Chapter 26:
Electric Charges and forces
From Last Time…
Object
• Two different kinds of electric charges
 Benjamin Franklin called these positive, negative
Lens
• Negative charges are electrons
• Positive charges are protons
Image
• Often bound in atoms:
Lenses and image
formation
Object
Example: Lithium
3 protons in nucleus,
3 electrons orbiting
 Positive protons in
central nucleus r~10-15 m
 Negative electrons
orbit around the nucleus
r~10-10 m
Image
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2
Separating charge
+ and - charges can be separated
•Rubber / fur: electrons
transferred to rod
• Triboelectric
• Rubber has
negative charge
 Charge is transferred as a result of
mechanical (frictional) action
•Glass / silk: electrons
taken from plastic
• Conduction
• Plastic has
positive charge
 charge transfer by contact (spark)
Charge is conserved.
Can be moved around, but not created or destroyed.
3
4
Charge by conduction (touching)
Electric Charges
units and quantization
+ + + + + + + + + + ++
• The SI unit of charge is Coulomb (C )
• The electric charge, q, is said to be quantized
Positively charged rod
(too few electrons)
 quantized = it is some integer multiple of a
fundamental amount of charge e
q = Ne
• N is an integer
• e is the magnitude of charge of electron
= +1.6 x 10-19 C
• Electron: q = -e
• Proton: q = +e
+ + + + + + + + + + ++
electron flow
+
5
+
+ +
+ + +
Less positively charged rod
+- +
- -+ + - +
Neutral
metal
+-+
- -+ + - +
+ +
+
+
+
Positively
charged
metal
6
1
Measuring charge
Charge motion and materials
• Insulators (e.g. plastic, wood, paper)
• Touch charged rod to
electroscope.
• Charge transferred from
+ ++
+
rod to electroscope.
Everything positively
charged.
Like charges on leaves
repel.
•
•
 electrons bound to atoms, do not move around
 Even extra charge is stuck
 Extra charge cannot move around on insulator
Positive
charged
rod results
in positive
leaves.
• Metals (e.g. copper, aluminum)
 Some electrons free, positive ions stuck in place
 Additional charge free to move, distributes over surface
• Ionic solutions (e.g. saltwater)
 Like conductor, but both positive, negative ions free to move
7
Cellular ionic solutions
K+
Interactions between charges
A-
Extracellular fluid
Why did the electrons flow?
+ + + + + +
7-8
nm
attractive force between
positive and negative charges.
Plasma membrane
-
-
-
Cytoplasm
Na+
8
- -
-
repulsive force between
two positive or two negative charges
Cl-
Inside and outside of a cell are ionic solutions.
Like charges repel, unlike charges attract
Has both positive and negative ions.
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Forces between charges
10
Induced charge
Like charges repel
Unlike charges attract
All of this without touching — a ‘noncontact’ force
• Charging by induction requires no contact with the
object inducing the charge
charged rubber rod
Attraction, repulsion decreases with distance
11
neutral metallic sphere
Electrons (-) free to move
Bring negative charge close.
Electrons on sphere
move away from rod.
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2
Quick quiz
Lightning
doorbell
What is the sense of the force
between these two objects?
+ +
+ +
A. Attractive
B. Repulsive
C. Zero
-
-
+ +
+ +
• Ben Franklin’s
‘door bell’.
• Announced presence
of lightning so knew to
go out and do his
experiments!
13
Electrical machines
Quick Quiz
Positive
charged
rod results
in positive
leaves.
A charged rod is brought close to
an initially uncharged
electroscope without
touching
The leaves
• Can mechanize the
•
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rubbing process to
continually separate
charge.
This charge can then
be transferred to
other objects.
A. move apart
B. only one moves away
C. move closer together
D. depends on sign of rod
E. do nothing
This is an induced dipole
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16
Quick Quiz
Vector Nature of Electric Force
a)The force is repulsive if charges are of like sign
b)The force is attractive if charges are of opposite sign
The force is a conservative force
Two charges are arranged as shown.
What is the direction of the force on the
the positively charged ‘test’ particle?
C
B
Electrical forces obey Newton’s Third Law:
D
+
A
F21 = -F12
E
+
17
18
3
Magnitude of force:
Coulomb’s Law
Quick Quiz
Equal but opposite charges
are connected by a rigid insulating rod.
They are placed near a negative charge as shown.
What is the net force on the two connected charges?
• Electrical force between two stationary charged particles
• The SI unit of charge is the coulomb (C ), µC = 10-6 C
• 1 C corresponds to 6.24 x 1018 electrons or protons
• ke = Coulomb constant ≈ 9 x 109 N. m2/C2 = 1/(4π εo)
 εo = permittivity of free space = 8.854 x 10-12 C2 / N.m2
A) Left
B) Right
C) Up
-
-
+
D) Down
F=
E) Zero
kq1q2
r2
Gravitational force: FG=GM1M 2/ r2
G=6.7x10-11 Nm2/kg2
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The electric dipole
Force on an electric dipole
• What is the direction of the force on the electric
• Can all be approximated
•
dipole from the positive point charge?
by electric dipole.
Two opposite charges
magnitude q
separated by distance s
B. Down
+
C. Left
D. Right
Dipole moment
Vector
r
p
A. Up
E. Force is zero
r
p
r
Points from - charge to + charge
Has magnitude qs
!
How does the magnitude of the force depend on p ?
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22
!
!
Induced dipoles (charge redistribution)
Unusual dipoles:
Electrogenic fish
• Dipole +
nearby conducting object
charged rubber rod
Some fish generate charge
separation - electric dipole.
Dipole is induced in nearby
(conducting) fish
Small changes detected by
fish.
Bring negative charge close.
Electrons on sphere
move away from rod.
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