From Last Time…
This Friday’s guest lecture
Biological Diffraction
Prof. Katrina Forest, Bacteriology
Friday 8:50 am, 2103 Chamberlin
Total internal
reflection
Image
Object
Lenses
and imaging
1
Chapter 25:
Electric Charges and forces
2
• Triboelectric
 Benjamin Franklin called these positive, negative
Negative charges are electrons
Positive charges are protons
Example: Lithium
• Often bound in atoms:
Real-space structure
+ and - charges can be separated
• Two different kinds of electric charges
•
•
X-ray diffraction
 Charge is transferred as a result of
mechanical (frictional) action
• Conduction
3 protons in nucleus,
3 electrons orbiting
 charge transfer by contact (spark)
 Positive protons in
central nucleus r~10-15 m
 Negative electrons
orbit around the nucleus
r~10-10 m
3
Separating charge
4
Electric Charges
units and quantization
•Rubber / fur: electrons
transferred to rod
• The SI unit of charge is Coulomb (C )
• The electric charge, q, is said to be quantized
• 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.
5
 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
6
1
Charge by conduction (touching)
+ + + + + + + + + + ++
Positively charged rod
(too few electrons)
+ + + + + + + + + + ++
electron flow
+
+
+ +
+ + +
Less positively charged rod
+- +
- -+ + - +
Measuring charge
Neutral
metal
• Transfer charge to
+-+
- -+ + - +
+ +
+
+
+
•
•
electroscope.
Everything equally charge.
Like charges on leaves
repel.
+ ++
+
Positive
charged
rod results
in positive
leaves.
Positively
charged
metal
7
8
Interactions between charges
Charge motion and materials
• Insulators (e.g. plastic, wood, paper)
Why did the electrons flow?
 electrons bound to atoms, do not move around
 Even extra charge is stuck
 Extra charge cannot move around on insulator
attractive force between
positive and negative charges.
• Metals (e.g. copper, aluminum)
 Some electrons free, positive ions stuck in place
 Additional charge free to move, distributes over surface
repulsive force between
two positive or two negative charges
• Ionic solutions (e.g. saltwater)
 Like conductor, but both positive, negative ions free to move
9
Forces between charges
10
Induced charge
Like charges repel
Opposite 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
neutral metallic sphere
Attraction, repulsion decreases with distance
11
Bring negative charge close.
Electrons on sphere
move away from rod.
12
2
Quick quiz
Lightning
doorbell
What is 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
•
14
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
15
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
19
20
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 ?
21
22
!
!
Induced dipoles (charge redistribution)
Induced dipole in insulators
• A process similar to
charged rubber rod
•
induction can take place in
insulators
The charges within the
molecules of the material
are rearranged
Bring negative charge close.
Electrons on sphere
move away from rod.
23
24
4
The idea of electric fields
Electric field of a point charge
Force on this charge…
• EM wave made up of
oscillating electric and magnetic fields.
Q2
+
• But what is an electric field?
• Electric field is a way to describe the force on a
+
+
charged particle due to other charges around it.
r
QQ
F = k 1 2 2 rˆ
r
Q1
• Force = charge × electric field
…due to this charge
!
electric field.
+
• The direction of the force is the direction of the
Force = (Charge) " (Electric field)
+
!
25
26
Question
• Which vector best represents the
electric field at the red dot?
A
B
C
D
E
A
B
E
C
-
D
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5