From Last Time…
Lenses and image
formation
Object
p
Image
q
Optical
Instruments
Exam 1
Tue. Sep. 29, 5:30-7 pm, 145 Birge
Covers Chap. 21.5-7, 22, 23.1-4, 23.7,
24.1-5, 26 + lecture, lab, discussion, HW
8 1/2 x 11 handwritten note sheet (both sides) allowed
Students with scheduled class conflicts:
stay after lecture today to arrange time
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Study ideas:
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Exam 1 Practice problems at Mastering Physics
Sample exams on website (blank & solutions)
Group/Quiz (blank & solutions).
Review lab question sheets.
2
Chapter 26:
Electric Charges and forces
• Two different kinds of electric charges
•
•
 Benjamin Franklin called these positive, negative
Negative charges are electrons
Positive charges are protons
Example: Lithium
• Often bound in atoms:
 Positive protons in
central nucleus r~10-15 m
 Negative electrons
orbit around the nucleus
r~10-10 m
3 protons in nucleus,
3 electrons orbiting
+ and - charges can be separated
• Triboelectric
 Charge is transferred as a result of
mechanical (frictional) action
• Conduction
 charge transfer by contact (spark)
Separating charge
•Rubber / fur: electrons
transferred to rod
• Rubber has
negative charge
•Glass / silk: electrons
taken from plastic
• Plastic has
positive charge
Charge is conserved.
Can be moved around, but not created or destroyed.
Electric Charges
units and quantization
• The SI unit of charge is Coulomb (C )
• The electric charge, q, is said to be quantized
 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
Charge by conduction (touching)
+ + + + + + + + + + ++
Positively charged rod
(too few electrons)
+ + + + + + + + + + ++
electron flow
+
+
+ + + + +
Less positively charged rod
+-+
- -+ + - +
Neutral
metal
+-+
- -+ + - +
+ +
+
+
+
Positively
charged
metal
Measuring charge
• Touch charged rod to
•
•
•
electroscope.
Charge transferred from
rod to electroscope.
Everything positively
charged.
Like charges on leaves
repel.
+ ++
+
Positive
charged
rod results
in positive
leaves.
Charge motion and materials
• Insulators (e.g. plastic, wood, paper)
 electrons bound to atoms, do not move around
 Even extra charge is stuck
 Extra charge cannot move around on insulator
• 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
Forces between charges
Like charges repel
Unlike charges attract
All of this without touching — a ‘noncontact’ force
Attraction, repulsion decreases with distance
Induced charge
• Charging by induction requires no contact with the
object inducing the charge
charged rubber rod
neutral metallic sphere
Electrons (-) free to move
Bring negative charge close.
Electrons on sphere
move away from rod.
Quick quiz
What is the sense of the force
between these two objects?
A. Attractive
B. Repulsive
C. Zero
Lightning
doorbell
+ +
+ +
• Ben Franklin’s
•
‘door bell’.
Announced presence
of lightning so knew to
go out and do his
experiments!
-
-
+ +
+ +
Quick Quiz
A charged rod is brought close to
an initially uncharged
electroscope without
touching
The leaves
Positive
charged
rod results
in positive
leaves.
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
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
Multiple forces add as vectors.
Electrical forces obey Newton’s Third Law:
F21 = -F12
Quick Quiz
Two charges are arranged as shown.
What is the direction of the force on the
the positively charged ‘test’ particle?
C
B
D
+
A
+
E
Magnitude of force:
Coulomb’s Law
• 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/(4πeo)
 eo  permittivity of free space = 8.854 x 10-12 C2 / N.m2
Gravitational force: FG=GM1M2/ r2
G=6.7x10-11 Nm2/kg2
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?
A) Left
B) Right
-
+
-
C) Up
D) Down
E) Zero
kq1q2
F 2
r
The electric dipole
• Can all be approximated
•
by electric dipole.
Two opposite charges
magnitude q
separated by distance s
Dipole moment
Vector
p
Points from - charge to + charge
Has magnitude qs
Force on an electric dipole
• What is the direction of the force on the electric
dipole from the positive point charge?
A. Up
B. Down
p
+
C. Left
D. Right
E. Force is zero

How does the magnitude of the force depend on p ?
Induced dipoles (charge redistribution)
charged rubber rod
Bring negative charge close.
Electrons on sphere
move away from rod.
Induced dipole in insulators
• A process similar to
•
induction can take place in
insulators
The charges within the
molecules of the material
are rearranged