Chapter 26 Capacitance and

Size: px
Start display at page:

Download "Chapter 26 Capacitance and"

Transcription

1 hapter 6 apacitance and Dielectrics We must do work, q, to bring a point charge q from far away ( at infinity) to a region where other charges are present. The work done is stored in electrostatic field energy. 6. Definition of apacitance 6. alculating apacitance Measure of the capacity to store charge: Unit: farad (F): F / ; µf 6 F; pf F The ratio of charge to the potential depends on the size and the shape of the conductor. apacitors A device consisting of two conductors carrying equal but opposite charges is called a capacitor. Parallel Plate apacitor E A, A d E, Ed d A A

2 ylindrical apacitor πrle > E πrl a b a b dr ln πrl L a π b π L b ln a Spherical apacitor 4π a r E, dr 4π r 4 a b b π ab 4π b a Selfapacitance The potential of a spherical conductor of radius carrying a charge is The selfcapacitance of a spherical conductor is: k 4π k k. 6. ombination of apacitors apacitors onnected in Parallel Obtain and to calculate. & /

3 ( ) / apacitors connected in parallel: eq 4... apacitors connected in series & / series > sum voltage & parallel > sum charges apacitors connected in series: 4... Example: Two capacitors are removed from the battery and carefully connected from each other. & & 96µ apacitors in Series and in Parallel??,, & > &

4 > 6.4 Energy Stored in a harged apacitor du dq q dq U du q dq Electrostatic Field Energy (derived from energy stored in a capacitor) A, Ed d U A d Electrostatic Energy Density: ( Ed ) E Ad E U u e E (energy per unit volume) Example: alculate the energy stored in the conductor carrying a charge. r < : E k r > : E r du u d e k ( 4πr dr) ( πr dr) E 4 4 r U du π k r k dr 4

5 6.5 apacitors and Dielectrics When the space between the two conductors of a capacitor is occupied by a dielectric, the capacitance is increased by a factor κ ( κ > ) that is characteristic of the dielectric. If the dielectric field is E before the dielectric slab is inserted, after the dielectric slab is inserted between the plates the field is E E > the potential is κ If Ed Ed κ κ ' κ., the capacitor is / κ The capacitance of a parallelplate capacitor filled with a dielectric of constant κ is Aσ Aσ κ κ E d Aσ κ σ d / permittivity of the dielectric. Aκ A d d acuum: κ v > κ is called the material: κ m > the Dielectric: κ > 5

6 Energy Stored in The Presence of a Dielectric The energy stored in a capacitor is: q q du dq > du dq > du U dq > U The energy of a capacitor with the dielectric is U u e E A d κe A d ( Ed ) ( Ed ) E ( Ad ) material: κ m > acuum: κ v E E the Dielectric: κ >. You lose electric force to separate the charge.. You enlarge the charging capacity as you know the dielectric will breakdown in a high electric field. (If the same charge > you lose some electric field,). You increase the energy per unit volume. ombination of apacitors Example: A parallelplate capacitor has square plates of edge length cm and a separation of d 4 mm. A dielectric slab of constant κ has dimensions cm X cm X 4 mm. (a) What is the capacitance without the dielectric? (b) What is the capacitance with the dielectric? (c) What is the capacitance if a dielectric slab with dimensions cm X cm X mm is inserted into the 4mm gap? (a) A, (b) d (c) series connection: A d A A d / 4 d / 4 A Aκ d / 4 d / 4 Example: The parallel plates of a given capacitor are square with A a and separation distance d. If the plates are maintained at a constant potential and a 6

7 square of dielectric slab of constant κ, area A a, thickness d is inserted between the capacitor plates to a distance x as shown in the following figure. Let σ be the free charge density at the conductorair surface. (a) alculate the free charge density σ κ at the capacitordielectric surface. (b) What is the effective capacitance? (c) What is the magnitude of the required force to prevent the dielectric slab from sliding into the plates? (a) In air: (b) (c) σ σ K Kσ E & d σ, in dielectric: ( a x) axk a a d d d U σ σ K E & d K K K ( a ( K ) x) d d d d a F K dx dx dx dx d ( ) The first term is due to charge redistribution and the second is due to the additional charges supplied by the constant voltage. Example: A parallel plate capacitor with plates of area LW and separation t has the region between its plates filled with wedges of two dielectric materials. Assume t is much less than both W and L. (a) Please determine its capacitance. The thickness of the k material decrease as a function of k material is of tx L For a short stripe of dx, The series connected capacitance A Wdx d t The total parallel connected capacitance ( κ ) ( L x) / L,, t ( L x) L ( κ ) A Wdx d tx / L k L W dx t κ κ κ while that of the x L k W total L W dx W L κ ln x κ t t κ κ κ L κ κ 7

8 6.6 Electric Dipole in an Electric Field Inside the material to make sure that the electric field lines are from the positive charge to the negative charge If the field is uniform, it can rotate the dipole. r r r r r r r r r τ qe qe qd E p v r r τ p E pe sinθ ( ) E The potential energy: du Fdx τdθ ( pe sinθ ) dθ θf U pe sinθdθ pe( cosθ cosθ ) θi f i q q E U r r p E 6.7 An Atomic Description of Dielectrics 8

9 bound charge total < total > total E bound charge E Example: A hydrogen atom consists of a proton nucleus of charge e and an electron of charge e. The charge distribution of the atom is spherically symmetric, so the atom is nonpolar. onsider a model in which the hydrogen atom consists of a positive charge e at the center of a uniformly charged spherical cloud of radius and total charge e. Show that when such an atom is placed in a uniform external field E r, the induced dipole moment is proportional to E r r r ; that is, p αe, where α is called 9

10 the polarizability. E 4π e r 4π A 4πr e 4π inside _ from _ e er p er α E α > 4π α 4π r Magnitude of The Bound harge b σ b E & E E E κ E E b σ f > E b E κ > σ b σ f κ σ σ σ σ σ κ σ κσ effective f b f f

Q24.1 The two conductors a and b are insulated from each other, forming a capacitor. You increase the charge on a to +2Q and increase the charge on b

Q24.1 The two conductors a and b are insulated from each other, forming a capacitor. You increase the charge on a to +2Q and increase the charge on b Q24.1 The two conductors a and b are insulated from each other, forming a capacitor. You increase the charge on a to +2Q and increase the charge on b to 2Q, while keeping the conductors in the same positions.

More information

CHAPTER 26 ELECTROSTATIC ENERGY AND CAPACITORS

CHAPTER 26 ELECTROSTATIC ENERGY AND CAPACITORS CHAPTER 6 ELECTROSTATIC ENERGY AND CAPACITORS. Three point charges, each of +q, are moved from infinity to the vertices of an equilateral triangle of side l. How much work is required? The sentence preceding

More information

Chapter 7: Polarization

Chapter 7: Polarization Chapter 7: Polarization Joaquín Bernal Méndez Group 4 1 Index Introduction Polarization Vector The Electric Displacement Vector Constitutive Laws: Linear Dielectrics Energy in Dielectric Systems Forces

More information

Chapter 4. Electrostatic Fields in Matter

Chapter 4. Electrostatic Fields in Matter Chapter 4. Electrostatic Fields in Matter 4.1. Polarization A neutral atom, placed in an external electric field, will experience no net force. However, even though the atom as a whole is neutral, the

More information

Last Name: First Name: Physics 102 Spring 2006: Exam #2 Multiple-Choice Questions 1. A charged particle, q, is moving with speed v perpendicular to a uniform magnetic field. A second identical charged

More information

Chapter 18. Electric Forces and Electric Fields

Chapter 18. Electric Forces and Electric Fields My lecture slides may be found on my website at http://www.physics.ohio-state.edu/~humanic/ ------------------------------------------------------------------- Chapter 18 Electric Forces and Electric Fields

More information

Electric Fields in Dielectrics

Electric Fields in Dielectrics Electric Fields in Dielectrics Any kind of matter is full of positive and negative electric charges. In a dielectric, these charges cannot move separately from each other through any macroscopic distance,

More information

Exam 2 Practice Problems Part 1 Solutions

Exam 2 Practice Problems Part 1 Solutions MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Exam Practice Problems Part 1 Solutions Problem 1 Electric Field and Charge Distributions from Electric Potential An electric potential V ( z

More information

Capacitors in Circuits

Capacitors in Circuits apacitors in ircuits apacitors store energy in the electric field E field created by the stored charge In circuit apacitor may be absorbing energy Thus causes circuit current to be reduced Effectively

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) If the voltage at a point in space is zero, then the electric field must be A) zero. B) positive.

More information

Exam 1 Practice Problems Solutions

Exam 1 Practice Problems Solutions MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8 Spring 13 Exam 1 Practice Problems Solutions Part I: Short Questions and Concept Questions Problem 1: Spark Plug Pictured at right is a typical

More information

ELECTRIC FIELD LINES AND EQUIPOTENTIAL SURFACES

ELECTRIC FIELD LINES AND EQUIPOTENTIAL SURFACES ELECTRIC FIELD LINES AND EQUIPOTENTIAL SURFACES The purpose of this lab session is to experimentally investigate the relation between electric field lines of force and equipotential surfaces in two dimensions.

More information

Measurement of Capacitance

Measurement of Capacitance Measurement of Capacitance Pre-Lab Questions Page Name: Class: Roster Number: Instructor:. A capacitor is used to store. 2. What is the SI unit for capacitance? 3. A capacitor basically consists of two

More information

( )( 10!12 ( 0.01) 2 2 = 624 ( ) Exam 1 Solutions. Phy 2049 Fall 2011

( )( 10!12 ( 0.01) 2 2 = 624 ( ) Exam 1 Solutions. Phy 2049 Fall 2011 Phy 49 Fall 11 Solutions 1. Three charges form an equilateral triangle of side length d = 1 cm. The top charge is q = - 4 μc, while the bottom two are q1 = q = +1 μc. What is the magnitude of the net force

More information

How to transform, with a capacitor, thermal energy into usable work.

How to transform, with a capacitor, thermal energy into usable work. How to transform, with a capacitor, thermal energy into usable work. E. N. Miranda 1 CONICET CCT Mendoza 55 Mendoza, Argentina and Facultad de Ingeniería Universidad de Mendoza 55 Mendoza, Argentina Abstract:

More information

Exercises on Voltage, Capacitance and Circuits. A d = (8.85 10 12 ) π(0.05)2 = 6.95 10 11 F

Exercises on Voltage, Capacitance and Circuits. A d = (8.85 10 12 ) π(0.05)2 = 6.95 10 11 F Exercises on Voltage, Capacitance and Circuits Exercise 1.1 Instead of buying a capacitor, you decide to make one. Your capacitor consists of two circular metal plates, each with a radius of 5 cm. The

More information

HW7 Solutions Notice numbers may change randomly in your assignments and you may have to recalculate solutions for your specific case.

HW7 Solutions Notice numbers may change randomly in your assignments and you may have to recalculate solutions for your specific case. HW7 Solutions Notice numbers may change randomly in your assignments and you may have to recalculate solutions for your specific case. Tipler 24.P.021 (a) Find the energy stored in a 20.00 nf capacitor

More information

Chapter 22: The Electric Field. Read Chapter 22 Do Ch. 22 Questions 3, 5, 7, 9 Do Ch. 22 Problems 5, 19, 24

Chapter 22: The Electric Field. Read Chapter 22 Do Ch. 22 Questions 3, 5, 7, 9 Do Ch. 22 Problems 5, 19, 24 Chapter : The Electric Field Read Chapter Do Ch. Questions 3, 5, 7, 9 Do Ch. Problems 5, 19, 4 The Electric Field Replaces action-at-a-distance Instead of Q 1 exerting a force directly on Q at a distance,

More information

HW6 Solutions Notice numbers may change randomly in your assignments and you may have to recalculate solutions for your specific case.

HW6 Solutions Notice numbers may change randomly in your assignments and you may have to recalculate solutions for your specific case. HW6 Solutions Notice numbers may change randomly in your assignments and you may have to recalculate solutions for your specific case. Tipler 22.P.053 The figure below shows a portion of an infinitely

More information

Parallel Plate Capacitor

Parallel Plate Capacitor Parallel Plate Capacitor Capacitor Charge, Plate Separation, and Voltage A capacitor is used to store electric charge. The more voltage (electrical pressure) you apply to the capacitor, the more charge

More information

Episode 126: Capacitance and the equation C =Q/V

Episode 126: Capacitance and the equation C =Q/V Episode 126: Capacitance and the equation C =Q/V Having established that there is charge on each capacitor plate, the next stage is to establish the relationship between charge and potential difference

More information

PHY114 S11 Term Exam 3

PHY114 S11 Term Exam 3 PHY4 S Term Exam S. G. Rajeev Mar 2 20 2:0 pm to :45 pm PLEASE write your workshop number and your workshop leader s name at the top of your book, so that you can collect your graded exams at the workshop.

More information

Objectives. Capacitors 262 CHAPTER 5 ENERGY

Objectives. Capacitors 262 CHAPTER 5 ENERGY Objectives Describe a capacitor. Explain how a capacitor stores energy. Define capacitance. Calculate the electrical energy stored in a capacitor. Describe an inductor. Explain how an inductor stores energy.

More information

EE301 Lesson 14 Reading: 10.1-10.4, 10.11-10.12, 11.1-11.4 and 11.11-11.13

EE301 Lesson 14 Reading: 10.1-10.4, 10.11-10.12, 11.1-11.4 and 11.11-11.13 CAPACITORS AND INDUCTORS Learning Objectives EE301 Lesson 14 a. Define capacitance and state its symbol and unit of measurement. b. Predict the capacitance of a parallel plate capacitor. c. Analyze how

More information

PHYSICS PAPER 1 (THEORY)

PHYSICS PAPER 1 (THEORY) PHYSICS PAPER 1 (THEORY) (Three hours) (Candidates are allowed additional 15 minutes for only reading the paper. They must NOT start writing during this time.) ---------------------------------------------------------------------------------------------------------------------

More information

CHAPTER 24 GAUSS S LAW

CHAPTER 24 GAUSS S LAW CHAPTER 4 GAUSS S LAW 4. The net charge shown in Fig. 4-40 is Q. Identify each of the charges A, B, C shown. A B C FIGURE 4-40 4. From the direction of the lines of force (away from positive and toward

More information

Chapter 22: Electric Flux and Gauss s Law

Chapter 22: Electric Flux and Gauss s Law 22.1 ntroduction We have seen in chapter 21 that determining the electric field of a continuous charge distribution can become very complicated for some charge distributions. t would be desirable if we

More information

Electromagnetism Laws and Equations

Electromagnetism Laws and Equations Electromagnetism Laws and Equations Andrew McHutchon Michaelmas 203 Contents Electrostatics. Electric E- and D-fields............................................. Electrostatic Force............................................2

More information

CLASS TEST GRADE 11. PHYSICAL SCIENCES: PHYSICS Test 3: Electricity and magnetism

CLASS TEST GRADE 11. PHYSICAL SCIENCES: PHYSICS Test 3: Electricity and magnetism CLASS TEST GRADE 11 PHYSICAL SCIENCES: PHYSICS Test 3: Electricity and magnetism MARKS: 45 TIME: 1 hour INSTRUCTIONS AND INFORMATION 1. Answer ALL the questions. 2. You may use non-programmable calculators.

More information

1. A wire carries 15 A. You form the wire into a single-turn circular loop with magnetic field 80 µ T at the loop center. What is the loop radius?

1. A wire carries 15 A. You form the wire into a single-turn circular loop with magnetic field 80 µ T at the loop center. What is the loop radius? CHAPTER 3 SOURCES O THE MAGNETC ELD 1. A wire carries 15 A. You form the wire into a single-turn circular loop with magnetic field 8 µ T at the loop center. What is the loop radius? Equation 3-3, with

More information

Capacitance and Ferroelectrics

Capacitance and Ferroelectrics Ram Seshadri MRL 2031, x6129 seshadri@mrl.ucsb.edu; http://www.mrl.ucsb.edu/ seshadri/teach.html Capacitance and Ferroelectrics A voltage V applied across a capacitor of caacitance C allows a quantity

More information

Experiments on the Basics of Electrostatics (Coulomb s law; Capacitor)

Experiments on the Basics of Electrostatics (Coulomb s law; Capacitor) Experiments on the Basics of Electrostatics (Coulomb s law; Capacitor) ZDENĚK ŠABATKA Department of Physics Education, Faculty of Mathematics and Physics, Charles University in Prague The physics textbooks

More information

Solution. Problem. Solution. Problem. Solution

Solution. Problem. Solution. Problem. Solution 4. A 2-g ping-pong ball rubbed against a wool jacket acquires a net positive charge of 1 µc. Estimate the fraction of the ball s electrons that have been removed. If half the ball s mass is protons, their

More information

Lecture 14 Capacitance and Conductance

Lecture 14 Capacitance and Conductance Lecture 14 Capacitance and Conductance ections: 6.3, 6.4, 6.5 Homework: ee homework file Definition of Capacitance capacitance is a measure of the ability of the physical structure to accumulate electrical

More information

Chapter 23 Electric Potential. Copyright 2009 Pearson Education, Inc.

Chapter 23 Electric Potential. Copyright 2009 Pearson Education, Inc. Chapter 23 Electric Potential 23-1 Electrostatic Potential Energy and Potential Difference The electrostatic force is conservative potential energy can be defined. Change in electric potential energy is

More information

45. The peak value of an alternating current in a 1500-W device is 5.4 A. What is the rms voltage across?

45. The peak value of an alternating current in a 1500-W device is 5.4 A. What is the rms voltage across? PHYS Practice Problems hapters 8- hapter 8. 45. The peak value of an alternating current in a 5-W device is 5.4 A. What is the rms voltage across? The power and current can be used to find the peak voltage,

More information

Chapter 30 Inductance

Chapter 30 Inductance Chapter 30 Inductance - Mutual Inductance - Self-Inductance and Inductors - Magnetic-Field Energy - The R- Circuit - The -C Circuit - The -R-C Series Circuit . Mutual Inductance - A changing current in

More information

Electric Energy and Potential

Electric Energy and Potential Electric Energy and Potential 15 In the last chapter we discussed the forces acting between electric charges. Electric fields were shown to be produced by all charges and electrical interactions between

More information

Phys222 Winter 2012 Quiz 4 Chapters 29-31. Name

Phys222 Winter 2012 Quiz 4 Chapters 29-31. Name Name If you think that no correct answer is provided, give your answer, state your reasoning briefly; append additional sheet of paper if necessary. 1. A particle (q = 5.0 nc, m = 3.0 µg) moves in a region

More information

Electric Field Mapping Lab 3. Precautions

Electric Field Mapping Lab 3. Precautions HB 09-25-07 Electric Field Mapping Lab 3 1 Electric Field Mapping Lab 3 Equipment mapping board, U-probe, resistive boards, templates, dc voltmeter (431B), 4 long leads, 16 V dc for wall strip Reading

More information

1. Units of a magnetic field might be: A. C m/s B. C s/m C. C/kg D. kg/c s E. N/C m ans: D

1. Units of a magnetic field might be: A. C m/s B. C s/m C. C/kg D. kg/c s E. N/C m ans: D Chapter 28: MAGNETIC FIELDS 1 Units of a magnetic field might be: A C m/s B C s/m C C/kg D kg/c s E N/C m 2 In the formula F = q v B: A F must be perpendicular to v but not necessarily to B B F must be

More information

Charges, voltage and current

Charges, voltage and current Charges, voltage and current Lecture 2 1 Atoms and electrons Atoms are built up from Positively charged nucleus Negatively charged electrons orbiting in shells (or more accurately clouds or orbitals) -

More information

Magnetism. d. gives the direction of the force on a charge moving in a magnetic field. b. results in negative charges moving. clockwise.

Magnetism. d. gives the direction of the force on a charge moving in a magnetic field. b. results in negative charges moving. clockwise. Magnetism 1. An electron which moves with a speed of 3.0 10 4 m/s parallel to a uniform magnetic field of 0.40 T experiences a force of what magnitude? (e = 1.6 10 19 C) a. 4.8 10 14 N c. 2.2 10 24 N b.

More information

19 ELECTRIC POTENTIAL AND ELECTRIC FIELD

19 ELECTRIC POTENTIAL AND ELECTRIC FIELD CHAPTER 19 ELECTRIC POTENTIAL AND ELECTRIC FIELD 663 19 ELECTRIC POTENTIAL AND ELECTRIC FIELD Figure 19.1 Automated external defibrillator unit (AED) (credit: U.S. Defense Department photo/tech. Sgt. Suzanne

More information

Electrostatic Fields: Coulomb s Law & the Electric Field Intensity

Electrostatic Fields: Coulomb s Law & the Electric Field Intensity Electrostatic Fields: Coulomb s Law & the Electric Field Intensity EE 141 Lecture Notes Topic 1 Professor K. E. Oughstun School of Engineering College of Engineering & Mathematical Sciences University

More information

Code number given on the right hand side of the question paper should be written on the title page of the answerbook by the candidate.

Code number given on the right hand side of the question paper should be written on the title page of the answerbook by the candidate. Series ONS SET-1 Roll No. Candiates must write code on the title page of the answer book Please check that this question paper contains 16 printed pages. Code number given on the right hand side of the

More information

Quiz: Work and Energy

Quiz: Work and Energy Quiz: Work and Energy A charged particle enters a uniform magnetic field. What happens to the kinetic energy of the particle? (1) it increases (2) it decreases (3) it stays the same (4) it changes with

More information

PHYSICS HIGHER SECONDARY SECOND YEAR VOLUME - I. Revised based on the recommendation of the Textbook Development Committee. Untouchability is a sin

PHYSICS HIGHER SECONDARY SECOND YEAR VOLUME - I. Revised based on the recommendation of the Textbook Development Committee. Untouchability is a sin PHYSICS HIGHER SECONDARY SECOND YEAR VOLUME - I Revised based on the recommendation of the Textbook Development Committee Untouchability is a sin Untouchability is a crime Untouchability is inhuman TAMILNADU

More information

potential in the centre of the sphere with respect to infinity.

potential in the centre of the sphere with respect to infinity. Umeå Universitet, Fysik 1 Vitaly Bychkov Prov i fysik, Electricity and Waves, 2006-09-27, kl 16.00-22.00 Hjälpmedel: Students can use any book. Define the notations you are using properly. Present your

More information

COURSE: PHYSICS DEGREE: COMPUTER ENGINEERING year: 1st SEMESTER: 1st

COURSE: PHYSICS DEGREE: COMPUTER ENGINEERING year: 1st SEMESTER: 1st COURSE: PHYSICS DEGREE: COMPUTER ENGINEERING year: 1st SEMESTER: 1st WEEKLY PROGRAMMING WEE K SESSI ON DESCRIPTION GROUPS GROUPS Special room for LECTU PRAC session RES TICAL (computer classroom, audiovisual

More information

DETERMINATION OF THE EFFECTIVE VOLUME OF AN EXTRAPOLATION CHAMBER FOR X-RAY DOSIMETRY

DETERMINATION OF THE EFFECTIVE VOLUME OF AN EXTRAPOLATION CHAMBER FOR X-RAY DOSIMETRY X Congreso Regional Latinoamericano IRPA de Protección y Seguridad Radiológica Radioprotección: Nuevos Desafíos para un Mundo en Evolución Buenos Aires, 12 al 17 de abril, 2015 SOCIEDAD ARGENTINA DE RADIOPROTECCIÓN

More information

AP2 Magnetism. (c) Explain why the magnetic field does no work on the particle as it moves in its circular path.

AP2 Magnetism. (c) Explain why the magnetic field does no work on the particle as it moves in its circular path. A charged particle is projected from point P with velocity v at a right angle to a uniform magnetic field directed out of the plane of the page as shown. The particle moves along a circle of radius R.

More information

A METHOD OF CALIBRATING HELMHOLTZ COILS FOR THE MEASUREMENT OF PERMANENT MAGNETS

A METHOD OF CALIBRATING HELMHOLTZ COILS FOR THE MEASUREMENT OF PERMANENT MAGNETS A METHOD OF CALIBRATING HELMHOLTZ COILS FOR THE MEASUREMENT OF PERMANENT MAGNETS Joseph J. Stupak Jr, Oersted Technology Tualatin, Oregon (reprinted from IMCSD 24th Annual Proceedings 1995) ABSTRACT The

More information

6 J - vector electric current density (A/m2 )

6 J - vector electric current density (A/m2 ) Determination of Antenna Radiation Fields Using Potential Functions Sources of Antenna Radiation Fields 6 J - vector electric current density (A/m2 ) M - vector magnetic current density (V/m 2 ) Some problems

More information

Digital Systems Ribbon Cables I CMPE 650. Ribbon Cables A ribbon cable is any cable having multiple conductors bound together in a flat, wide strip.

Digital Systems Ribbon Cables I CMPE 650. Ribbon Cables A ribbon cable is any cable having multiple conductors bound together in a flat, wide strip. Ribbon Cables A ribbon cable is any cable having multiple conductors bound together in a flat, wide strip. Each dielectric configuration has different high-frequency characteristics. All configurations

More information

Edmund Li. Where is defined as the mutual inductance between and and has the SI units of Henries (H).

Edmund Li. Where is defined as the mutual inductance between and and has the SI units of Henries (H). INDUCTANCE MUTUAL INDUCTANCE If we consider two neighbouring closed loops and with bounding surfaces respectively then a current through will create a magnetic field which will link with as the flux passes

More information

Review Questions PHYS 2426 Exam 2

Review Questions PHYS 2426 Exam 2 Review Questions PHYS 2426 Exam 2 1. If 4.7 x 10 16 electrons pass a particular point in a wire every second, what is the current in the wire? A) 4.7 ma B) 7.5 A C) 2.9 A D) 7.5 ma E) 0.29 A Ans: D 2.

More information

Supercapacitors. Advantages Power density Recycle ability Environmentally friendly Safe Light weight

Supercapacitors. Advantages Power density Recycle ability Environmentally friendly Safe Light weight Supercapacitors Supercapacitors also called ultracapacitors and electric double layer capacitors (EDLC) are capacitors with capacitance values greater than any other capacitor type available today. Capacitance

More information

Problem 1 (25 points)

Problem 1 (25 points) MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2012 Exam Three Solutions Problem 1 (25 points) Question 1 (5 points) Consider two circular rings of radius R, each perpendicular

More information

Section 3: Crystal Binding

Section 3: Crystal Binding Physics 97 Interatomic forces Section 3: rystal Binding Solids are stable structures, and therefore there exist interactions holding atoms in a crystal together. For example a crystal of sodium chloride

More information

Chapter 7. DC Circuits

Chapter 7. DC Circuits Chapter 7 DC Circuits 7.1 Introduction... 7-3 Example 7.1.1: Junctions, branches and loops... 7-4 7.2 Electromotive Force... 7-5 7.3 Electrical Energy and Power... 7-9 7.4 Resistors in Series and in Parallel...

More information

MOS (metal-oxidesemiconductor) 李 2003/12/19

MOS (metal-oxidesemiconductor) 李 2003/12/19 MOS (metal-oxidesemiconductor) 李 2003/12/19 Outline Structure Ideal MOS The surface depletion region Ideal MOS curves The SiO 2 -Si MOS diode (real case) Structure A basic MOS consisting of three layers.

More information

Energy in Electrical Systems. Overview

Energy in Electrical Systems. Overview Energy in Electrical Systems Overview How can Potential Energy be stored in electrical systems? Battery Stored as chemical energy then transformed to electrical energy on usage Water behind a dam Water

More information

MECHANICS OF SOLIDS - BEAMS TUTORIAL 1 STRESSES IN BEAMS DUE TO BENDING. On completion of this tutorial you should be able to do the following.

MECHANICS OF SOLIDS - BEAMS TUTORIAL 1 STRESSES IN BEAMS DUE TO BENDING. On completion of this tutorial you should be able to do the following. MECHANICS OF SOLIDS - BEAMS TUTOIAL 1 STESSES IN BEAMS DUE TO BENDING This is the first tutorial on bending of beams designed for anyone wishing to study it at a fairly advanced level. You should judge

More information

Induced voltages and Inductance Faraday s Law

Induced voltages and Inductance Faraday s Law Induced voltages and Inductance Faraday s Law concept #1, 4, 5, 8, 13 Problem # 1, 3, 4, 5, 6, 9, 10, 13, 15, 24, 23, 25, 31, 32a, 34, 37, 41, 43, 51, 61 Last chapter we saw that a current produces a magnetic

More information

ElectroMagnetic Induction. AP Physics B

ElectroMagnetic Induction. AP Physics B ElectroMagnetic Induction AP Physics B What is E/M Induction? Electromagnetic Induction is the process of using magnetic fields to produce voltage, and in a complete circuit, a current. Michael Faraday

More information

Physics 202, Lecture 3. The Electric Field

Physics 202, Lecture 3. The Electric Field Physics 202, Lecture 3 Today s Topics Electric Field Quick Review Motion of Charged Particles in an Electric Field Gauss s Law (Ch. 24, Serway) Conductors in Electrostatic Equilibrium (Ch. 24) Homework

More information

Force on Moving Charges in a Magnetic Field

Force on Moving Charges in a Magnetic Field [ Assignment View ] [ Eðlisfræði 2, vor 2007 27. Magnetic Field and Magnetic Forces Assignment is due at 2:00am on Wednesday, February 28, 2007 Credit for problems submitted late will decrease to 0% after

More information

Chapter 12 Driven RLC Circuits

Chapter 12 Driven RLC Circuits hapter Driven ircuits. A Sources... -. A ircuits with a Source and One ircuit Element... -3.. Purely esistive oad... -3.. Purely Inductive oad... -6..3 Purely apacitive oad... -8.3 The Series ircuit...

More information

Inductors and Capacitors Energy Storage Devices

Inductors and Capacitors Energy Storage Devices Inuctors an Capacitors Energy Storage Devices Aims: To know: Basics of energy storage evices. Storage leas to time elays. Basic equations for inuctors an capacitors. To be able to o escribe: Energy storage

More information

Notes on Elastic and Inelastic Collisions

Notes on Elastic and Inelastic Collisions Notes on Elastic and Inelastic Collisions In any collision of 2 bodies, their net momentus conserved. That is, the net momentum vector of the bodies just after the collision is the same as it was just

More information

As customary, choice (a) is the correct answer in all the following problems.

As customary, choice (a) is the correct answer in all the following problems. PHY2049 Summer 2012 Instructor: Francisco Rojas Exam 1 As customary, choice (a) is the correct answer in all the following problems. Problem 1 A uniformly charge (thin) non-conucting ro is locate on the

More information

CHAPTER - 1. Chapter ONE: WAVES CHAPTER - 2. Chapter TWO: RAY OPTICS AND OPTICAL INSTRUMENTS. CHAPTER - 3 Chapter THREE: WAVE OPTICS PERIODS PERIODS

CHAPTER - 1. Chapter ONE: WAVES CHAPTER - 2. Chapter TWO: RAY OPTICS AND OPTICAL INSTRUMENTS. CHAPTER - 3 Chapter THREE: WAVE OPTICS PERIODS PERIODS BOARD OF INTERMEDIATE EDUCATION, A.P., HYDERABAD REVISION OF SYLLABUS Subject PHYSICS-II (w.e.f 2013-14) Chapter ONE: WAVES CHAPTER - 1 1.1 INTRODUCTION 1.2 Transverse and longitudinal waves 1.3 Displacement

More information

Slide 1 / 26. Inductance. 2011 by Bryan Pflueger

Slide 1 / 26. Inductance. 2011 by Bryan Pflueger Slide 1 / 26 Inductance 2011 by Bryan Pflueger Slide 2 / 26 Mutual Inductance If two coils of wire are placed near each other and have a current passing through them, they will each induce an emf on one

More information

Non-contact surface charge/voltage measurements Fieldmeter and voltmeter methods

Non-contact surface charge/voltage measurements Fieldmeter and voltmeter methods Dr. Maciej A. Noras Abstract Methods of measurements of surface electric charges and potentials using electrostatic fieldmeters and voltmeters are discussed. The differences and similarities between those

More information

Lecture 5. Electric Flux and Flux Density, Gauss Law in Integral Form

Lecture 5. Electric Flux and Flux Density, Gauss Law in Integral Form Lecture 5 Electric Flux and Flux ensity, Gauss Law in Integral Form ections: 3.1, 3., 3.3 Homework: ee homework file LECTURE 5 slide 1 Faraday s Experiment (1837), Flux charge transfer from inner to outer

More information

Practice Final Math 122 Spring 12 Instructor: Jeff Lang

Practice Final Math 122 Spring 12 Instructor: Jeff Lang Practice Final Math Spring Instructor: Jeff Lang. Find the limit of the sequence a n = ln (n 5) ln (3n + 8). A) ln ( ) 3 B) ln C) ln ( ) 3 D) does not exist. Find the limit of the sequence a n = (ln n)6

More information

Conceptual: 1, 3, 5, 6, 8, 16, 18, 19. Problems: 4, 6, 8, 11, 16, 20, 23, 27, 34, 41, 45, 56, 60, 65. Conceptual Questions

Conceptual: 1, 3, 5, 6, 8, 16, 18, 19. Problems: 4, 6, 8, 11, 16, 20, 23, 27, 34, 41, 45, 56, 60, 65. Conceptual Questions Conceptual: 1, 3, 5, 6, 8, 16, 18, 19 Problems: 4, 6, 8, 11, 16, 20, 23, 27, 34, 41, 45, 56, 60, 65 Conceptual Questions 1. The magnetic field cannot be described as the magnetic force per unit charge

More information

104 Practice Exam 2-3/21/02

104 Practice Exam 2-3/21/02 104 Practice Exam 2-3/21/02 1. Two electrons are located in a region of space where the magnetic field is zero. Electron A is at rest; and electron B is moving westward with a constant velocity. A non-zero

More information

Looking at Capacitors

Looking at Capacitors Module 2 AC Theory Looking at What you'll learn in Module 2: In section 2.1 Common capacitor types and their uses. Basic Circuit Symbols for. In section 2.2 Charge & Discharge How capacitors work. What

More information

Atoms and Elements. Outline Atoms Orbitals and Energy Levels Periodic Properties Homework

Atoms and Elements. Outline Atoms Orbitals and Energy Levels Periodic Properties Homework Atoms and the Periodic Table The very hot early universe was a plasma with cationic nuclei separated from negatively charged electrons. Plasmas exist today where the energy of the particles is very high,

More information

Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level

Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level *0123456789* PHYSICS 9702/02 Paper 2 AS Level Structured Questions For Examination from 2016 SPECIMEN

More information

Objectives 200 CHAPTER 4 RESISTANCE

Objectives 200 CHAPTER 4 RESISTANCE Objectives Explain the differences among conductors, insulators, and semiconductors. Define electrical resistance. Solve problems using resistance, voltage, and current. Describe a material that obeys

More information

Chapter 21. Magnetic Forces and Magnetic Fields

Chapter 21. Magnetic Forces and Magnetic Fields Chapter 21 Magnetic Forces and Magnetic Fields 21.1 Magnetic Fields The needle of a compass is permanent magnet that has a north magnetic pole (N) at one end and a south magnetic pole (S) at the other.

More information

DEGREE: Bachelor's Degree in Industrial Electronics and Automation COURSE: 1º TERM: 2º WEEKLY PLANNING

DEGREE: Bachelor's Degree in Industrial Electronics and Automation COURSE: 1º TERM: 2º WEEKLY PLANNING SESSION WEEK COURSE: Physics II DEGREE: Bachelor's Degree in Industrial Electronics and Automation COURSE: 1º TERM: 2º WEEKLY PLANNING DESCRIPTION GROUPS (mark ) Indicate YES/NO If the session needs 2

More information

Magnetic Fields. I. Magnetic Field and Magnetic Field Lines

Magnetic Fields. I. Magnetic Field and Magnetic Field Lines Magnetic Fields I. Magnetic Field and Magnetic Field Lines A. The concept of the magnetic field can be developed in a manner similar to the way we developed the electric field. The magnitude of the magnetic

More information

Alternating-Current Circuits

Alternating-Current Circuits hapter 1 Alternating-urrent ircuits 1.1 A Sources... 1-1. Simple A circuits... 1-3 1..1 Purely esistive load... 1-3 1.. Purely Inductive oad... 1-5 1..3 Purely apacitive oad... 1-7 1.3 The Series ircuit...

More information

LUXEON LEDs. Circuit Design and Layout Practices to Minimize Electrical Stress. Introduction. Scope LED PORTFOLIO

LUXEON LEDs. Circuit Design and Layout Practices to Minimize Electrical Stress. Introduction. Scope LED PORTFOLIO LED PORTFOLIO LUXEON LEDs Circuit Design and Layout Practices to Minimize Electrical Stress Introduction LED circuits operating in the real world can be subjected to various abnormal electrical overstress

More information

H 2O gas: molecules are very far apart

H 2O gas: molecules are very far apart Non-Covalent Molecular Forces 2/27/06 3/1/06 How does this reaction occur: H 2 O (liquid) H 2 O (gas)? Add energy H 2O gas: molecules are very far apart H 2O liquid: bonding between molecules Use heat

More information

Faraday s Law of Induction

Faraday s Law of Induction Chapter 10 Faraday s Law of Induction 10.1 Faraday s Law of Induction...10-10.1.1 Magnetic Flux...10-3 10.1. Lenz s Law...10-5 10. Motional EMF...10-7 10.3 Induced Electric Field...10-10 10.4 Generators...10-1

More information

Chapter 6. Current and Resistance

Chapter 6. Current and Resistance 6 6 6-0 Chapter 6 Current and Resistance 6.1 Electric Current... 6-2 6.1.1 Current Density... 6-2 6.2 Ohm s Law... 6-5 6.3 Summary... 6-8 6.4 Solved Problems... 6-9 6.4.1 Resistivity of a Cable... 6-9

More information

Candidate Number. General Certificate of Education Advanced Level Examination June 2010

Candidate Number. General Certificate of Education Advanced Level Examination June 2010 entre Number andidate Number Surname Other Names andidate Signature General ertificate of Education dvanced Level Examination June 1 Physics PHY4/1 Unit 4 Fields and Further Mechanics Section Friday 18

More information

INTERMOLECULAR FORCES

INTERMOLECULAR FORCES INTERMOLECULAR FORCES Intermolecular forces- forces of attraction and repulsion between molecules that hold molecules, ions, and atoms together. Intramolecular - forces of chemical bonds within a molecule

More information

GenTech Practice Questions

GenTech Practice Questions GenTech Practice Questions Basic Electronics Test: This test will assess your knowledge of and ability to apply the principles of Basic Electronics. This test is comprised of 90 questions in the following

More information

Bonds. Bond Length. Forces that hold groups of atoms together and make them function as a unit. Bond Energy. Chapter 8. Bonding: General Concepts

Bonds. Bond Length. Forces that hold groups of atoms together and make them function as a unit. Bond Energy. Chapter 8. Bonding: General Concepts Bonds hapter 8 Bonding: General oncepts Forces that hold groups of atoms together and make them function as a unit. Bond Energy Bond Length It is the energy required to break a bond. The distance where

More information

The Electric Field. Electric Charge, Electric Field and a Goofy Analogy

The Electric Field. Electric Charge, Electric Field and a Goofy Analogy . The Electric Field Concepts and Principles Electric Charge, Electric Field and a Goofy Analogy We all know that electrons and protons have electric charge. But what is electric charge and what does it

More information

VOLUME AND SURFACE AREAS OF SOLIDS

VOLUME AND SURFACE AREAS OF SOLIDS VOLUME AND SURFACE AREAS OF SOLIDS Q.1. Find the total surface area and volume of a rectangular solid (cuboid) measuring 1 m by 50 cm by 0.5 m. 50 1 Ans. Length of cuboid l = 1 m, Breadth of cuboid, b

More information

Eðlisfræði 2, vor 2007

Eðlisfræði 2, vor 2007 [ Assignment View ] [ Pri Eðlisfræði 2, vor 2007 28. Sources of Magnetic Field Assignment is due at 2:00am on Wednesday, March 7, 2007 Credit for problems submitted late will decrease to 0% after the deadline

More information

Chapter 30 - Magnetic Fields and Torque. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University

Chapter 30 - Magnetic Fields and Torque. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University Chapter 30 - Magnetic Fields and Torque A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University 2007 Objectives: After completing this module, you should

More information

Experiment 8: Undriven & Driven RLC Circuits

Experiment 8: Undriven & Driven RLC Circuits Experiment 8: Undriven & Driven RLC Circuits Answer these questions on a separate sheet of paper and turn them in before the lab 1. RLC Circuits Consider the circuit at left, consisting of an AC function

More information