Instructor: T. Waldek ZerdaInstructor: T. Waldek Zerda office: 142 SWR or 307 SWRoffice: 142 SWR or 307 SWR campus phone: 817-257-7124campus phone: 817-257-7124 email: t.zerda@tcu.eduemail: t.zerda@tcu.edu office hours: M.Tu.W. 2-4 PM; or by office hours: M.Tu.W. 2-4 PM; or by

appointmentappointment

eCollege contains syllabus, lecture notes eCollege contains syllabus, lecture notes and homework solutionsand homework solutions

Lecture notes can also be found:Lecture notes can also be found:http://personal.tcu.edu/zerda/10164/ch**_lecture.ppthttp://personal.tcu.edu/zerda/10164/ch**_lecture.ppt Lab instructions can be found: Lab instructions can be found: http://personal.tcu.edu/zerda/manual/lab**.pdfhttp://personal.tcu.edu/zerda/manual/lab**.pdf

PHYS 10163PHYS 10163

Working problems is the only way to learn physics. You are encouraged to consult your classmates or TCU physics graduate students in solving the homework problems. DO NOT COPY the answers of your fellow students. I reserve rights to reject a homework that I suspect was copied from another student, a web site, a solution manual, or any other source.

Homework must be turn in on time, usually by 10 AM on the day following the day we completely covered a chapter of the textbook. No late homework will be accepted because I will post the homework solution on the class web page immediately after the deadline.

Each homework assignment is worth 100 points. By the end of the semester I will calculate the average of all assignments and it will count for up to 16% of your final grade.

HomeworkHomework

ExamsExamsThere will be 3 partial tests and a final. Each will count for

16% of the final grade.

If you are unable to make it to a scheduled exam, please contact me in advance to make alternate arrangements. Missing the final exam will result in an incomplete in the course. You will have to retake the final at a later date.

During the test all books and notebooks must be closed. You will be allowed to bring ONE 3”x 5” index card with hand written note, equations, etc. and a calculator. The index card may not be photocopied, reduced or computer generated. Violation of this rule will result in failure of the examination.

I will provide relevant constants.

Exams, cont.Exams, cont.Each exam is a partial test and will cover material discussed

between the tests. The final will be structured in a similar way as the partial exams, but may contain additional review questions/problems.

There will be about five questions and about five problems on each exam, a total of ten questions/problems. The problems will be similar to those solved in class, solved examples in the textbook, and homework problems. Questions will be based on conceptual questions, quick quizzes, and additional questions discussed in class.

You have ONE week from the day the exam was returned to you to appeal the grade. After the seventh day the grade becomes permanent.

Class participationClass participation

I encourage you to make every effort to attend class. Due to the nature of this short course, I may have to make changes/announcements and the only way you can learn about them is to attend the class.

I will not read the class roll or check students attendance, except for the first two or three lectures, when I will try to memorize your names.

Remember that you must bring homework assignments to class by 10 AM.

Make-up workMake-up work

Make-ups for missed homework and exams can be granted only under exceptional circumstances (medical emergency, official university business, wedding, etc.). If you know of such impeding circumstances, please contact me in advance so alternative arrangements can be prepared. If it is impossible to notify me in advance, please send an email as soon afterward as possible.

Final gradeFinal gradeThe final grade will be determined by adding scores for the partial exams,

the final, and the average homework. Each of these components will count for 16% of the final grade, 5*16%=80%. The lab will count to the remaining 20%                      

94 - 100 = A94 - 100 = A 90 - 93 = A-90 - 93 = A- 87 - 90 = B+87 - 90 = B+ 84 - 86 = B84 - 86 = B 80 - 83 = B-80 - 83 = B- 77 - 80 = C+77 - 80 = C+ 74 - 76 = C 74 - 76 = C 70 - 73 = C-70 - 73 = C- 66 - 70 = D+66 - 70 = D+ 60 - 65 = D60 - 65 = D 55 - 60 = D-55 - 60 = D- Below 55 FBelow 55 F

HomeworkHomework

Ch.15:3,10,17,31Ch.15:3,10,17,31 Ch.16:3,13,29,39Ch.16:3,13,29,39 Ch.17:15,19,36,47Ch.17:15,19,36,47 Ch.18:2,14,39,45Ch.18:2,14,39,45 Ch.19:7,20,31,45Ch.19:7,20,31,45 Ch.20:10,17,22,37Ch.20:10,17,22,37 Ch.21:5,7,23,35Ch.21:5,7,23,35 Ch.22:7,17,30,45Ch.22:7,17,30,45

Ch.23:6,13,32,39Ch.23:6,13,32,39 Ch.24:3,15,23,39Ch.24:3,15,23,39 Ch.25:9,12,13,19Ch.25:9,12,13,19 Ch.26:5,9,13,19Ch.26:5,9,13,19 Ch.27:6,13,23,43Ch.27:6,13,23,43 Ch.28:7,15,17,38Ch.28:7,15,17,38 Ch.29:1,9,15,30Ch.29:1,9,15,30

Chapter 15Chapter 15Electric Forces andElectric Forces and

Electric FieldsElectric Fields

Conceptual questions: 2,4,7,9,12,14Quizzes: 1,2,3,4,5,6Problems: 11,21,28, 48 Examples: 1,3,6,7,8

Electric ChargesElectric Charges Two types of charges exist; positive and Two types of charges exist; positive and

negativenegative Like charges repel and unlike charges attract Like charges repel and unlike charges attract

one anotherone another Nature’s basic carrier of positive charge is the Nature’s basic carrier of positive charge is the

proton and of negative charge is the electronproton and of negative charge is the electron Protons do not move from one material to another Protons do not move from one material to another

because they are held firmly in the nucleusbecause they are held firmly in the nucleus Negative charges are primarily carried by electronsNegative charges are primarily carried by electrons Gaining or losing electrons is how an object Gaining or losing electrons is how an object

becomes chargedbecomes charged

Properties of ChargeProperties of Charge Electric charge is always conservedElectric charge is always conserved

Charge is not created, only exchangedCharge is not created, only exchanged Objects become charged because Objects become charged because

negative charge is transferred from one negative charge is transferred from one object to anotherobject to another

All charge is a multiple of a fundamental All charge is a multiple of a fundamental unit of charge, symbolized by eunit of charge, symbolized by e

Electrons have a charge of –eElectrons have a charge of –e Protons have a charge of +eProtons have a charge of +e The SI unit of charge is the Coulomb (C)The SI unit of charge is the Coulomb (C)

e = 1.6 x 10e = 1.6 x 10-19-19 C C

InsulatorsInsulators Insulators are materials in which Insulators are materials in which

electric charges do not move freelyelectric charges do not move freely Glass and rubber are examples of Glass and rubber are examples of

insulatorsinsulators When insulators are charged by When insulators are charged by

rubbing, only the rubbed area rubbing, only the rubbed area becomes charged. The charges do becomes charged. The charges do not move.not move.Conductors

Electrons move freely.Metals are examples of conducting materials

Charging by ConductionCharging by Conduction

A charged object (the A charged object (the rod) is placed in contact rod) is placed in contact with another object (the with another object (the sphere)sphere)

Some electrons on the Some electrons on the rod can move to the rod can move to the spheresphere

When the rod is removed, When the rod is removed, the sphere is left with a the sphere is left with a chargecharge

The object being charged The object being charged is always left with a is always left with a charge having the same charge having the same sign as the object doing sign as the object doing the chargingthe charging

Charging by InductionCharging by Induction A negatively charged rubber rod A negatively charged rubber rod

is brought near an uncharged is brought near an uncharged spheresphere

The charges in the sphere are The charges in the sphere are redistributed. Some electrons in redistributed. Some electrons in the sphere are repelled from the the sphere are repelled from the electrons in the rod. After the electrons in the rod. After the sphere is grounded they leave sphere is grounded they leave the sphere.the sphere.

The positive charge on the The positive charge on the sphere is evenly distributed due sphere is evenly distributed due to the repulsion between the to the repulsion between the positive chargespositive charges

Charging by induction requires Charging by induction requires no contact with the object no contact with the object inducing the chargeinducing the charge

Examples of Examples of PolarizationPolarization

The charged object The charged object (on the left) (on the left) induces charge on induces charge on the surface of the the surface of the insulatorinsulator

A charged comb A charged comb attracts bits of attracts bits of paper due to paper due to polarization of the polarization of the paperpaper

If a suspended object A is attracted to object B, which is charged, we can conclude that (a) object A is uncharged, (b) object A is charged, (c) object B is positively charged, or (d) object A may be either charged or uncharged.

QUICK QUIZ 15.1

2. Operating room personnel must wear special conducting shoes while working around oxygen. Why?

7. When a metal object receives a positive charge, does its mass increase, decrease or remain the same?

14. Would life be different if the electrons were positively charged and the protons were negatively charged?Does the choice of signs have any bearings on physical and chemical interactions?

Conceptual questions:

Coulomb’s LawCoulomb’s Law Coulomb’s electrical force has the Coulomb’s electrical force has the

following properties:following properties: It is inversely proportional to the square It is inversely proportional to the square

of the separation between the two of the separation between the two particles and is along the line joining particles and is along the line joining themthem

It is proportional to the product of the It is proportional to the product of the magnitudes of the charges qmagnitudes of the charges q11 and q and q22 on on the two particlesthe two particles

It is attractive if the charges are of It is attractive if the charges are of opposite signs and repulsive if the opposite signs and repulsive if the charges have the same signscharges have the same signs

Coulomb’s LawCoulomb’s Law

1 2

2e

q qF k

r

kkee is called the is called the Coulomb ConstantCoulomb Constant

kkee = 8.99 x 10 = 8.99 x 1099 N m N m22/C/C22

Vector Nature of Electric Vector Nature of Electric ForcesForces

Two point charges are Two point charges are separated by a distance separated by a distance rr

The like charges produce The like charges produce a repulsive force a repulsive force between thembetween them

The force on qThe force on q11 is equal is equal in magnitude and in magnitude and opposite in direction to opposite in direction to the force on qthe force on q22

QUICK QUIZ 15.2Object A has a charge of +2 µC, and object B has a charge of +6 µC. Which statement is true:(a) FAB = –3FBA

(b) FAB = –FBA (c) 3FAB = –FBA

Superposition Principle Superposition Principle ExampleExample

The force exerted The force exerted by qby q11 on q on q3 3 is is FF1313

The force exerted The force exerted by qby q22 on q on q33 is is FF2323

The The total forcetotal force exerted on qexerted on q33 is the is the vector vector sum of sum of FF1313 and and FF2323

The resultant force on any one charge The resultant force on any one charge equals the vector sum of the forces exerted equals the vector sum of the forces exerted by the other individual charges that are by the other individual charges that are present. present.

Remember to add the forces Remember to add the forces vectoriallyvectorially

.

Electric FieldElectric Field

A charged particle, A charged particle, with charge Q, with charge Q, produces an produces an electric field in the electric field in the region of space region of space around itaround it

A small A small test test chargecharge, q, qoo, placed , placed in the field, will in the field, will experience a forceexperience a force

Electric FieldElectric Field Use this Eq. for the magnitude of the fieldUse this Eq. for the magnitude of the field The electric field is a vector quantityThe electric field is a vector quantity The direction of the field is defined to be The direction of the field is defined to be

the direction of the electric force that the direction of the electric force that would be exerted on a small positive test would be exerted on a small positive test charge placed at that pointcharge placed at that point

o

FE

q

Electric field of a point charge is given by

2ek QEr

Direction of Electric FieldDirection of Electric Field

The electric field produced The electric field produced by a negative charge is by a negative charge is directed toward the directed toward the chargecharge A positive test charge would A positive test charge would

be attracted to the negative be attracted to the negative source chargesource charge

The test charge is a VERY small positive chargeThe test charge is a VERY small positive charge

A test charge of +3 µC is at a point P where the electric field due to other charges is directed to the right and has a magnitude of 4 106 N/C. If the test charge is replaced with a –3 µC charge, the electric field at P (a) has the same magnitude but changes direction, (b) increases in magnitude and changes direction, (c) remains the same,(d) decreases in magnitude and changes direction.

QUICK QUIZ 15.3

A Styrofoam ball covered with a conducting paint has a mass of 5.0 10-3 kg and has a charge of 4.0 C. What electric field directed upward will produce an electric force on the ball that will balance the weight of the ball?

15-21

A circular ring of radius b has a total charge q uniformly distributed around it. The magnitude of the electric field at the center of the ring is (a) 0 (b) keq/b2 (c) keq2/b2 (d) keq2/b (e) none of these.

QUICK QUIZ 15.4

QUICK QUIZ 15.5A "free" electron and "free" proton are placed in an identical electric field. Which of the following statements are true? (a) Each particle experiences the same electric force and the same acceleration. (b) The electric force on the proton is greater in magnitude than the force on the electron but in the opposite direction. (c) The electric force on the proton is equal in magnitude to the force on the electron, but in the opposite direction. (d) The magnitude of the acceleration of the electron is greater than that of the proton. (e) Both particles experience the same acceleration.

Problem 15-24Problem 15-24

Positive charges are situated at three corners of a rectangle of size 0.200m by 0.600m. Find the electric field at the fourth corner.

6.00 nC

5.00 nC3.00 nC

Electric Field LinesElectric Field Lines

The field lines are related to the The field lines are related to the field byfield by The electric field vector, E, is tangent The electric field vector, E, is tangent

to the electric field lines at each pointto the electric field lines at each point The number of lines per unit area The number of lines per unit area

through a surface perpendicular to through a surface perpendicular to the lines is proportional to the the lines is proportional to the strength of the electric field in a given strength of the electric field in a given regionregion

Electric Field Line PatternsElectric Field Line Patterns

Point chargePoint charge The lines radiate The lines radiate

equally in all equally in all directionsdirections

For a positive For a positive source charge, source charge, the lines will the lines will radiate outwardradiate outward

Electric Field Line PatternsElectric Field Line Patterns

For a negative For a negative source charge, source charge, the lines will point the lines will point inwardinward

Electric Field Lines of a Electric Field Lines of a DipoleDipole

An electric An electric dipoledipole consists of two consists of two equal and opposite equal and opposite chargescharges

The high density of The high density of lines between the lines between the charges indicates charges indicates the strong electric the strong electric field in this regionfield in this region

Electric Field PatternsElectric Field Patterns

Unequal and unlike Unequal and unlike chargescharges

Note that two lines leave Note that two lines leave the +2q charge for each the +2q charge for each line that terminates on line that terminates on -q -q

Rules for Drawing Electric Rules for Drawing Electric Field LinesField Lines

The lines for a group of charges The lines for a group of charges must begin on positive charges must begin on positive charges and end on negative chargesand end on negative charges

The number of lines drawn leaving The number of lines drawn leaving a positive charge or ending on a a positive charge or ending on a negative charge is proportional to negative charge is proportional to the magnitude of the chargethe magnitude of the charge

No two field lines can cross each No two field lines can cross each otherother

Rank the magnitudes of the electric field at points A, B, and C in the figure below, largest magnitude first.

QUICK QUIZ 15.6

Figure P15.28 shows the electric field lines for two point charges separated by a small distance. (a) Determine the ratio q1/q2.

(b) What are the signs of q1 and q2?  

Fig. 15.28

15.2815.28

Conductors in Electrostatic Conductors in Electrostatic EquilibriumEquilibrium

The electric field is zero everywhere inside The electric field is zero everywhere inside the conducting materialthe conducting material

Any excess charge on an isolated conductor Any excess charge on an isolated conductor resides entirely on its surfaceresides entirely on its surface

The electric field just outside a charged The electric field just outside a charged conductor is perpendicular to the conductor is perpendicular to the conductor’s surfaceconductor’s surface

On an irregularly shaped conductor, the On an irregularly shaped conductor, the charge accumulates at locations where the charge accumulates at locations where the radius of curvature of the surface is smallest radius of curvature of the surface is smallest (that is, at sharp points)(that is, at sharp points)

Two charged parallel Two charged parallel platesplates

+

+

+

-

-

-

Electric field in between the plates is uniform and it magnitude is given by

E=

= Q/A (surface charge density)

ke=1/4o

o =8.85 x 10-12 C2/Nm2

permittivity of the empty space

9. In fair weather there is an electric field at the surface of the Earth, pointing down into the ground. What is the electric charge on the ground in this situation?

12. Is it possible for the electric field to exist in empty space?

18. Why is it a bad idea to seek shelter under a tree during a lightning storm?

Conceptual questionsConceptual questions

In the Bohr theory of the hydrogen atom, an electron moves in a circular orbit about a proton, where the radius of the orbit is 0.53 × 10–10 m. (a) Find the electrostatic force acting on each particle.

21 22 2

e ek q q k e

Fr r

29 2 2 19

210

8 99 10 N m C 1 60 10 C

0 53 10 m

. .

. 8.2 10-8N

(b) If this force causes the centripetal acceleration of the electron, what is the speed of the electron?

2e c eF m a m v r

10 8

-31

0.53 10 m 8.2 10 N

9.11 10 kge

r Fv

m

2.2 106 m/s

Review problem based on Example 15.1

Additional Additional questionsquestions

MCAD MCAD questionquestions s

MCAT questionsMCAT questions1. Which electric charge is possible?

a. 6.02 x 1023 C

b. 3.2 x 10-19 C

c. 2.4 x 10-19 C

d. 8.0 x 10-20 C

2. A sphere with a net charge of +3.0 x 10-3 C is touched by a second identical sphere B, which has a net charge of –9.0 x 10-3C. The two spheres then separate. The net charge on sphere A is now:

a. 3.0 x 10-3 C

b. -3.0 x 10-3 C

c. -6.0 x 10-3 C

d. -9.0 x 10-3 C