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Chapter 20
Electric Forces and Fields
Topics:
• Electric charge
• Forces between charged
•
•
objects
The field model and the
electric field
Forces and torques on
charged objects in electric
fields
Sample question:
In electrophoresis, what force causes DNA fragments to migrate
through the gel? How can an investigator adjust the migration rate?
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Slide 20-1
Newton’s Laws of Motion
Newton’s Zeroeth Law of Motion
Objects are dumb. They do not know the past and they are not good predictors of the
future. They only know what forces act on them right now.
Newton’s First Law of Motion
Every object continues in a state of rest or a state of motion with a constant speed in a
straight line unless acted on by an unbalanced net force.
Newton’s 2nd Law of Motion
When a force, F, acts on an object with a mass, m, it produces an acceleration, a, equal
to the force divided by the mass.
a = Fnet
m
Newton’s Third Law of Motion
To every action there is an equal and opposite reaction.
Or, when one object exerts a force on a second object, the second exerts an equal and
opposite force on first.
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Nature of Electric Field Vectors
• Test charge is a small positive charge to sample the E-Field
• Charge of test charge is small compared to source charges
(source charges are the charges that generate the E-field)
• E-field vectors
• E-field is the force per charge
• E-field vectors points away from + charges
• E-field vectors point towards - charges
• E-field for point charges gets weaker as distance from source
point charges increases
• E-fields add as vectors, at a point in space Enet,x = E1x + E2x + …
• For a point charge E = Fe / |q| = [k |Q| |qt| / r2] / |qt| = k |Q| / r2
• Electric Force
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Checking Understanding
Positive charges create an electric field in the space around them.
In which case is the field at the black dot the smallest?
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Slide 20-36
Checking Understanding
All charges in the diagram below are of equal magnitude. In each of
the four cases below, two charges lie along a line, and we consider
the electric field due to these two charges at a point along this line
represented by the black dot. In which of the cases below is the net
field to the right?
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Slide 20-36
Checking Understanding
All charges in the diagram below are of equal magnitude. In each of
the four cases below, two charges lie along a line, and we consider
the electric field due to these two charges at a point along this line
represented by the black dot. In which case is the magnitude of the
field at the black dot the largest?
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Slide 20-41
Are the Fields Real???
Are either or both of these a possible electric field?
Explain the reasoning behind your answer
(Focus on the vectors, not the source charges)
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E-field lines
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E field
lines
• E field lines point away from an area of positive
charge and point toward an area of negative
charge.
• Closer to the charged objects, the lines are
closer together; the number of lines per unit area
(the density of lines) is larger where the E field is
stronger.
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Tip
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E field
lines
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Are E-field lines trajectories?
E-field Applet 2
http://webphysics.davidson.edu/physlet_resources/bu_semester2
/menu_semester2.html
E-field and trajectory => gravitational example with thrown eraser
E-Field Applets
• Field lines and field vectors
• Electric Field from a point Charge
• Electric Field from two charges (like and unlike – dipole)
• Plate of Charge (different Applet - falstad.com/vector2de
• Motion of a Test Charge
What observations can we make about E-field lines?
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E-field Strength and Symmetry
• Examples from Gravity
• Spherical Earth
• Flat Earth
• Field Strength
• Field converges => Magnitude of Field increases
• Field diverges => Magnitude of Field decreases
• Field uniform => ???
• E-field Symmetry
• Point Charge => Spherical Symmetry
• Line of Charge => Cylindrical Symmetry
• Plate of Charge => ???
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Consider an infinite sheet of charge
• What kind of symmetry would we expect?
• What will the field look like?
• Is the field (A) converging, (B) diverging, or
(C) neither -- (D) can’t tell
• What can we say about E-field strength?
• A charged sheet can be considered to be like
an infinite sheet when we look at points a
distance d away where d << L, where L is the
length of a side of the sheet
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Consider an infinite sheet of charge
h
Q
E=
where h =
2e0
A
• Epsilon nought, e 0 = 8.85 ´ 10
-12
C2
N × m2
is electric permitivity of free space
• Electric permitivity is a measure of how well
electric field can pass through space or
material
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Consider two infinite sheets of charge
What is the E-field at
points A, B, and C ?
Case 1:
A
B
C
Qleft = +Q
Qright = -Q
Case 2:
Qleft = 2Q
Qright = Q
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Conceptual Exercise 15.2
• Draw E field lines for a very large, uniformly
charged plate of glass.
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Dipole and Uniform Electric Fields
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Slide 20-45
Electric Field Lines
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Slide 20-50
Equipotential surfaces and E field
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Checking Understanding
A set of electric field lines is directed as below. At which of the noted
points is the magnitude of the field the greatest?
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Slide 20-46
Checking Understanding
Two parallel plates have charges of equal magnitude but opposite
sign. What change could be made to increase the field strength
between the plates?
A.
B.
C.
D.
E.
Increase the magnitude of the charge on both plates
Decrease the magnitude of the charge on both plates
Increase the distance between the plates
Decrease the distance between the plates
Increase the area of the plates (while keeping the magnitude of
the charges the same)
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Answer
Two parallel plates have charges of equal magnitude but opposite
sign. What change could be made to increase the field strength
between the plates?
A.
B.
C.
D.
E.
Increase the magnitude of the charge on both plates
Decrease the magnitude of the charge on both plates
Increase the distance between the plates
Decrease the distance between the plates
Increase the area of the plates (while keeping the magnitude of
the charges the same)
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Nature of Electric Field Lines
• E-Field lines start on + charges and end on -- charges
• Larger charges will have more field lines going out/coming in
• Density of Field lines is a measure of field strength – the higher
the density the stronger the field
• The E-field vector at a point in space is tangent to the field line
at that point. If there is no field line, extrapolate
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Conductors and Electric Fields
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Slide 20-55
Forces and Torques on Charges in Electric Fields
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Slide 20-56
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Slide 20-5
Determining the E field produced
by given source charges
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E-field Superposition Example
1. Determine the magnitude and the direction of the electric field
at point A.
In your physical diagram, make sure you label
your r’s
as well as your angles
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E-field Superposition Examples
1. Determine the magnitude and the direction of the electric field
at point A.
2. Determine the individual forces and the net force on charge B
for each of the following cases.
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Slide 20-66
Example Problem 1
• Two small metal spheres attached to
insulating stands reside on a table a
distance d apart. The left sphere has
positive charge +q and the right sphere
has negative charge −q. Determine the
magnitude and direction for the E field at
a distance d above the center of the line
connecting the spheres.
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Problem-solving strategy:
Incorporating the E field into Newton's second law
• In the ”Prepare" step, be sure to
determine the E field produced by the
environment. Is it produced by point-like
charges (making it non-uniform) or by
large charged plates (making it uniform)?
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•
Example Problem 2
Inside an inkjet printer, a tiny ball of black
ink of mass 1.1 x 10−11 kg with charge
−6.7 x 10−12 C moves horizontally at a
speed of 40 m/s. The ink ball enters an
upward-pointing uniform E field of
magnitude 1.0 x 104 N/C produced by a
negatively charged plate above and a
positively charged plate below. The
plates deflect the ink ball so that it lands
at a particular spot on a piece of paper.
Determine the deflection of the ink ball
after it travels 0.010 m in the E field.
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What to do to do well in this class
A. Focus on key physics concepts
• May seem like basics but will help you solve even complex
problems
• Focus on principle rather than recipes
• Need to have a functional understanding of key concepts
• Express key equations as sentences
• Know where they come from and what they mean
• Know how and when to apply them
• Know which equations are general and which are special cases
• Must know when not to apply special cases
• Look at a problem after a good physics diagram and maybe a
good physical diagram and know what key physics concepts apply
in that problem
• Memorize key concepts so you can look at a problem, say that’s
Newton 2, and know the associated equation in a snap
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Slide 21-16
What to do to do well in this class
A. Focus on key physics concepts
• How to do this
• When you look at problems, mentally group problems by
the physics rather than the physical situation
• After each class or at least each week, create a notesheet
to organize a structure of the new key concepts for each
chapter and note how they fit in with previous key
concepts
• Use the note sheet to do homework problems (a) do as
many homework problems as you can just using this
sheet. (b) then go to your notes and the textbook for your
missing pieces
• Use flash cards to memorize key concepts - include the
concept description, relevant equations, diagrams, and
what types of problems benefit from using that concept
• Pay close attention to examples done in class and note the
physics and assume/observes in each example and how
these are used
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Slide 21-16
Chapter 21 Key Equations (Physics 151)
Key Energy Equations from Physics 151
Types of Energy
Conservation of Energy Equation (key concept)
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Slide 21-16
Chapter 21 Key Ideas (Physics 151)
Conservation of Energy
Energy Bar Charts
(Visualization for Conservation of Energy)
Displays Conservation of Energy
Equation in graphical form
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Slide 21-16
Energy Bar Graph Sample
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Chapter 21 Key Equations (Physics 151)
Key Energy Equations from Physics 151
Definition of Work
Work W = F i Dr = F Dr cos a
Where a = angle between the vectors
Work done by a conservative force (Fg, Fs, & Fe)
Wg = -DPEg
Also work done by conservative force is path independent
Conservation of Energy Equation
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Slide 21-16
Electric potential energy: A qualitative analysis
•
•
A positively charged
cannonball is held near
another fixed positively
charged object in the
barrel of the cannon.
Some type of energy
must decrease if
gravitational and kinetic
energies increase in this
process.
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Electric potential energy
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The V field
• Can we describe electric fields using the
concepts of work and energy?
• To do so, we need to describe the
electric field not as a force-related E field,
but as an energy-related field.
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Electric potential due to a single charged
object
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Finding the electric potential energy when
the V field is known
•
If we know the electric potential at a specific
location, we can rearrange the definition of the
V field to determine the electric potential
energy:
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Chapter 21 Key Equations (3)
Key Points about Electric Potential
Electric Potential increases as you approach positive source
charges and decreases as you approach negative source
charges (source charges are the charges generating the electric
field)
A line where Delta V= 0 V is an equipotential line
(The electric force does zero work on a test charge that moves
on an equipotential line and Delta Pee = Delta Ue = 0 J)
For a point charge
q
1 q
V=K =
r 4pe 0 r
For very large charged plates, must use
DPEe
We
Fe i Dr
qtest E i Dr
DV =
==== -E i Dr = - E Dr cos a
qtest
qtest
qtest
qtest
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Slide 21-16
Electric Potential Energy Example Problem
The electric field between two
charged plates is uniform with a
strength of 4 N/C.
a. Draw several electric field lines in the
region between the plates.
b. Determine the change in electrical
potential energy in moving a positive
4 microCoulomb charge from A to B.
c. Find Delta V between A and B.
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Slide 21-16
Define Capacitance
Capacitance is a measure of how much charge can be stored in a
capacitor for a given amount of voltage
Determine the capacitance of a parallel plate capacitor
(most common type of capacitor)
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Slide 21-16
The Capacitance of a Parallel-Plate Capacitor
e0 A
C=
d
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Slide 21-31
Capacitance and Capacitors
The charge ±Q on each
electrode is proportional to the
potential difference ΔVC between
the electrodes:
Q = C DVC
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Slide 21-29
Dielectrics and Capacitors
The molecules in a dielectric become oriented in a way that reduces
the electric field from external source charges in the dielectric.
This means that the electric field within the dielectric is
less than it would be in air, allowing more charge to be
stored for the same potential.
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Choosing the System
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Slide 10-16
Dot Product
Dot product or scalar product is a way of
multiplying two vectors to get a scalar result
Dot products can be calculated
either
a
a system where
independent of a coordinate
the angle between the two vectors
is
A × B = A B cos a
Note that in this vector form the sign of the dot
product only depends on the angle
Component form of Dot Product
A × B = Ax Bx + Ay By + Az Bz
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Slide 4-19
Chapter 21 Key Ideas (Physics 151)
Dot Product
Method for multiplying two vectors to get a scalar
Definition of Work
Work is how forces add energy to or take away energy from a
system. It is the effect of a force applied over a displacement.
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Dot Product: Example 1
Dot product or scalar product is a way of
multiplying two vectors to get a scalar result
Dot products can
a be calculated either
a system where
independent of a coordinate
the angle between the two vectors
is
A × B = A B cos a
Vector A has a magnitude of 4 units
Vector B has a magnitude of 3 units
Angle between them = 60 degrees
A × B = 4 units ´ 3units ´ cos(60°) = 6units
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Energy Bar Chart Example 1
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Energy Bar Chart Example II
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Energy Bar Chart Example III
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