Grades
•Homework/Quizzes/Attendance
•3 Exams
•Final Exam
•TOTAL
90-100
80-89.9
70-79.9
60-69.9
Below 60
30%
45%
25%
100%
A (A+, A, A-)
B (“)
C (“)
D (“)
F
Exams
Valid 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.
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:







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 (your answer must agree
with mine to 3 sig. fig.)
Homework

Homework 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 graded
 Due dates are specified and a late penalty will
apply

Labs
You must go to the lab you have signed up
for
 If you have any questions or problems
during lab, please let me know.
 Labs start today
 Each person must do their own lab report.

How to do well in my Class
Read the appropriate chapters before class.
 Do not get behind, keep up with the work
 Pay special attention to problems done in
class and the homework problems
 Download the power point lectures before
class and use them to take notes on
 Listen for things I find interesting, they
make good concept questions for exams

Pet Peeves
1.
Cell phones:
–
–
2.
Getting up and leaving during class:
–
3.
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
If you have a legitimate reason to leave during
class, sit by the door to minimize the class
disruption
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
•
•
•
Definitions
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 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)
(This is actually absence of charge)
Properties of Electric Charges cont
The interaction between electric charges is
such that like charges repel each other and
unlike charges attract each other
2. Electric charge is always conserved
3. Electric charge is quantized with the
fundamental amount of charge
e=1.6x10 -19C
1.
Positive charges are made by taking away
electrons.
Negative charges are made by adding
electrons.
Types 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 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 Nature

Gravitational Force

m1m2
Fg  G 2 rˆ
r

2
Nm
G  6.67 1011 2
kg
Electric Force
2

1 q1q2
q1q2
9 Nm
FE 
r  ke 2 rˆ ke  8.99 10
2 ˆ
4 0 r
r
C2

Magnetic Force

 
FB  qv  B 
Spherical 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 Definitions

Electric 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 Properties
A small positive test charge is used to
determine the electric field at a given point
 The 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 Equation


Electric Field

 F
E
qo

1 qsource
qsource
E
rˆ  ke 2 rˆ
2
4 o r
r
For a continuous charge distribution


dq
dq
dE  ke 2 rˆ  E  ke  2 rˆ
r
r
For a line of charge dq  ds
 For a area of charge dq  dA
 For a volume of charge dq  dV

Electric Field Lines Properties

Relation 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 point
b.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 cont
Flux—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 Flux
•
•
The flux for an electric field is
  E  A  EA cos
For an arbitrary surface and
nonuniform E field
 
   E  dA
where the “area vector” is a vector with
magnitude of the area A and direction
normal to the plane of A
Definitions
Symmetry—The balanced structure of an
object, the halves of which are alike
 Closed 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 depends on the enclosed
  qenc
charge only
   E  dA 
o
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 simplifies calculations in
cases of symmetry
Simple types of Symmetry
Cylindrical symmetry— e.g., a can
 Spherical symmetry— e.g., a ball
 Rectangular symmetry—e.g., a box—
rarely used (why?)

Steps to Applying Gauss’ Law
To 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 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 up
 The 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 cont
On a conducting surface

E
o
 If there were a cavity inside the
isolated conductor, no charges would
be on the surface of the cavity, the
charge would stay on the surface of
the conductor

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
Electrostatic Equilibrium
1.
2.
3.
4.
The E field is zero everywhere inside the
conductor
If an isolated conductor carries a charge,
the charge resides on its surface
The electric field just outside a charged
conductor is perpendicular to the surface
and has the magnitude given above
On an irregularly shaped conductor, the
surface charge density is greatest at
locations where the radius of curvature of
the surface is smallest
Definitions





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 Potential
Electric 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.


 

WEfield  FE  ds  qE  ds
 
dU   qE  ds

B
U   q A E  ds
U

B
V    A E  ds
q

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 Potential
We can pick a 0 for the electric potential
energy
U 0r 
 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

Some Useful Electric Potentials


For a uniform electric field
 

 

V   E  ds   E   ds   E  s
For a point charge
q
V  ke
r

For a series of point charges
qi
V  ke 
ri
Negative charges are a potential minimum
 Positive charges are a potential maximum

Positive 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 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 System

The potential energy of a system of two
point charges
q1q2
U  q2V1  ke
r12

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
U total  ke 
i, j
qi q j
rij
 q1q2 q1q3 q2 q3 
U total  ke 



r13
r23 
 r12
Calculating Potential from a Charge
Distribution
dq
V  ke 
r
Calculating Potential from E field

To calculate potential function from E field
 
V   i E  ds
f
  i ( E xiˆ  E y ˆj  E z kˆ)  dxiˆ  dyˆj  dzkˆ 
f
  i E x dx  E y dy  E z dz
f
Calculating E field from Potential

Remembering E is perpendicular to
equipotential surfaces
E  V
 V ˆ V ˆ V ˆ 
E  
i
j
k
y
z 
 x
V
V
V
Ex  
 Ey  
 Ez  
x
y
z
Potential of Charged Isolated Conductor
 The 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 Surfaces
Equipotential 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
Definitions
Voltage—potential difference between two
points in space (or a circuit)
 Capacitor—device to store energy as
potential energy in an E field
 Capacitance—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 cont
Electric circuit—a path through which
charge can flow
 Battery—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

Capacitors
A 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 Capacitance
1.
2.
Put a charge q on the plates
Find E by Gauss’s law, use a surface
such that
 
qenc
 E  dA  EA 
3.
4.
0
Find V by (use a line such that V =
Es) 

V   E  ds  Es
Find C by
q
C
V
Some Capacitances

Parallel Plate Capacitor C   0 A
d

Cylindrical Capacitor C  2 0
ln

Spherical Capacitor

Isolated Sphere
L
Rb
 R
a
Ra Rb
C  4 0
Rb  R a
C  4 0 R
Spherical Capacitor
Cylindrical Capacitor
Definitions
Equivalent 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 Capacitors

Series
1
Cequivalence

1 1
1
  
C1 C2 C3
Parallel
Cequivalent  C1  C2  C3

Combination: utilize the two relations
above to solve the combination circuit
Energy Stored in Capacitor

To 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
2 Q
2



q
1
q
Q
1
1
Q
2
U  Wapplied  0 dq  

 CV  QV

C
2
C 2  0 2C 2

Energy density between the plates
1
1 o A
1
2
2
Ed    o AdE 2
U  CV 
2
2 d
2
1
u  oE2
2
2 Cases of capacitors:

Case 1: Capacitor hooked up to a battery
– The potential is constant because of the battery
– If capacitance changes the charge on the plates must
change.
q1 q 2

C1 C 2

Case 2: Capacitor removed from battery
– The charge must be constant
– If capacitance changes then the potential between the
plates changes
C1V1  C 2V 2
Definitions
Dielectric—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 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
Emax di  Emax air  Vmax di  Vmax 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
Electric Dipoles
        Fx sin   F d  x sin 
  Fd sin  qEd sin   pE sin 
 
  p E

U  W 
0
 90d
U   pE cos 
 
U  pE
Setting potential energy = 0 at  = 90
Atomic View of Dielectrics
Edi  Eair  E pol