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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
Coulomb’s Law
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Slide 20-15
The Force of Gravity
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Slide 6-35
Conceptual Example Problem
All charges in the diagrams below are equal magnitude. In each
case, a small positive charge is placed at the blank dot. In which
cases is the force on this charge:
• to the right?
• to the left?
• zero?
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Slide 20-28
Checking Understanding
All charges in the diagrams below are of equal magnitude. In each
case, a small, positive charge is placed at the black dot.
In which case is the force on the small, positive charge the largest?
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Slide 20-25
Coulomb Force Problems
1. Sum of Electric Forces from Point Charges
2. Levitation
3. Static Equilibrium
4. Comparing Electric Forces and Gravitational Forces
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Coulomb’s Law and Three Charges
Two charged particles, with charges q1= +q and q2 = +4q,
are located at a distance d = 2 cm apart on the x axis.
Where can a 3rd charge be placed so that this 3rd charge
has Fenet = 0 N, i.e the 3rd charge is in equilibrium.
Hint: Draw a diagram of the electric forces on the 3rd
charge in various positions.
What are the conditions of equilibrium?
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Coulomb’s Law and Three Charges
Two charged particles, with charges q1= +q and q2 = +4q,
are located at a distance d = 2 cm apart on the x axis.
Where should a third charged particle, with charge
q3= +q , is placed so that Fenet = 0 (equilibrium).
For equilibrium, there are 3 conditions
• Charges must be on x-axis
• Fe,1=>3 = Fe,2=>3
• The two forces must point in opposite directions
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Charge & Forces
1. Draw individual and net forces acting on object B for the four situations below.
2. Calculate the magnitude and direction of the net force on object B.
Be sure to state your assumptions
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Slide 20-3
Strategic Problem Solving Strategy (SPS)
When solving problems, it is important to show how you reasoned from the information
given in the problem and key physics ideas to your final answer. The correct final
answer with units is only worth 1-3 points. The remainder of the points (70-90% of
credit) are awarded for the quality of your solution. You are expected to include the
following to receive full credit:
Prepare
• Identify the Physics: State explicitly which physics’ principle(s) apply to the
problem situation and that you will use to solve the problem
• Drawing a Picture: Draw at least one picture to visualize the physics of the
problem and define your variables and constants. For motion problems this could
be a motion diagram, motion graph, or pictorial diagram
• Collecting Necessary Information: State all the information given in the problem
with correct units. Include preliminary calculations such as unit conversions
• Assume/Observe: State assumptions or observations that would be useful
Solve
• Start with key equation(s) in symbol form
• Solve for the unknown quantity in symbols before numeric calculations
• Then substitute numbers with units and calculate the numeric answer
Assess
• Check to see if your answer is reasonable
• Does it answer the question that was asked
• Does it have the right units?
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Solving Problems - Prepare (also identify key physics)
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Solving Problems (continued)
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Two hanging cans
You and a friend are doing the laundry when you unload the dryer and
your friend wants to get some idea of the amount of charge that
causes static cling. You immediately take two empty soda cans, which
each have a mass of 120 grams, from the recycling bin. You tie the
cans to the two ends of a string (one to each end) and hang the center
of the string over a nail sticking out of the wall. Each can now hangs
straight down 30 cm from the nail. You take your flannel shirt from the
dryer and touch it to the cans, which are touching each other. The
cans move apart until they hang stationary at an angle of 10º from the
vertical. Assuming that there are equal amounts of charge on each
can, you now calculate the amount of charge transferred from your
shirt.
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Slide 20-3
•
A model of the mechanism for electrostatic
interactions
A model for electric
interactions, suggested by
Michael Faraday, involves
some sort of electric
disturbance in the region
surrounding a charged
object.
• Physicists call this electric
disturbance an electric
field.
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Gravitational field due to a single object with
mass
•
We find a mathematical description of the
"strength" of Earth's gravitational field at a
particular location that is independent of the test
mass:
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Electric field due to a single point-like charged
object
•
We use a similar approach of test charges to construct a
physical quantity for the "strength" of the electric field:
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Electric field due to a single point-like charged
object
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•
Electric field due to a single point-like charged
object
We can interpret this field as follows:
• The E field vector at any location points
away from the object creating the field if
Q is positive, and toward the object
creating the field if Q is negative.
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Observational
experiment
Go through Force and Force / qtest
Movie Link
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Observational experiment (movie link)
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Superposition principle
• When multiple charged objects are
present, each object makes its own
contribution to the E field.
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Using the superposition principle
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The Electric Field
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Slide 20-34
The Electric Field of a Point Charge
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Slide 20-35
Nature of Electric Field
E-field Applet 1
http://physics.weber.edu/schroeder/software/EField/
Back-up
applet:https://phet.colorado.edu/en/simulation/charges-andfields
What observations can we make about E-fields?
Source Charges and Test Charges?
Superposition of E-fields?
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Electric Field Warm-up
1. Check your predicted vectors with the applet at the locations
marked
with an “x”.
2. Compare your predictions and resolve discrepancies.
3. Draw the positive charge off the bottom of screen – check
predictions.
4. Note the magnitude and direction of the top, middle vector
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Nature of Electric Field
• 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 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
• For a point charge E = Fe / q = [k Q q / r2] / q = k Q / r2
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Find the Electric Field
Given the following forces that a positive test charge feels if placed
at these three points, find the E-field vectors at these points.
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Find the Electric Field
Given the following forces that a positive test charge feels if placed
at these three points, find the E-field vectors at these points.
How would the Force vectors and E-field vectors change at point 3
for the following changes:
• Replace the positive test charge (+q) with a negative test
charge (-q)
• Replace the positive test charge (+q) with a test charge twice
as large (+2q)
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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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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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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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Conceptual Exercise 15.2
• Draw E field lines for a large, uniformly
charged plate of glass.
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Lab Prep: Work, Potential Energy,
Conservative Forces, Conservation of Energy, and
Electric Potential
1. Dot Product
2. Work
3. Potential Energy
4. Conservation of Energy, Bar Charts, Potential Energy and
Work
5. Electric Energy
6. Conservation of Energy
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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: A qualitative analysis
•
Consider two oppositely charged blocks, one of
which can slide without friction. When the
negatively charged block is released and moves
nearer the nut, the kinetic energy of the system
increases.
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Electric potential energy: A quantitative analysis
•
Use the generalized workenergy principle
to analyze a situation where
only the electric potential
energy changes when work
is done.
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Electric potential energy
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•
Example
Two oppositely charged objects (with positive
charge +q and negative charge –q) are
separated by distance ri. Will the electric
potential energy of the system decrease or
increase if you pull the objects farther apart?
Explain.
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Electric potential energy of multiple charge
• Each pair of charged
objects has an
systems
associated electric potential energy, and
the total electric potential energy of the
system is the sum of the energies of all
pairs.
• For three charged objects, the total
electric potential energy is:
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Skills for analyzing processes involving electric
force and electric potential energy
In conjunction with your problem-solving strategy:
• Decide whether you can consider the charged
objects to be point-like.
• If you are using the work-energy principle,
construct an energy bar chart. Decide where
the zeros for potential energies are.
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Equipotential surfaces and E field
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Lab Prep: Work, Potential Energy,
Conservative Forces, Conservation of Energy, and
Electric Potential
7. Using Work by the electric force to find equipotential
surfaces
8. In equilibrium, no work is done by the electric force to move
a charge around on a conductor, the charge has the same
the same electric potential everywhere on a conductor =>
therefore, the surface of a conductor is an equipotential
surface.
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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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The superposition principle and the V field
due to multiple charges
• where Q , Q , Q , … are the source charges
1
2
3
(including their signs) creating the field and r1,
r2, r3, … are the distances between the source
charges and the location where we are
determining the V field.
• So Electric Potentials (V) add just like
Electric Potential Energies
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