Gauss s law relates to total electric flux through a closed surface to the total enclosed charge.

Size: px
Start display at page:

Download "Gauss s law relates to total electric flux through a closed surface to the total enclosed charge."

Transcription

1 Chapte : Gauss s Law Gauss s Law is an altenative fomulation of the elation between an electic field and the souces of that field in tems of electic flu. lectic Flu Φ though an aea ~ Numbe of Field Lines which piece the aea depends upon geomety (oientation and size of aea, diection of ) electic field stength ( ~ density of field lines) Φ Φ cosθ θ θ pc: Gauss s law elates to total electic flu though a closed suface to the total chage. Stat with single point chage within an abitay closed suface. dd up all contibutions dφ. d Φ Φ pc:

2 intemediate steps: chage at the cente of a spheical suface two patches of aea subtending the same solid angle constant dφ dφ dding up the flu ove the suface of one of the sphees Φ k k o 4 π pc: Fo a chage in an abitay suface dφ cosθ sphee Poject aea incement onto neaest sphee : Flu though aea flu though aea incement on neaest sphee with same solid angle. Flu though neaest sphee aea incement flu though aea incement on a common sphee fo same solid angle. dd up ove all solid angles > ove entie suface of common sphee > simple sphee esults. Φ o pc: 4

3 Fo chages located outside the closed suface numbe of field lines eiting the suface (Φ ) numbe of field lines enteing the suface (Φ ) > no net contibution to Φ Gauss s Law: Φ Q o pc: 5 Using Gauss s Law Select the mathematical suface (a.k.a. Gaussian Suface) - to detemine the field at a paticula point, that point must lie on the suface - Gaussian suface need not be a eal physical suface in empty space, patially o totally embedded in a solid body Gaussian suface should have the same symmeties as chage distibution. - concentic sphee, coaial cylinde, etc. Closed Gaussian suface can be thought of as seveal sepaate aeas ove which the integal is (elatively) easy to evaluate. -e.g. coaial cylinde cylinde walls caps If is pependicula to the suface ( paallel to ) and has constant magnitude then If is tangent (paallel) to the suface ( pependicula to ) then pc: 6

4 Conductos and lectic Fields in lectostatics Conductos contain chages which ae fee to move lectostatics: no chages ae moving F > fo a conducto unde static conditions, the electic field within the conducto is zeo. Fo any point within a conducto, and all Gaussian sufaces completely imbedded within the conducto within bulk conducto > all (ecess) chage lies on the suface! (fo a conducto unde static conditions) pc: 7 Conducto with void: all chage lies on oute suface unless thee is an isolated chage within void. Faaday ice-pail epeiment chaged conducting ball loweed to inteio of ice-pail ball touches pail > pat of inteio of conducto Ball comes out unchaged > veifies Gauss s Law > Coulomb s Law Moden vesions establish eponent in Coulomb s to 6 decimal places pc: 8

5 Field of a conducting sphee, with total chage and adius R R Spheical symmety > spheical Gaussian sufaces constant on suface, pependicula to suface on inteio eteio: 4π 4π R pc: 9 Field of a unifom ball of chage, with total chage and adius R R R Spheical symmety > spheical Gaussian sufaces constant on suface, pependicula to suface eteio: inteio: 4π 4π 4π 4π 4 π 4 πr R 4π R 4π R pc:

6 Line of chage (infinite), chage pe unit length λ cylindical symmety, is adially outwad (fo positive λ) Gaussian suface: finite cylinde, length l and adius l Caps: paallel to suface, Φ Cylinde: pependicula to the suface lπ lπ λ π λl pc: Symmety is the Key! Spheical Symmety Cylindical Symmety kq kλ enc enc pc:

7 pc: Field of an infinite sheet of chage, chage pe aea infinite plane, is pependicula to the plane (fo positive ) with eflection symmety Gaussian suface: finite cylinde, length centeed on plane, caps with aea Tube: paallel to suface, Φ Caps: pependicula to the sufaces pc: 4 Two oppositely chaged infinite conducting plates (/ ) plana geomety, is pependicula to the plane Gaussian sufaces: finite cylinde, length l centeed on plane, caps with aea Tube: paallel to suface, Φ Caps: pependicula to the sufaces

Gauss Law. Physics 231 Lecture 2-1

Gauss Law. Physics 231 Lecture 2-1 Gauss Law Physics 31 Lectue -1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing

More information

Chapter 26 - Electric Field. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University

Chapter 26 - Electric Field. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University Chapte 6 lectic Field A PowePoint Pesentation by Paul. Tippens, Pofesso of Physics Southen Polytechnic State Univesity 7 Objectives: Afte finishing this unit you should be able to: Define the electic field

More information

Chapter 22 The Electric Field II: Continuous Charge Distributions

Chapter 22 The Electric Field II: Continuous Charge Distributions Chapte The lectic Field II: Continuous Chage Distibutions 1 [M] A unifom line chage that has a linea chage density l equal to.5 nc/m is on the x axis between x and x 5. m. (a) What is its total chage?

More information

Chapter 23: Gauss s Law

Chapter 23: Gauss s Law Chapte 3: Gauss s Law Homewok: Read Chapte 3 Questions, 5, 1 Poblems 1, 5, 3 Gauss s Law Gauss s Law is the fist of the fou Maxwell Equations which summaize all of electomagnetic theoy. Gauss s Law gives

More information

F = kq 1q 2 r 2. F 13 = k( q)(2q) 2a 2 cosθˆx + sinθŷ F 14 = k( 2q)(2q) F 12 = k(q)(2q) a 2. tanθ = a a

F = kq 1q 2 r 2. F 13 = k( q)(2q) 2a 2 cosθˆx + sinθŷ F 14 = k( 2q)(2q) F 12 = k(q)(2q) a 2. tanθ = a a .1 What ae the hoizontal and vetical components of the esultant electostatic foce on the chage in the lowe left cone of the squae if q =1. 1 7 and a =5.cm? +q -q a +q a -q F = kq 1q F 1 = k(q)(q) a F 13

More information

Chapter 4. Gauss s Law

Chapter 4. Gauss s Law Chapte 4 Gauss s Law 4.1 lectic Flux...4-4. Gauss s Law...4-3 xample 4.1: Infinitely Long Rod of Unifom Chage Density...4-8 xample 4.: Infinite Plane of Chage...4-9 xample 4.3: Spheical Shell...4-1 xample

More information

Physics 202, Lecture 4. Gauss s Law: Review

Physics 202, Lecture 4. Gauss s Law: Review Physics 202, Lectue 4 Today s Topics Review: Gauss s Law Electic Potential (Ch. 25-Pat I) Electic Potential Enegy and Electic Potential Electic Potential and Electic Field Next Tuesday: Electic Potential

More information

Chapter 22. Outside a uniformly charged sphere, the field looks like that of a point charge at the center of the sphere.

Chapter 22. Outside a uniformly charged sphere, the field looks like that of a point charge at the center of the sphere. Chapte.3 What is the magnitude of a point chage whose electic field 5 cm away has the magnitude of.n/c. E E 5.56 1 11 C.5 An atom of plutonium-39 has a nuclea adius of 6.64 fm and atomic numbe Z94. Assuming

More information

2 - ELECTROSTATIC POTENTIAL AND CAPACITANCE Page 1

2 - ELECTROSTATIC POTENTIAL AND CAPACITANCE Page 1 - ELECTROSTATIC POTENTIAL AND CAPACITANCE Page. Line Integal of Electic Field If a unit positive chage is displaced by `given by dw E. dl dl in an electic field of intensity E, wok done is Line integation

More information

Lesson 7 Gauss s Law and Electric Fields

Lesson 7 Gauss s Law and Electric Fields Lesson 7 Gauss s Law and Electic Fields Lawence B. Rees 7. You may make a single copy of this document fo pesonal use without witten pemission. 7. Intoduction While it is impotant to gain a solid conceptual

More information

Gauss Law in dielectrics

Gauss Law in dielectrics Gauss Law in dielectics We fist deive the diffeential fom of Gauss s law in the pesence of a dielectic. Recall, the diffeential fom of Gauss Law is This law is always tue. E In the pesence of dielectics,

More information

Today in Physics 217: multipole expansion

Today in Physics 217: multipole expansion Today in Physics 17: multipole expansion Multipole expansions Electic multipoles and thei moments Monopole and dipole, in detail Quadupole, octupole, Example use of multipole expansion as appoximate solution

More information

Physics: Electromagnetism Spring PROBLEM SET 6 Solutions

Physics: Electromagnetism Spring PROBLEM SET 6 Solutions Physics: Electomagnetism Sping 7 Physics: Electomagnetism Sping 7 PROBEM SET 6 Solutions Electostatic Enegy Basics: Wolfson and Pasachoff h 6 Poblem 7 p 679 Thee ae si diffeent pais of equal chages and

More information

Chapter 2. Electrostatics

Chapter 2. Electrostatics Chapte. Electostatics.. The Electostatic Field To calculate the foce exeted by some electic chages,,, 3,... (the souce chages) on anothe chage Q (the test chage) we can use the pinciple of supeposition.

More information

14. Gravitation Universal Law of Gravitation (Newton):

14. Gravitation Universal Law of Gravitation (Newton): 14. Gavitation 1 Univesal Law of Gavitation (ewton): The attactive foce between two paticles: F = G m 1m 2 2 whee G = 6.67 10 11 m 2 / kg 2 is the univesal gavitational constant. F m 2 m 1 F Paticle #1

More information

The Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = -W/q 0 1V [Volt] =1 Nm/C

The Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = -W/q 0 1V [Volt] =1 Nm/C Geneal Physics - PH Winte 6 Bjoen Seipel The Electic Potential, Electic Potential Enegy and Enegy Consevation Electic Potential Enegy U is the enegy of a chaged object in an extenal electic field (Unit

More information

2008 Quarter-Final Exam Solutions

2008 Quarter-Final Exam Solutions 2008 Quate-final Exam - Solutions 1 2008 Quate-Final Exam Solutions 1 A chaged paticle with chage q and mass m stats with an initial kinetic enegy K at the middle of a unifomly chaged spheical egion of

More information

A r. (Can you see that this just gives the formula we had above?)

A r. (Can you see that this just gives the formula we had above?) 24-1 (SJP, Phys 1120) lectic flux, and Gauss' law Finding the lectic field due to a bunch of chages is KY! Once you know, you know the foce on any chage you put down - you can pedict (o contol) motion

More information

4.1 Cylindrical and Polar Coordinates

4.1 Cylindrical and Polar Coordinates 4.1 Cylindical and Pola Coodinates 4.1.1 Geometical Axisymmety A lage numbe of pactical engineeing poblems involve geometical featues which have a natual axis of symmety, such as the solid cylinde, shown

More information

Problems on Force Exerted by a Magnetic Fields from Ch 26 T&M

Problems on Force Exerted by a Magnetic Fields from Ch 26 T&M Poblems on oce Exeted by a Magnetic ields fom Ch 6 TM Poblem 6.7 A cuent-caying wie is bent into a semicicula loop of adius that lies in the xy plane. Thee is a unifom magnetic field B Bk pependicula to

More information

Chapter 13 Gravitation

Chapter 13 Gravitation Chapte 13 Gavitation Newton, who extended the concept of inetia to all bodies, ealized that the moon is acceleating and is theefoe subject to a centipetal foce. He guessed that the foce that keeps the

More information

Magnetism: a new force!

Magnetism: a new force! -1 Magnetism: a new foce! o fa, we'e leaned about two foces: gaity and the electic field foce. F E = E, FE = E Definition of E-field kq E-fields ae ceated by chages: E = 2 E-field exets a foce on othe

More information

Gauss s Law. Figure 22.1 A great white shark can detect tiny electric fields generated by its prey.

Gauss s Law. Figure 22.1 A great white shark can detect tiny electric fields generated by its prey. lectic Fields and Gauss s Law What We Will Lean 711.1 Definition of an lectic Field 711. Field Lines 71 Point Chage 71 Two Point Chages of Opposite Sign 71 Two Point Chages with the Same Sign 71 Geneal

More information

GAUSS S LAW APPLIED TO CYLINDRICAL AND PLANAR CHARGE DISTRIBUTIONS ` E MISN-0-133. CHARGE DISTRIBUTIONS by Peter Signell, Michigan State University

GAUSS S LAW APPLIED TO CYLINDRICAL AND PLANAR CHARGE DISTRIBUTIONS ` E MISN-0-133. CHARGE DISTRIBUTIONS by Peter Signell, Michigan State University MISN-0-133 GAUSS S LAW APPLIED TO CYLINDRICAL AND PLANAR CHARGE DISTRIBUTIONS GAUSS S LAW APPLIED TO CYLINDRICAL AND PLANAR CHARGE DISTRIBUTIONS by Pete Signell, Michigan State Univesity 1. Intoduction..............................................

More information

Revision Guide for Chapter 11

Revision Guide for Chapter 11 Revision Guide fo Chapte 11 Contents Student s Checklist Revision Notes Momentum... 4 Newton's laws of motion... 4 Gavitational field... 5 Gavitational potential... 6 Motion in a cicle... 7 Summay Diagams

More information

Samples of conceptual and analytical/numerical questions from chap 21, C&J, 7E

Samples of conceptual and analytical/numerical questions from chap 21, C&J, 7E CHAPTER 1 Magnetism CONCEPTUAL QUESTIONS Cutnell & Johnson 7E 3. ssm A chaged paticle, passing though a cetain egion of space, has a velocity whose magnitude and diection emain constant, (a) If it is known

More information

Chapter 13 Gravitation. Problems: 1, 4, 5, 7, 18, 19, 25, 29, 31, 33, 43

Chapter 13 Gravitation. Problems: 1, 4, 5, 7, 18, 19, 25, 29, 31, 33, 43 Chapte 13 Gavitation Poblems: 1, 4, 5, 7, 18, 19, 5, 9, 31, 33, 43 Evey object in the univese attacts evey othe object. This is called gavitation. We e use to dealing with falling bodies nea the Eath.

More information

Voltage ( = Electric Potential )

Voltage ( = Electric Potential ) V-1 of 9 Voltage ( = lectic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage

More information

Chapter 30: Magnetic Fields Due to Currents

Chapter 30: Magnetic Fields Due to Currents d Chapte 3: Magnetic Field Due to Cuent A moving electic chage ceate a magnetic field. One of the moe pactical way of geneating a lage magnetic field (.1-1 T) i to ue a lage cuent flowing though a wie.

More information

Notes on Electric Fields of Continuous Charge Distributions

Notes on Electric Fields of Continuous Charge Distributions Notes on Electic Fields of Continuous Chage Distibutions Fo discete point-like electic chages, the net electic field is a vecto sum of the fields due to individual chages. Fo a continuous chage distibution

More information

Chapter F. Magnetism. Blinn College - Physics Terry Honan

Chapter F. Magnetism. Blinn College - Physics Terry Honan Chapte F Magnetism Blinn College - Physics 46 - Tey Honan F. - Magnetic Dipoles and Magnetic Fields Electomagnetic Duality Thee ae two types of "magnetic chage" o poles, Noth poles N and South poles S.

More information

XIIth PHYSICS (C2, G2, C, G) Solution

XIIth PHYSICS (C2, G2, C, G) Solution XIIth PHYSICS (C, G, C, G) -6- Solution. A 5 W, 0 V bulb and a 00 W, 0 V bulb ae connected in paallel acoss a 0 V line nly 00 watt bulb will fuse nly 5 watt bulb will fuse Both bulbs will fuse None of

More information

Magnetic Field and Magnetic Forces. Young and Freedman Chapter 27

Magnetic Field and Magnetic Forces. Young and Freedman Chapter 27 Magnetic Field and Magnetic Foces Young and Feedman Chapte 27 Intoduction Reiew - electic fields 1) A chage (o collection of chages) poduces an electic field in the space aound it. 2) The electic field

More information

9. Mathematics Practice Paper for Class XII (CBSE) Available Online Tutoring for students of classes 4 to 12 in Physics, Chemistry, Mathematics

9. Mathematics Practice Paper for Class XII (CBSE) Available Online Tutoring for students of classes 4 to 12 in Physics, Chemistry, Mathematics Available Online Tutoing fo students of classes 4 to 1 in Physics, 9. Mathematics Class 1 Pactice Pape 1 3 1. Wite the pincipal value of cos.. Wite the ange of the pincipal banch of sec 1 defined on the

More information

Fluids Lecture 15 Notes

Fluids Lecture 15 Notes Fluids Lectue 15 Notes 1. Unifom flow, Souces, Sinks, Doublets Reading: Andeson 3.9 3.12 Unifom Flow Definition A unifom flow consists of a velocit field whee V = uî + vĵ is a constant. In 2-D, this velocit

More information

Poynting Vector and Energy Flow in a Capacitor Challenge Problem Solutions

Poynting Vector and Energy Flow in a Capacitor Challenge Problem Solutions Poynting Vecto an Enegy Flow in a Capacito Challenge Poblem Solutions Poblem 1: A paallel-plate capacito consists of two cicula plates, each with aius R, sepaate by a istance. A steay cuent I is flowing

More information

Physics 235 Chapter 5. Chapter 5 Gravitation

Physics 235 Chapter 5. Chapter 5 Gravitation Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus

More information

12. Rolling, Torque, and Angular Momentum

12. Rolling, Torque, and Angular Momentum 12. olling, Toque, and Angula Momentum 1 olling Motion: A motion that is a combination of otational and tanslational motion, e.g. a wheel olling down the oad. Will only conside olling with out slipping.

More information

LINES AND TANGENTS IN POLAR COORDINATES

LINES AND TANGENTS IN POLAR COORDINATES LINES AND TANGENTS IN POLAR COORDINATES ROGER ALEXANDER DEPARTMENT OF MATHEMATICS 1. Pola-coodinate equations fo lines A pola coodinate system in the plane is detemined by a point P, called the pole, and

More information

Electric Fields and Gauss s Law law. January 21, 2014 Physics for Scientists & Engineers 2, Chapter 22 1

Electric Fields and Gauss s Law law. January 21, 2014 Physics for Scientists & Engineers 2, Chapter 22 1 Electric Fields and Gauss s Law law January 21, 2014 Physics for Scientists & Engineers 2, Chapter 22 1 Announcements! First exam is next Tuesday, January 28 45 minute exam during lecture time You can

More information

Forces & Magnetic Dipoles. r r τ = μ B r

Forces & Magnetic Dipoles. r r τ = μ B r Foces & Magnetic Dipoles x θ F θ F. = AI τ = U = Fist electic moto invented by Faaday, 1821 Wie with cuent flow (in cup of Hg) otates aound a a magnet Faaday s moto Wie with cuent otates aound a Pemanent

More information

Gravitation and Kepler s Laws Newton s Law of Universal Gravitation in vectorial. Gm 1 m 2. r 2

Gravitation and Kepler s Laws Newton s Law of Universal Gravitation in vectorial. Gm 1 m 2. r 2 F Gm Gavitation and Keple s Laws Newton s Law of Univesal Gavitation in vectoial fom: F 12 21 Gm 1 m 2 12 2 ˆ 12 whee the hat (ˆ) denotes a unit vecto as usual. Gavity obeys the supeposition pinciple,

More information

Module 3: Sections 2.1 through 2.8 Module 4: Sections 2.9 through

Module 3: Sections 2.1 through 2.8 Module 4: Sections 2.9 through Module 3: Sections.1 though.8 Module 4: Sections.9 though.14 1 Table of Contents.1 Electic Chage... -3. Coulomb's Law... -3..1 Van de Gaaff Geneato (link)... -4.3 Pinciple of Supeposition... -5 Example.1:

More information

Review Module: Dot Product

Review Module: Dot Product MASSACHUSETTS INSTITUTE OF TECHNOLOGY Depatment of Physics 801 Fall 2009 Review Module: Dot Poduct We shall intoduce a vecto opeation, called the dot poduct o scala poduct that takes any two vectos and

More information

TRIGONOMETRY REVIEW. The Cosines and Sines of the Standard Angles

TRIGONOMETRY REVIEW. The Cosines and Sines of the Standard Angles TRIGONOMETRY REVIEW The Cosines and Sines of the Standad Angles P θ = ( cos θ, sin θ ) . ANGLES AND THEIR MEASURE In ode to define the tigonometic functions so that they can be used not only fo tiangula

More information

Chapter 22 Solutions

Chapter 22 Solutions PHY49 Chapte Solutions Poblem : A +5 micoc chage is located 4 cm fom a +3 micoc chage The magnitude of the electostatic foce on the lage chage and on the smalle chage (in N) is espectively Answe: 5 5 Solution:

More information

Lecture 16: Color and Intensity. and he made him a coat of many colours. Genesis 37:3

Lecture 16: Color and Intensity. and he made him a coat of many colours. Genesis 37:3 Lectue 16: Colo and Intensity and he made him a coat of many colous. Genesis 37:3 1. Intoduction To display a pictue using Compute Gaphics, we need to compute the colo and intensity of the light at each

More information

Algebra and Trig. I. A point is a location or position that has no size or dimension.

Algebra and Trig. I. A point is a location or position that has no size or dimension. Algeba and Tig. I 4.1 Angles and Radian Measues A Point A A B Line AB AB A point is a location o position that has no size o dimension. A line extends indefinitely in both diections and contains an infinite

More information

Magnetic Field in a Time-Dependent Capacitor

Magnetic Field in a Time-Dependent Capacitor Magnetic Field in a Time-Dependent Capacito 1 Poblem Kik T. McDonald Joseph Heny Laboatoies, Pinceton Univesity, Pinceton, NJ 8544 (Octobe 3, 23) Reconside the classic example of the use of Maxwell s displacement

More information

Coordinate Systems L. M. Kalnins, March 2009

Coordinate Systems L. M. Kalnins, March 2009 Coodinate Sstems L. M. Kalnins, Mach 2009 Pupose of a Coodinate Sstem The pupose of a coodinate sstem is to uniquel detemine the position of an object o data point in space. B space we ma liteall mean

More information

Lab 5: Circular Motion

Lab 5: Circular Motion Lab 5: Cicula motion Physics 193 Fall 2006 Lab 5: Cicula Motion I. Intoduction The lab today involves the analysis of objects that ae moving in a cicle. Newton s second law as applied to cicula motion

More information

In the lecture on double integrals over non-rectangular domains we used to demonstrate the basic idea

In the lecture on double integrals over non-rectangular domains we used to demonstrate the basic idea Double Integals in Pola Coodinates In the lectue on double integals ove non-ectangula domains we used to demonstate the basic idea with gaphics and animations the following: Howeve this paticula example

More information

SELF-INDUCTANCE AND INDUCTORS

SELF-INDUCTANCE AND INDUCTORS MISN-0-144 SELF-INDUCTANCE AND INDUCTORS SELF-INDUCTANCE AND INDUCTORS by Pete Signell Michigan State Univesity 1. Intoduction.............................................. 1 A 2. Self-Inductance L.........................................

More information

Nuclear models: Fermi-Gas Model Shell Model

Nuclear models: Fermi-Gas Model Shell Model Lectue Nuclea mode: Femi-Gas Model Shell Model WS/: Intoduction to Nuclea and Paticle Physics The basic concept of the Femi-gas model The theoetical concept of a Femi-gas may be applied fo systems of weakly

More information

TALLINN UNIVERSITY OF TECHNOLOGY, INSTITUTE OF PHYSICS 14. NEWTON'S RINGS

TALLINN UNIVERSITY OF TECHNOLOGY, INSTITUTE OF PHYSICS 14. NEWTON'S RINGS 4. NEWTON'S RINGS. Obective Detemining adius of cuvatue of a long focal length plano-convex lens (lage adius of cuvatue).. Equipment needed Measuing micoscope, plano-convex long focal length lens, monochomatic

More information

Seventh Edition DYNAMICS 15Ferdinand P. Beer E. Russell Johnston, Jr. Lecture Notes: J. Walt Oler Texas Tech University

Seventh Edition DYNAMICS 15Ferdinand P. Beer E. Russell Johnston, Jr. Lecture Notes: J. Walt Oler Texas Tech University Seenth 15Fedinand P. ee E. Russell Johnston, J. Kinematics of Lectue Notes: J. Walt Ole Texas Tech Uniesity Rigid odies CHPTER VECTOR MECHNICS FOR ENGINEERS: YNMICS 003 The McGaw-Hill Companies, Inc. ll

More information

Lesson 8 Ampère s Law and Differential Operators

Lesson 8 Ampère s Law and Differential Operators Lesson 8 Ampèe s Law and Diffeential Opeatos Lawence Rees 7 You ma make a single cop of this document fo pesonal use without witten pemission 8 Intoduction Thee ae significant diffeences between the electic

More information

Learning Objectives. Decreasing size. ~10 3 m. ~10 6 m. ~10 10 m 1/22/2013. Describe ionic, covalent, and metallic, hydrogen, and van der Waals bonds.

Learning Objectives. Decreasing size. ~10 3 m. ~10 6 m. ~10 10 m 1/22/2013. Describe ionic, covalent, and metallic, hydrogen, and van der Waals bonds. Lectue #0 Chapte Atomic Bonding Leaning Objectives Descibe ionic, covalent, and metallic, hydogen, and van de Waals bonds. Which mateials exhibit each of these bonding types? What is coulombic foce of

More information

Your Comments. did not understand any of this wtf. so over my head I have no idea what I am doing :(

Your Comments. did not understand any of this wtf. so over my head I have no idea what I am doing :( You Comments Llamas, and why it is so difficult to get someone to buy me one as a pet. All ask is that it beathes fie. have simple needs people. Seiously. p.s. this lectue was had. did not undestand any

More information

UNIVERSITY OF CALIFORNIA BERKELEY Structural Engineering, Professor: S. Govindjee. Elastic-Perfectly Plastic Thick Walled Sphere

UNIVERSITY OF CALIFORNIA BERKELEY Structural Engineering, Professor: S. Govindjee. Elastic-Perfectly Plastic Thick Walled Sphere UNIVERSITY OF CALIFORNIA BERKELEY Stuctual Engineeing, Depatment of Civil Engineeing Mechanics and Mateials Fall 00 Pofesso: S Govindjee Elastic-Pefectly Plastic Thick Walled Sphee Conside a thick walled

More information

FXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it.

FXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it. Candidates should be able to : Descibe how a mass ceates a gavitational field in the space aound it. Define gavitational field stength as foce pe unit mass. Define and use the peiod of an object descibing

More information

The Critical Angle and Percent Efficiency of Parabolic Solar Cookers

The Critical Angle and Percent Efficiency of Parabolic Solar Cookers The Citical Angle and Pecent Eiciency o Paabolic Sola Cookes Aiel Chen Abstact: The paabola is commonly used as the cuve o sola cookes because o its ability to elect incoming light with an incoming angle

More information

Physics 107 HOMEWORK ASSIGNMENT #14

Physics 107 HOMEWORK ASSIGNMENT #14 Physics 107 HOMEWORK ASSIGNMENT #14 Cutnell & Johnson, 7 th edition Chapte 17: Poblem 44, 60 Chapte 18: Poblems 14, 18, 8 **44 A tube, open at only one end, is cut into two shote (nonequal) lengths. The

More information

Heat transfer has direction as well as magnitude. The rate of heat conduction

Heat transfer has direction as well as magnitude. The rate of heat conduction HEAT CONDUCTION EQUATION CHAPTER 2 Heat tansfe has diection as well as magnitude. The ate of heat conduction in a specified diection is popotional to the tempeatue gadient, which is the ate of change in

More information

UNIT 21: ELECTRICAL AND GRAVITATIONAL POTENTIAL Approximate time two 100-minute sessions

UNIT 21: ELECTRICAL AND GRAVITATIONAL POTENTIAL Approximate time two 100-minute sessions Name St.No. - Date(YY/MM/DD) / / Section Goup# UNIT 21: ELECTRICAL AND GRAVITATIONAL POTENTIAL Appoximate time two 100-minute sessions OBJECTIVES I began to think of gavity extending to the ob of the moon,

More information

GRAVITATIONAL FIELD: CHAPTER 11. The groundwork for Newton s great contribution to understanding gravity was laid by three majors players:

GRAVITATIONAL FIELD: CHAPTER 11. The groundwork for Newton s great contribution to understanding gravity was laid by three majors players: CHAPT 11 TH GAVITATIONAL FILD (GAVITY) GAVITATIONAL FILD: The goundwok fo Newton s geat contibution to undestanding gavity was laid by thee majos playes: Newton s Law of Gavitation o gavitational and inetial

More information

Thomas J. Osler, Mathematics Department and Tirupathi R. Chandrupatla, Mechanical Engineering. Rowan University Glassboro, NJ

Thomas J. Osler, Mathematics Department and Tirupathi R. Chandrupatla, Mechanical Engineering. Rowan University Glassboro, NJ /9/04 SOME UNUSUAL EXPRESSIONS FOR THE INRADIUS OF A TRIANGLE Tomas J. Osle, Matematics Depatment and Tiupati R. Candupatla, Mecanical Engineeing Rowan Univesity Glassboo, NJ 0808 Osle@owan.edu Candupatla@owan.edu

More information

Deflection of Electrons by Electric and Magnetic Fields

Deflection of Electrons by Electric and Magnetic Fields Physics 233 Expeiment 42 Deflection of Electons by Electic and Magnetic Fields Refeences Loain, P. and D.R. Coson, Electomagnetism, Pinciples and Applications, 2nd ed., W.H. Feeman, 199. Intoduction An

More information

PHYSICS 111 HOMEWORK SOLUTION #5. March 3, 2013

PHYSICS 111 HOMEWORK SOLUTION #5. March 3, 2013 PHYSICS 111 HOMEWORK SOLUTION #5 Mach 3, 2013 0.1 You 3.80-kg physics book is placed next to you on the hoizontal seat of you ca. The coefficient of static fiction between the book and the seat is 0.650,

More information

A couple is a pair of forces, equal in magnitude, oppositely directed, and displaced by perpendicular distance, d. F A F B (= -F A

A couple is a pair of forces, equal in magnitude, oppositely directed, and displaced by perpendicular distance, d. F A F B (= -F A 5 Moment of a Couple Ref: Hibbele 4.6, edfod & Fowle: Statics 4.4 couple is a pai of foces, equal in magnitude, oppositely diected, and displaced by pependicula distance, d. d (= - ) Since the foces ae

More information

Problem Set 6: Solutions

Problem Set 6: Solutions UNIVESITY OF ALABAMA Depatment of Physics and Astonomy PH 16-4 / LeClai Fall 28 Poblem Set 6: Solutions 1. Seway 29.55 Potons having a kinetic enegy of 5. MeV ae moving in the positive x diection and ente

More information

(References to) "Introduction to Electrodynamics" by David J. Griffiths 3rd ed., Prentice-Hall, 1999. ISBN 0-13-805326-X

(References to) Introduction to Electrodynamics by David J. Griffiths 3rd ed., Prentice-Hall, 1999. ISBN 0-13-805326-X lectic Fields in Matte page. Capstones in Physics: lectomagnetism. LCTRIC FILDS IN MATTR.. Multipole xpansion A. Multipole expansion of potential B. Dipole moment C. lectic field of dipole D. Dipole in

More information

Carter-Penrose diagrams and black holes

Carter-Penrose diagrams and black holes Cate-Penose diagams and black holes Ewa Felinska The basic intoduction to the method of building Penose diagams has been pesented, stating with obtaining a Penose diagam fom Minkowski space. An example

More information

CHAPTER 5 GRAVITATIONAL FIELD AND POTENTIAL

CHAPTER 5 GRAVITATIONAL FIELD AND POTENTIAL CHATER 5 GRAVITATIONAL FIELD AND OTENTIAL 5. Intoduction. This chapte deals with the calculation of gavitational fields and potentials in the vicinity of vaious shapes and sizes of massive bodies. The

More information

Magnetism. The Magnetic Force. B x x x x x x x x x x x x v x x x x x x. F = q

Magnetism. The Magnetic Force. B x x x x x x x x x x x x v x x x x x x. F = q Magnetism The Magnetic Foce F = qe + qv x x x x x x x x x x x x v x x x x x x F q v q F v F = q 0 IM intoduced the fist had disk in 1957, when data usually was stoed on tapes. It consisted of 50 plattes,

More information

Physics 111 Fall 2007 Electrostatic Forces and the Electric Field - Solutions

Physics 111 Fall 2007 Electrostatic Forces and the Electric Field - Solutions Physics 111 Fall 007 Electostatic Foces an the Electic Fiel - Solutions 1. Two point chages, 5 µc an -8 µc ae 1. m apat. Whee shoul a thi chage, equal to 5 µc, be place to make the electic fiel at the

More information

Vector Calculus: Are you ready? Vectors in 2D and 3D Space: Review

Vector Calculus: Are you ready? Vectors in 2D and 3D Space: Review Vecto Calculus: Ae you eady? Vectos in D and 3D Space: Review Pupose: Make cetain that you can define, and use in context, vecto tems, concepts and fomulas listed below: Section 7.-7. find the vecto defined

More information

AP-C Magnetism. AP-C Objectives (from College Board Learning Objectives for AP Physics)

AP-C Magnetism. AP-C Objectives (from College Board Learning Objectives for AP Physics) AP-C Magnetism AP-C (fom Coege oad Leaning fo AP Physics) 1. oces on moving chages in magnetic fieds a. Cacuate the magnitude and diection of the foce in tems of q, v, and, and expain why the magnetic

More information

Set 3: 120 N/m units 0.25 Kg. 1A The unit of the damping constant is a) Kg/s b) N/m c) N d) Joule/s e) NA

Set 3: 120 N/m units 0.25 Kg. 1A The unit of the damping constant is a) Kg/s b) N/m c) N d) Joule/s e) NA 05/05/04 PHYSICS 3 Exa #1 NAME Please wite down you nae also on the back side of this exa 1. Hee ae thee sets of values fo the sping constant k, daping constant b, and ass fo thee daped oscillatos: Set

More information

Newton s Shell Theorem

Newton s Shell Theorem Newton Shell Theoem Abtact One of the pincipal eaon Iaac Newton wa motivated to invent the Calculu wa to how that in applying hi Law of Univeal Gavitation to pheically-ymmetic maive bodie (like planet,

More information

mv2. Equating the two gives 4! 2. The angular velocity is the angle swept per GM (2! )2 4! 2 " 2 = GM . Combining the results we get !

mv2. Equating the two gives 4! 2. The angular velocity is the angle swept per GM (2! )2 4! 2  2 = GM . Combining the results we get ! Chapte. he net foce on the satellite is F = G Mm and this plays the ole of the centipetal foce on the satellite i.e. mv mv. Equating the two gives = G Mm i.e. v = G M. Fo cicula motion we have that v =!

More information

Exam 3: Equation Summary

Exam 3: Equation Summary MASSACHUSETTS INSTITUTE OF TECHNOLOGY Depatment of Physics Physics 8.1 TEAL Fall Tem 4 Momentum: p = mv, F t = p, Fext ave t= t f t= Exam 3: Equation Summay total = Impulse: I F( t ) = p Toque: τ = S S,P

More information

Voltage ( = Electric Potential )

Voltage ( = Electric Potential ) V-1 Voltage ( = Electic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage is

More information

Moment and couple. In 3-D, because the determination of the distance can be tedious, a vector approach becomes advantageous. r r

Moment and couple. In 3-D, because the determination of the distance can be tedious, a vector approach becomes advantageous. r r Moment and couple In 3-D, because the detemination of the distance can be tedious, a vecto appoach becomes advantageous. o k j i M k j i M o ) ( ) ( ) ( + + M o M + + + + M M + O A Moment about an abita

More information

2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses,

2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses, 3.4. KEPLER S LAWS 145 3.4 Keple s laws You ae familia with the idea that one can solve some mechanics poblems using only consevation of enegy and (linea) momentum. Thus, some of what we see as objects

More information

Solutions to Homework Set #5 Phys2414 Fall 2005

Solutions to Homework Set #5 Phys2414 Fall 2005 Solution Set #5 1 Solutions to Homewok Set #5 Phys414 Fall 005 Note: The numbes in the boxes coespond to those that ae geneated by WebAssign. The numbes on you individual assignment will vay. Any calculated

More information

The Grating Spectrometer and Atomic Spectra

The Grating Spectrometer and Atomic Spectra PHY 19 Gating Spectomete 1 The Gating Spectomete and Atomic Specta Intoduction In the pevious expeiment diffaction and intefeence wee discussed and at the end a diffaction gating was intoduced. In this

More information

Lab M4: The Torsional Pendulum and Moment of Inertia

Lab M4: The Torsional Pendulum and Moment of Inertia M4.1 Lab M4: The Tosional Pendulum and Moment of netia ntoduction A tosional pendulum, o tosional oscillato, consists of a disk-like mass suspended fom a thin od o wie. When the mass is twisted about the

More information

Chapter 4. Electric Potential

Chapter 4. Electric Potential Chapte 4 Electic Potential 4.1 Potential and Potential Enegy... 4-3 4.2 Electic Potential in a Unifom Field... 4-7 4.3 Electic Potential due to Point Chages... 4-8 4.3.1 Potential Enegy in a System of

More information

Chapter 8, Rotational Kinematics. Angular Displacement

Chapter 8, Rotational Kinematics. Angular Displacement Chapte 8, Rotational Kinematics Sections 1 3 only Rotational motion and angula displacement Angula velocity and angula acceleation Equations of otational kinematics 1 Angula Displacement! B l A The length

More information

1.1 KINEMATIC RELATIONSHIPS

1.1 KINEMATIC RELATIONSHIPS 1.1 KINEMATIC RELATIONSHIPS Thoughout the Advanced Highe Physics couse calculus techniques will be used. These techniques ae vey poweful and knowledge of integation and diffeentiation will allow a deepe

More information

Review of Coordinate Systems

Review of Coordinate Systems Review o Coodinate Sstems good undestanding o coodinate sstems can be ve helpul in solving poblems elated to Mawell s Equations. The thee most common coodinate sstems ae ectangula (,, ), clindical (,,

More information

K.S.E.E.B., Malleshwaram, Bangalore SSLC Mathematics-Model Question Paper-1 (2015) Regular Private Candidates (New Syllabus)

K.S.E.E.B., Malleshwaram, Bangalore SSLC Mathematics-Model Question Paper-1 (2015) Regular Private Candidates (New Syllabus) K.S.E.E.B., Malleshwaam, Bangaloe SSLC Mathematics-Model Question Pape-1 (015) Regula Pivate Candidates (New Syllabus) Max Maks: 100 No. of Questions: 50 Time: 3 Hous Code No. : Fou altenatives ae given

More information

In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature.

In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature. Radians At school we usually lean to measue an angle in degees. Howeve, thee ae othe ways of measuing an angle. One that we ae going to have a look at hee is measuing angles in units called adians. In

More information

2.2. Trigonometric Ratios of Any Angle. Investigate Trigonometric Ratios for Angles Greater Than 90

2.2. Trigonometric Ratios of Any Angle. Investigate Trigonometric Ratios for Angles Greater Than 90 . Tigonometic Ratios of An Angle Focus on... detemining the distance fom the oigin to a point (, ) on the teminal am of an angle detemining the value of sin, cos, o tan given an point (, ) on the teminal

More information

Chapter 19: Electric Charges, Forces, and Fields ( ) ( 6 )( 6

Chapter 19: Electric Charges, Forces, and Fields ( ) ( 6 )( 6 Chapte 9 lectic Chages, Foces, an Fiels 6 9. One in a million (0 ) ogen molecules in a containe has lost an electon. We assume that the lost electons have been emove fom the gas altogethe. Fin the numbe

More information

Chapter 2 Coulomb s Law

Chapter 2 Coulomb s Law Chapte Coulomb s Law.1 lectic Chage...-3. Coulomb's Law...-3 Animation.1: Van de Gaaff Geneato...-4.3 Pinciple of Supeposition...-5 xample.1: Thee Chages...-5.4 lectic Field...-7 Animation.: lectic Field

More information

Internal Resistance of cell & Combinations of Cells By R. S. Saini. (M.Sc. Physics, M.Ed.) Kendriya Vidyalaya, Sector 47, Chandigarh

Internal Resistance of cell & Combinations of Cells By R. S. Saini. (M.Sc. Physics, M.Ed.) Kendriya Vidyalaya, Sector 47, Chandigarh ntenal Resistance of cell & Combinations of Cells 01.06.09 By R. S. Saini (M.Sc. Physics, M.d.) Kendiya idyalaya, Secto 47, Chandigah 9417071540 Souces of emf: The electo motive foce is the maximum potential

More information

Introduction to Electric Potential

Introduction to Electric Potential Univesiti Teknologi MARA Fakulti Sains Gunaan Intoduction to Electic Potential : A Physical Science Activity Name: HP: Lab # 3: The goal of today s activity is fo you to exploe and descibe the electic

More information