13, 17, 21, 25, 27 33, 35, 37a, 43, 45, 49, 51
Chapter 16 Electrical Energy Capacitance HW: 1, 2, 3, 5, 7, 12, 13, 17, 21, 25, 27 33, 35, 37a, 43, 45, 49, 51 Electrical Potential Reminder from physics 1: Work done by a conservative force, depends only
More informationPaper 1 Mark scheme. Question number. Acceptable answers Additional guidance Mark 1 D 1 2 A 1 3 D 1 4 D 1 5 B 1 6 C 1 7 D 1 8 D 1 9 C 1 10 A 1
!"#$%&'()*"+,"(."/"(0(1*/#',"*(3)(4'(!56%4,%(!" Paper 1 Mark scheme 1 D 1 A 1 3 D 1 4 D 1 5 B 1 6 C 1 7 D 1 8 D 1 9 C 1 10 A 1 (Total for Multiple Choice s = 10 marks) !# 11 An explanation that makes
More informationb) What is its position when its velocity (magnitude) is largest? When it is at x=0 all the energy is kinetic.
Question 1. The electrostatic force between two charges, Q 1 and F 1 /4 Q 2 a separated by a distance D, is F 1. What is the force between them after they are moved to a distance 2D apart? (Give in terms
More informationL.6 Absolute Value Equations and Inequalities
L.6 Absolute Value Equations and Inequalities 1 The concept of absolute value (also called numerical value) was introduced in Section R. Recall that when using geometrical visualisation of real numbers
More informationChapter 33  Electric Fields and Potential. Chapter 34  Electric Current
Chapter 33  Electric Fields and Potential Chapter 34  Electric Current Electric Force acts through a field An electric field surrounds every electric charge. It exerts a force that causes electric charges
More informationWave Motion. Chapter 14 of Essential University Physics, Richard Wolfson, 3 rd Edition
Wave Motion Chapter 14 of Essential University Physics, Richard Wolfson, 3 rd Edition 1 Waves: propagation of energy, not particles 2 Longitudinal Waves: disturbance is along the direction of wave propagation
More informationDynamics and control of mechanical systems
Dynamics and control of mechanical systems Date Day 1 (03/05)  05/05 Day 2 (07/05) Day 3 (09/05) Day 4 (11/05) Day 5 (14/05) Day 6 (16/05) Content Review of the basics of mechanics. Kinematics of rigid
More informationObjects usually are charged up through the transfer of electrons from one object to the other.
1 Part 1: Electric Force Review of Vectors Review your vectors! You should know how to convert from polar form to component form and vice versa add and subtract vectors multiply vectors by scalars Find
More informationPhysics 222, Spring 2010 Quiz 3, Form: A
Physics 222, Spring 2010 Quiz 3, Form: A Name: Date: Instructions You must sketch correct pictures and vectors, you must show all calculations, and you must explain all answers for full credit. Neatness
More informationNational 5 Mathematics. Practice Paper E. Worked Solutions
National 5 Mathematics Practice Paper E Worked Solutions Paper One: NonCalculator Copyright www.national5maths.co.uk 2015. All rights reserved. SQA Past Papers & Specimen Papers Working through SQA Past
More informationRelativistic Kinetic Energy Simplified. Copyright Joseph A. Rybczyk
Relativistic Kinetic Energy Simplified Copyright 207 Joseph A. Rybczyk Abstract The relativistic form of the kinetic energy formula is derived directly from the relativized principles of the classical
More informationLecture 6. Notes on Linear Algebra. Perceptron
Lecture 6. Notes on Linear Algebra. Perceptron COMP90051 Statistical Machine Learning Semester 2, 2017 Lecturer: Andrey Kan Copyright: University of Melbourne This lecture Notes on linear algebra Vectors
More informationElectric Potential and Potential Energy. A reformulation from a vector approach to a scalar approach
Electric Potential and Potential Energy A reformulation from a vector approach to a scalar approach Once again, compare to gravity, be very careful though Potential is not the same thing as potential energy
More informationAngular Momentum, Electromagnetic Waves
Angular Momentum, Electromagnetic Waves Lecture33: Electromagnetic Theory Professor D. K. Ghosh, Physics Department, I.I.T., Bombay As before, we keep in view the four Maxwell s equations for all our discussions.
More informationReview for Exam Hyunse Yoon, Ph.D. Adjunct Assistant Professor Department of Mechanical Engineering, University of Iowa
Review for Exam2 11. 13. 2015 Hyunse Yoon, Ph.D. Adjunct Assistant Professor Department of Mechanical Engineering, University of Iowa Assistant Research Scientist IIHRHydroscience & Engineering, University
More informationNAME: NITROMETHANE CHEMISTRY 443, Fall, 2015(15F) Section Number: 10 Final Examination, December 18, 2015
NAME: NITROMETHANE CHEMISTRY 443, Fall, 015(15F) Section Number: 10 Final Examination, December 18, 015 Answer each question in the space provided; use back of page if extra space is needed. Answer questions
More informationGeneral Physics (PHY 2140)
General Physics (PHY 2140) Lecture 5 Electrostatics Electrical energy potential difference and electric potential potential energy of charged conductors Capacitance and capacitors http://www.physics.wayne.edu/~apetrov/phy2140/
More informationChapter 6 Work and Energy
Chapter 6 Work and Energy Units of Chapter 6 Work Done by a Constant Force Work Done by a Varying Force Kinetic Energy, and the WorkEnergy Principle Potential Energy Conservative and Nonconservative Forces
More informationLowell Dam Gone Out. Streets Turned I n t o Rivers. No Cause For Alarm Now However As This Happened 35 Years A&o
V ()\\ ))? K K Y 6 96 Y  Y Y V 5 Z ( z x z \  \   z  q q x x  x 5 9 Q \ V   Y x 59 7 x x  Y  x   x z  z x  ( 7 x V 9 z q &?  9  V ( x    V [ Z x z  x > )   > X Z z ( V V V
More informationReview for Exam Hyunse Yoon, Ph.D. Assistant Research Scientist IIHRHydroscience & Engineering University of Iowa
57:020 Fluids Mechanics Fall2013 1 Review for Exam3 12. 11. 2013 Hyunse Yoon, Ph.D. Assistant Research Scientist IIHRHydroscience & Engineering University of Iowa 57:020 Fluids Mechanics Fall2013 2 Chapter
More informationChapter 10. Simple Harmonic Motion and Elasticity
Chapter 10 Simple Harmonic Motion and Elasticity 10.1 The Ideal Spring and Simple Harmonic Motion F Applied x = k x spring constant Units: N/m FF SSSSSSSSSSSS = kkkk 10.1 The Ideal Spring and Simple Harmonic
More informationElectric Potential Energy & Electric Potential
Electric Potential Energy & Electric Potential Consider the following scenario. F E F E pt.a If we release the ve charge from pt.a The ELECTRIC FIELD produced by the ve charge pulls the ve charge to the
More informationLecture 2 Electrons and Holes in Semiconductors
EE 471: Transport Phenomena in Solid State Devices Spring 2018 Lecture 2 Electrons and Holes in Semiconductors Bryan Ackland Department of Electrical and Computer Engineering Stevens Institute of Technology
More informationInteraction with matter
Interaction with matter accelerated motion: ss = bb 2 tt2 tt = 2 ss bb vv = vv 0 bb tt = vv 0 2 ss bb EE = 1 2 mmvv2 dddd dddd = mm vv 0 2 ss bb 1 bb eeeeeeeeeeee llllllll bbbbbbbbbbbbbb dddddddddddddddd
More information(b) The type of matter is irrelevant since the energy is directly proportional to mass only
Exercise J.3.1. Answers 1. m = 800kg v = 70kmh 1 = 70 103 = 60 60 19.4ms1 KK. EE = 1 2 mmvv2 = 800 19.42 2 = 150544JJ Using E= mc 2 and the kinetic energy of the car we obtain mm = EE cc 2 = 151235 (3
More informationSimple Harmonic Motion
1. Object Simple Harmonic Motion To determine the period of motion of objects that are executing simple harmonic motion and to check the theoretical prediction of such periods. 2. Apparatus Assorted weights
More informationChapter 21: Electric Potential Solutions
Chapter 21: Electric Potential Solutions Questions: 2, 7, 14 Exercises & Problems: 1, 6, 10, 12, 16, 21, 25, 27, 71 Q21.2: Charge q is fired through a small hole in the positive plate of a capacitor. a)
More information