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Electrostatics
Lessons from the Lab
• Opposites attract, likes repel
• Charged objects can attract neutral
objects
• Attraction is proportional to charge,
distance
• Positive charge results from removing
electrons from a substance
• Negative charge results from adding
electrons to a substance
• Conducting materials allow charge to
flow freely
• Insulating materials do not
Properties of “Charge”
• Reflects relative number of electrons in
a substance
• Conserved
• Units of Coulombs (C)
• An electron has a charge of
1.6 x 10-19C of charge
Significant Charge Amounts
• When we rub balloons on rabbit hair in
the lab, we’re generating 10’s of mC
Which of the following will tell you
without a doubt that an object is
charged
• 1) It attracts another object that has
been rubbed with rabbit fur
• 2) It repels another object that has
been rubbed with fur
• 3) It does not attract a neutral object
Three aluminum balls are suspended from
the ceiling. All three are charged with
various materials. It is found that 1 and 2
repel one another, and 2 and 3 repel one
another. From this, we can conclude that:
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1) 1 and 3 carry the same charge
2) 1 and 3 carry opposite charges
3) all three carry the same charge
4) one of the objects carries no charge
5) we need more experiments to
determine charge
Three aluminum balls are suspended from
the ceiling. Two of the three are then
charged with various materials. It is found
that 1 and 2 attract one another, and 2 and
3 repel one another. From this, we can
conclude that:
•
•
•
•
•
1) 1 and 3 carry the same charge
2) 1 and 3 carry opposite charges
3) all three carry the same charge
4) one of the objects carries no charge
5) we need more experiments to
determine charge
Which spheres experience the
greatest attraction?
Methods of Charging
Charging by Friction
• http://phet.colorado.edu/new/simulatio
ns/sims.php?sim=John_Travoltage
Charging by Induction
• http://phet.colorado.edu/new/simulatio
ns/sims.php?sim=Balloons_and_Static_
Electricity
Charge polarization
• When the charges in a material arrange
themselves in such a way that the
material has + and – sides, the material
is said to be polarized
Why does Induction Work?
• Both positive and negative charges are
still in a substance
• Why is it attracted?
Charging by Contact/Conduction
• The physical movement of charge from
one object to another
What will happen to two neutral spheres below
when you bring a + charged rod close by?
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1)
2)
3)
4)
5)
A and B will become +
A and B will become The spheres will remain neutral
A will become – and B will become +
A will become + and B will become -
If you want A to remain – and B to remain
+, what should you do?
• 1) Remove the rod
• 2) Separate the spheres and then
remove the rod
• 3) Remove the rod, then separate the
spheres
• 4) Touch the spheres with the rod
Lightning
• We’ve talked about ways to generate
attraction and repulsion with charged
objects
• Just to review, on what does the
attraction depend?
• Assuming you’ve got two charged
objects, write a basic equation that
describes the force of attraction
between them (just worry about the
magnitude)
Coulomb's Law
• Coulomb’s Law gives us a way to
calculate the force between two
charged objects
• FE = kq1q2/d2
• k is a constant = 8.99 x 109 N m2/C2
Similarities to Gravity
• Recall how we calculated the
gravitational force between objects:
• FG = Gm1m2/d2
• G is a constant = 6.67 x 10-11 N m2/kg2
• Look familiar?
Different Constants
• G = 6.67E-11, k = 8.99e9
• What does this tell us about the
difference between gravitational forces
and electrostatic forces?
• Calculate the electrostatic force
between a +6mC charge and a -5mC
charge, located 2m apart
• Calculate the electrostatic force
between a proton in the nucleus of the
atom (q = +1.60e-19C) and an electron
(q = -1.60e-19C) located in an outer
energy level (d = 3e-11m)
• Calculate the electron’s acceleration
Levitation
• I once heard a person ask, couldn’t you
make a person float using charges?
• Perhaps
• Imagine a person (m = 70kg) gathered
-10mC of charge by rubbing herself
with rabbit fur
• What charge would we need to lift her
off the ground?
Examine the configuration below.
Which charge would exert the
greatest force on the -2 charge?
• 1. +8
• 3. +6
2. +4
4. +20
Which list below ranks the
charges in order of increasing
force on the -2 charge?
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1.
2.
3.
4.
5.
A, B, D, C
A, C, B, D
D, C, B, A
C, A, B, D
D, B, C, A
Which arrow represents the direction of the net
force on the -2 charge?
Electric Fields
• Like gravity, the electrostatic force is a
non-contact force
• To conceptually deal with this, we talk
about electric fields
• This is a region of space surrounding a
charged particle that “carries” the
electrostatic force
• An electric field tells us the direction of
the electrostatic force
• It also gives us a sense of the force
magnitude
Drawing the Field
• Place a positive “test” charge near a
charge, or charge configuration
• Determine the direction of the net force
acting on that positive charge
• Draw an arrow in that direction (arrow
length represents force magnitude)
• Move the charge to another place and
repeat
A single positive charge
Which diagram correctly
illustrates the field surrounding a
negative point charge?
Field Strength
• For a single point charge, electric field
strength a distance r from the charge:
• E = kq/r2
• Units?
• N/C
Calculate the electric field
strength, 2m away from a
3mC charge
Force on a charge placed in an E
field
• F = qE
• F = mg
Calculate the force on a 2mC
charge, placed in an electric
field of strength 500N/C
Calculate the acceleration of
an electron (m = 9E-31kg, q
= 1.6E-19C), placed in a field
of strength 3E-7 N/C
A sphere (m = 2kg, q = 5mC)
accelerates at 6m/s/s when
placed in an electric field.
Find the field strength
• F = q1E = q1 (kq2/r2)
• F = kq1q2/r2
Fields Add
• Imagine three charges, each with its
own electric field
• At point P, E1 = 20N/C to the right, E2 =
10N/C to the left, and E3 = 15N/C to
the right
• What is the net field at this point
(assume right is +)?
Moving Charges
• Imagine two positive charges, located
1.0m apart
• An outside force moves one charge 50
cm closer to the other
• What happens to the system?
• The system gains energy
• What type?
• Electric Potential Energy
• What happens if you let the charge go
• It moves to a lower energy state
• Analogies to gravity?
Connections to E Fields?
• Imagine a positive test charged, placed
near a point charge
• As the test charge moves with the field
lines (ie, in the direction of the arrows),
what happens to its EPE?
• A negative test charge?
Field Lines
• Tell us the direction in which EPE
decreases for a + charge
• Tell us the direction in which EPE
increases for a - charge
• http://phet.colorado.edu/new/simulatio
ns/sims.php?sim=Charges_and_Fields
Which charge configuration has
the highest EPE?
• One way to think about the previous
question: in which situation do you
have to do more work to arrange the
charges?
Statics to Dyamics
• We’ll focus primarily upon situations
where a charge’s EPE changes
• We’ve been discussing electrostatics
(stationary charges)
• This EPE discussion gets us into the
realm of electrodynamics (moving
charges)
A Sense of Scale
• Often times, we talk about groups of
charge
• To deal with this, we talk about the
amount of EPE/total charge
• We call this quantity, electric potential
Units?
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Potential = EPE/charge
Units = J/C
1 J/C = 1 Volt
Electric Potential is often called voltage
Van de Graaff Voltage?
• A Van de Graaff is normally charged to
thousands of volts, yet it won’t hurt you
if you touch it
• Why then, can an outlet (V = 110V)
really hurt you?
•Voltage = EPE/
• Voltage =
charge
EPE/charge
Connection to E Fields?
• How does test charges electric potential
change as it moves through a constnat
E field?
• Let’s assume constant field strength to
make life easy…
A Mathematical Expression
• How does the change in potential relate
to the field strength E?
• The distance moved, d?
• DV = Ed
• This only works for constant E Fields
(we need to use calculus if E is not
constant)
Voltage Difference on the Van de
Graaf?
• Let’s measure the length of a spark to
find DV between the Van de Graaff
• Knowing the electric field strength
necessary to ionize air (1E6 N/m), we
can find DV
Energy Conservation with Charge
• A 3mC charge is travels through a
potential difference of 110V
• How much KE does it gain as it travels
through this potential difference?
• In a television, an electron travels
through a potential difference of
32,000V
• How fast is it traveling when it strikes
the television screen?
• When charges are in a region where a
potential difference exists, what do they
do?
• They move
• The movement of charge is called
electric current
• Units = C/s = Amperes (A)