Electricity & MagnetismElectricity & Magnetism

Dr Tarlochan Singh DhillonOffice: DAMA 089bEmail: tdhillon@nmsu.eduOffice Phone: 575 527 7586

Office hours: TR 3:00-5:00 pm

Discussion TopicsDiscussion Topics

SyllabusElectric ChargeInsulators and ConductorsCoulomb’s Law

Syllabus Phys 216Syllabus Phys 216Class Times:Tues. & Thurs. 10:20-11:35am January 14 through May 05-2009Final Exam will be May 5 10:00-12:00  Class Room: FH 231Text: University Physics 12th edition by Young & Freedman

GradesGrades•Homework 25%•Quizzes/Attendance 5%• Exams 75%

TOTAL

105%

90-100 A (A+, A, A-)80-89.9 B (“)70-79.9 C (“)60-69.9 D (“)Below 60 F

ExamsExamsValid picture ID must be on desk for

checking during exams.Calculators must be used in exams. Conceptual section of matching and

multiple choice Problem section. (show all work including

equations) Do exams in ink. Exams will be closed book and formulas

will be provided

Exams cont.Exams cont.Any question about an exam grade

must be addressed by the next class day after receipt of the exam by class. After that all grades are final.

There is a cumulative final exam based on the previous exams.

Any student involved in cheating will be reported to the Dean of Students.

Show all work means:Show all work means:

the information given in the problem a drawing of the problem to help you

visualize it (where applicable) a beginning equation from those given calculations or reasoning detailing

steps necessary to achieve answer correct units correct significant digits (or 3 sig. fig.) also use at least 5 sig. fig. until your

final answer.

QuizzesQuizzesThere will be short Quizzes given for extra

credit.They will be on the reading assignment for each

class or on lesson taught on previous day/days.They will be a portion your final grade.There is no make for quizzes. Bring paper to every class for attendance.

HomeworkHomeworkHomework assignments are on the web page http://www.masteringphysics.com They are done online and are computer graded,

therefore give yourself plenty of time to do them (it takes time to figure out how to use the system)

Homework will be gradedDue dates are specified and a late penalty will

apply

LabsLabs

You must go to the lab you have signed up for

If you have any questions or problems during lab, please let me know. I will talk to your TA.

Labs start---Ask your instructor/TA

How to do well in my ClassHow to do well in my ClassRead the appropriate chapters before class.Do not get behind, keep up with the workPay special attention to problems done in

class and the homework problemsDownload the power point lectures before

class and use them to take notes onListen for things I find interesting, they

make good concept questions for exams

Pet PeevesPet Peeves1. Cell phones:

– Please do not have cell phones ring in class– During a test a cell phone ring is cause for

taking up the test and a 0 on that test

2. Getting up and leaving during class:– If you have a legitimate reason to leave during

class, sit by the door to minimize the class disruption

3. Attendance– Don’t come if you don’t want to be there, but I

don’t have to give you a very good grade either

DefinitionsDefinitions• Electromagnetism – the science of

electrical and magnetic phenomena• Electric Charge – an intrinsic

characteristic of the fundamental particles making up all objects

• Coulomb – the SI unit for measuring basic charge

Properties of Electric ChargesProperties of Electric Charges

1. Types of charges:a. Positive – the charge a glass rod rubbed

with silk acquires (proton)

b. Negative – the charge a rubber rod rubbed with fur acquires (electron)

c. Neutral – if a body has equal amounts of these two charges  (neutron)

Properties of Electric Charges contProperties of Electric Charges cont

1. The interaction between electric charges is such that like charges repel each other and unlike charges attract each other

2. Electric charge is always conserved3. Electric charge is quantized with the

fundamental amount of charge e=1.6x10-

19C

Positive charges are made by taking away electrons.Negative charges are made by adding electrons.

Types of MaterialsTypes of Materials• Conductors—materials in which electric charges

move freely• examples include metals, tap water, body

• Insulators—materials in which electric charges cannot move freely• examples include glass, chemically pure water, plastic

• Semiconductors—materials that are in between the two.

• Superconductors—materials with no resistance to the movement of charge

Movement of chargesMovement of charges• Conduction – movement of charge between two

connected objects.• Induction – charging a conductor without contact

with a second charged object. When the charged object is nearby, it induces the electrons in the neutral conductor to move in such a way that the side nearest to the charged object has a charge opposite to that of the charged object. And the side opposite the charged object has a charge equal to the charged object.

• Grounding – conductor connected to the earth, which acts as an infinite charge sink.

Fundamental Forces of NatureFundamental Forces of Nature Gravitational Force

Electric Force

Magnetic Force

rr

mmGFg ˆ2

21

rr

qqkr

r

qqF eE ˆˆ

41

221

221

0

BvqFB

2

2111067.6

kg

NmG

2

291099.8

C

Nmke

Spherical Shells of ChargeSpherical Shells of Charge

A shell of uniform charge attracts or repels another charge outside the shell as if all the shell’s charge was concentrated at the center of the shell

A charged particle inside a shell of charge feels no net electrostatic force from the shell

Some DefinitionsSome DefinitionsElectric Field—Field set up by an electric charge

in the space surrounding it, which will produce a force on any other charged particle brought into the field.

Vector Field—A field that has both magnitude and direction. It is symbolized by lines; vectors in space.

Test charge—A small positive charge used to determine the electric field. It has to be much smaller than the source charge so that it doesn’t affect the electric field.

Electric Field Lines—Lines that follow the same direction as the electric field vector at any point

Electric Field PropertiesElectric Field PropertiesA small positive test charge is used to

determine the electric field at a given pointThe electric field is a vector field that can

be symbolized by lines in space called electric field lines

The electric field is continuous, existing at every point, it just changes in magnitude with distance from the source

Electric Field EquationElectric Field EquationElectric Field

For a continuous charge distribution

For a line of charge For a area of charge For a volume of charge

oqF

E

r

r

qkr

r

qE source

esource

o

ˆˆ4

122

rr

dqkEr

r

dqkEd ee ˆˆ 22

dsdq dAdq

dVdq

Electric Field Lines PropertiesElectric Field Lines PropertiesRelation between field lines and electric field

vectors:a.The direction of the tangent to a field line is the

direction of the electric field E at that pointb.The number of field lines per unit area is

proportional to the magnitude of E: the more field lines the stronger E

Electric field lines point in direction of force on a positive test charge therefore away from a positive charge and toward a negative charge

Electric field lines begin on positive charges and end on negative charges or infinity

No two electric field lines can cross

More Definitions contMore Definitions contFlux—The rate of flow through an area or

volume. It can also be viewed as the product of an area and the vector field across the area

Electric Flux—The rate of flow of an electric field through an area or volume—represented by the number of E field lines penetrating a surface

Electric FluxElectric Flux• The flux for an electric field is

• For an arbitrary surface and nonuniform E field

Where the area vector is a vector with magnitude of the area A and direction normal to the plane of A

AE

AdE

DefinitionsDefinitionsSymmetry—The balanced structure of an

object, the halves of which are alikeClosed surface—A surface that divides

space into an inside and outside region, so one can’t move from one region to another without crossing the surface

Gaussian surface—A hypothetical closed surface that has the same symmetry as the problem we are working on—note this is not a real surface it is just an mathematical one

Gauss’ Law Gauss’ Law

Gauss’ Law depends on the enclosed charge only

1. If there is a positive net flux there is a net positive charge enclosed

2. If there is a negative net flux there is a net negative charge enclosed

3. If there is a zero net flux there is no net charge enclosed

Gauss’ Law works in cases of symmetry

o

encqAdE

Types of SymmetryTypes of SymmetryCylindrical symmetry—example a canSpherical symmetry—example a ballRectangular symmetry—example a

box—rarely used

Steps to Applying Gauss’ LawSteps to Applying Gauss’ LawTo find the E field produced by a charge

distribution at a point of distance r from the center 1. Decide which type of symmetry best

complements the problem

2. Draw a Gaussian surface (mathematical not real) reflecting the symmetry you chose around the charge distribution at a distance of r from the center

3. Using Gauss’s law obtain the magnitude of E

Cylindrical – long straight wire

Spherical – sphere of charge

Charged Isolated ConductorsCharged Isolated Conductors In a charged isolated conductor all the

charge moves to the surface The E field inside a conductor must be

0 otherwise a current would be set upThe charges do not necessarily

distribute themselves uniformly, they distribute themselves so the net force on each other is 0.

This means the surface charge density varies over a nonspherical conductor

Charged Isolated Conductors contCharged Isolated Conductors contOn a conducting surface

If there were a cavity in the isolated conductor, no charges would be on the surface of the cavity, they would stay on the surface of the conductor

o

E

Charge on solid conductor resides on surface.

Charge in cavity makes a equal but opposite charge reside on inner surface of conductor.

Properties of a Conductor in Properties of a Conductor in Electrostatic EquilibriumElectrostatic Equilibrium

1. The E field is zero everywhere inside the conductor

2. If an isolated conductor carries a charge, the charge resides on its surface

3. The electric field just outside a charged conductor is perpendicular to the surface and has the magnitude given above

4. On an irregularly shaped conductor, the surface charge density is greatest at locations where the radius of curvature of the surface is smallest

DefinitionsDefinitions Electric potential—Potential energy per unit charge

at a point in an electric field Path integral (line integral)—An integral performed

over a path such as the path a charge q follows as it moves from one point to another

Volt—The unit of electric potential. 1V = 1 J/C Electron volt (eV)—the energy that an electron (or

proton) gains or loses by moving through a potential difference of 1 V.

Equipotential surface—A surface consisting of a continuous distribution of points having the same electric potential

Electric PotentialElectric PotentialElectric force is a conservative force,

therefore there is a potential energy associated with it.

We can define a scalar quantity, the electric potential, associated with it.

BA sdE

qU

V

BA

EEfield

sdEqU

sdEqdU

sdEqsdFW

The line integral used to calculate V does not depend on the path taken from A to B; therefore pick the most convenient path to integrate over

Electric PotentialElectric Potential

We can pick a 0 for the electric potential energy

V is independent of any charge q that can be placed in the Electric field

V has a unique value at every point in the electric field

V depends on a location in the E field only

rU 0

Some Useful Electric PotentialsSome Useful Electric PotentialsFor a uniform electric field

For a point charge

For a series of point charges

sEsdEsdEV

rq

kV e

i

ie r

qkV

Negative charges are a potential minimum Positive charges are a potential maximum

Positive Electric Charge FactsPositive Electric Charge Facts

For a positive source charge– Electric field points away from a positive

source charge– Electric potential is a maximum– A positive object charge gains potential energy

as it moves toward the source– A negative object charge loses potential

energy as it moves toward the source

Negative Electric Charge FactsNegative Electric Charge Facts

For a negative source charge– Electric field points toward a negative source

charge– Electric potential is a minimum– A positive object charge loses potential energy

as it moves toward the source– A negative object charge gains potential

energy as it moves toward the source

Electric Potential Energy of SystemElectric Potential Energy of SystemThe potential energy of a system of two

point charges

If more than two charges are present, sum the energies of every pair of two charges that are present to get the total potential energy

12

2112 r

qqkVqU e

ji ij

jietotal r

qqkU

,

23

32

13

31

12

21

rqq

rqq

rqq

kU etotal

Calculating Potential from a Charge Calculating Potential from a Charge DistributionDistribution

rdq

kV e

Calculating Potential from E field Calculating Potential from E field

To calculate potential function from E field

fi zyx

fi zyx

fi

dzEdyEdxE

kdzjdyidxkEjEiE

sdEV

ˆˆˆ)ˆˆˆ(

Calculating E field from PotentialCalculating E field from Potential

Remembering E is perpendicular to equipotential surfaces

ˆˆ ˆ

x y z

E V

V V VE i j k

x y z

V V VE E E

x y z

Potential of Charged Isolated Potential of Charged Isolated ConductorConductorThe excess charge on an isolated conductor will distribute itself so all points of the conductor are the same potential (inside and surface).

The surface charge density (and E) is high where the radius of curvature is small and the surface is convex

At sharp points or edges (and thus external E) may reach high values.

The potential in a cavity in a conductor is the same as the potential throughout the conductor and its surface

Equipotential SurfacesEquipotential SurfacesEquipotential surface—A surface

consisting of a continuous distribution of points having the same electric potential

Equipotential surfaces and the E field lines are always perpendicular to each other

No work is done moving charges along an equipotential surface – For a uniform E field the equipotential

surfaces are planes– For a point charge the equipotential surfaces

are spheres

DefinitionsDefinitionsVoltage—potential difference between two

points in space (or a circuit)Capacitor—device to store energy as

potential energy in an E fieldCapacitance—the charge on the plates of a

capacitor divided by the potential difference of the plates C = q/V

Farad—unit of capacitance, 1F = 1 C/V. This is a very large unit of capacitance, in practice we use F (10-6) or pF (10-12)

Definitions contDefinitions contElectric circuit—a path through which

charge can flowBattery—device maintaining a potential

difference V between its terminals by means of an internal electrochemical reaction.

Terminals—points at which charge can enter or leave a battery

CapacitorsCapacitorsA capacitor consists of two conductors called

plates which get equal but opposite charges on them

The capacitance of a capacitor C = q/V is a constant of proportionality between q and V and is totally independent of q and V

The capacitance just depends on the geometry of the capacitor, not q and V

To charge a capacitor, it is placed in an electric circuit with a source of potential difference or a battery

Any 2 conductors insulated from one another form a capacitor

Calculating CapacitanceCalculating Capacitance1. Put a charge q on the plates2. Find E by Gauss’s law, use a surface

such that

3. Find V by (use a line such that V = Es)

4. Find C by

0encq

EAAdE

EssdEV

Vq

C

Some CapacitancesSome CapacitancesParallel Plate Capacitor

Cylindrical Capacitor

Spherical Capacitor

Isolated Sphere

dA

C 0

02ln b

a

LC

RR

04 a b

b a

R RC

R R

RC 04

Spherical CapacitorSpherical Capacitor

Cylindrical CapacitorCylindrical Capacitor

DefinitionsDefinitionsEquivalent Capacitor—a single capacitor

that has the same capacitance as a combination of capacitors.

Parallel Circuit—a circuit in which a potential difference applied across a combination of circuit elements results in the potential difference being applied across each element.

Series Circuit—a circuit in which a potential difference applied across a combination of circuit elements is the sum of the resulting potential differences across each element.

Groups of CapacitorsGroups of CapacitorsSeries

Parallel

Combination: utilize the two relations above to solve the combination circuit

321 CCCCequivalent

321

1111CCCC eequivalenc

Energy Stored in CapacitorEnergy Stored in CapacitorTo calculate energy look at the work it

takes to move a charge from one plate to the other against the electric field present between the plates

Energy density between the plates

QQ

applied QVCVC

QqC

qdCq

WU 02

2

0

2

21

21

221

2

222

21

21

21

21

Eu

AdEEddA

CVU

o

oo

DefinitionsDefinitionsDielectric—an insulating material placed

between plates of a capacitor to increase capacitance.

Dielectric constant—a dimensionless factor that determines how much the capacitance is increased by a dielectric. It is a property of the dielectric and varies from one material to another.

Breakdown potential—maximum potential difference before sparking

Dielectric strength—maximum E field before dielectric breaks down and acts as a conductor between the plates (sparks)

Capacitors with DielectricsCapacitors with Dielectrics Advantages of a dielectric include:

1. Increase capacitance

2. Increase in the maximum operating voltage. Since dielectric strength for a dielectric is greater than the dielectric strength for air

3. Possible mechanical support between the plates which decreases d and increases C.

To get the expression for anything in the presence of a dielectric you replace o with o

airdiairdi VVEE maxmaxmaxmax

Electric DipolesElectric Dipoles

Ep

pEqEdFd

xdFFx

sinsinsin

sinsin

EpU

pEU

dWU

cos

090

Setting potential energy = 0 at = 90

Atomic View of DielectricsAtomic View of Dielectrics

polairdi EEE