Electricity & MagnetismElectricity & Magnetism
Dr Tarlochan Singh DhillonOffice: DAMA 089bEmail: [email protected] 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
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
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