LECTURE 12
CHARGES
Instructor: Kazumi Tolich
Lecture 12
2
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Reading chapter 19.1 to 19.3.
¤ Electrical
charge
n Positive
and negative charge
n Charge quantization and conservation
¤ Conductors
and insulators
¤ Coulomb’s law
¤ Coulomb force by a system of charges
Electric charge/Demo: 1
3
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Charge can be positive or negative. Like charges repel each
other, and opposite charges attract each other.
Electric charge is quantized in units of the magnitude of an
electron charge: e = 1.602×10-19 C.
Charge can be separated, but the total charge is conserved.
A positive ion is an atom that has lost an electron, and a
negative ion is an atom that has gained an electron.
Example: 1
4
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How many electrons must be
transferred to a body to result
in a charge of q = 125 nC?
Insulators and conductors
5
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In a conductor charged particles are free to move within the object.
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Metals are good electrical conductors because typically the outermost electron (conduction
electron) from the atom disassociates from a particular atom and is free to move about the
metal.
In an insulator charged particles are not free to move within the object.
Semiconductors have properties intermediate between conductors and insulators;
their properties change with their chemical composition.
Photoconductive materials become conductors when light shines on them.
¤
Photocopier and laser printer use photoconductive material.
Quiz: 1
6
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Two electrons are placed in the middle of a conductor as shown. What
happens to this excess negative charge?
A.
B.
C.
D.
Nothing. The electrons remain where they were placed.
The electrons move about but do not have a preferred position.
The electrons combine with an atom to leave no net charge.
The electrons will be at the opposite ends of the conductor.
e- e-
Quiz: 12-1 answer
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The electrons will be at the opposite ends of the
conductor.
Like particles repel each other, so the electrons move to
opposite ends of the conductor.
The electrons typically do not escape the conductor. If
they did, there would likely be a spark.
If a conductor carries excess charge, the excess is
distributed over the surface of the conductor.
e-
e-
Demo: 2
8
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Electroscope
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A needle electroscope has a part of the conductor (the
needle) free to rotate.
Because like charge repels, the needle is repelled from the
rest of the conductor.
Conducting and Non-conducting “T”
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Demonstration of a conductor (aluminum) and an insulator
(plastic) using an electroscope
Coulomb’s law
9
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Coulomb’s law gives the force for an electrostatic system,
between two point charges 𝑞" and 𝑞# at rest, separated by a
distance 𝑟:
𝐹=𝑘
𝑞" 𝑞#
𝑟#
𝑘 = 8.99×109 N·∙m2/C2 (Coulomb’s constant).
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The force is along the line connecting the charges and
attractive if the charges are opposite, and repulsive if the
charges are like.
If there are lots of charged objects, the total force on an
object can be obtained by adding the individual force
vectors.
Quiz: 2
10
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Rank the forces on charge Q in the three situations below,
smallest first.
1
Q
q
+
+
Q
2
2q
++
+
Q
3
r
2r
4q
++++
+
2r
Quiz: 12-2 answer
11
𝐹# < 𝐹" = 𝐹)
¨ We can use Coulomb’s law to determine the ranking.
¨
1.
*+
,*#+
𝑘
#, *.+
𝑘
#, -
𝐹" = 𝑘
2.
𝐹# =
3.
𝐹) =
=
=
" *+
𝑘
# ,*+
𝑘 ,
Quiz: 3
12
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Each case below (1-3) shows two point charges separated by a distance d. In which
case is the electric force on the left charge larger than the force on the right charge?
Choose all that apply.
A.
B.
C.
D.
Case 1
Case 2
Case 3
None of the cases.
-e
Case 1
+2e
d
-e
Case 2
d
-e
+e
Case 3
d
+e
Quiz: 12-3 answer
13
None of the cases
rd
¨ The forces on the two charges are Newton’s 3 law pair,
action-reaction forces.
¨ The forces are equal in magnitude and opposite in directions.
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Demo: 3
14
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Metal rod on pivot
¤ Demonstration
of attraction between a charged object of either sign and a
conductor due to induction in the conductor
Polarization
15
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Some materials can become
polarized – this means that
their atoms rotate in response
to an external charge.
This is how a charged object
can attract a neutral one.
Quiz: 4
16
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Two small spheres repel one another electrostatically. Which of the
following statements is true?
A.
B.
C.
D.
At least one sphere must be charged.
Neither sphere need be charged.
Both spheres must be charged and the charges must have the same sign.
Both spheres must be charged and the charges must have opposite signs.
Quiz: 12-4 answer
17
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Both spheres must be charged and the charges must have the same sign.
A charged object can attract a neutral object by induction, but a charged
object cannot repel a neutral object.
Two charged objects with the same sign would repel each other.
Example: 2
18
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The figure shows three charged particles. What
electrostatic force, due to the other two charges,
acts on q1?
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q1 = -1.2 μC
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q2 = +3.7 μC
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q3 = -2.3 μC
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r12 = 15 cm
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r13 = 10. cm
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θ = 32°
Spherically symmetric charge distributions
19
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Coulomb’s law is stated in terms of point charges, but it is also valid
for spherically symmetric charge distributions, as long as the distance
is measured from the center of the sphere.
The amount of charge per unit area is referred to as the surface
charge density σ:
Q =σ A
where A is the surface area.