Transcript Lecture 29 - USU Department of Physics

Physics of Technology
PHYS 1800
Lecture 29
Introduction
Electricity and Charge
Section 0
Lecture 1
Slide 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Electric Fields and Potential
Lecture 29 Slide 1
PHYSICS OF TOF
ECHNOLOGY
- PHYS 1800
PHYSICS
TECHNOLOGY
ASSIGNMENT SHEET
Spring 2009Spring
Assignment
Sheet
2009
Date
Day
Lecture
Feb 16
M
Presidents Day
17
Tu
Angular Momentum (Virtual Monday)
18
W
Review
19
H
Test 2
20
F*
Static Fluids, Pressure
Feb 23
M
Flotation
25
W
Fluids in Motion
27
F*
Temperature and Heat
Mar 2
M
First Law of Thermodynamics
4
W
Heat flow and Greenhouse Effect
6
F*
Climate Change
Mar 9-13
M-F
Spring Break
Mar 16
M
Heat Engines
18
W
Power and Refrigeration
20
F*
Electric Charge
Mar 23
M
Electric Fields and Electric Potential
25
W
Review
26
H
Test 3
27
F*
Electric Circuits
Mar 30
M
Magnetic Force Review
Apr 1
W
Electromagnets
3
F
Motors and Generators
Apr 6
M
Making Waves
8
W
Sound Waves
10
F*
E-M Waves, Light and Color
Apr 13
M
Mirrors and Reflections
Introduction
Section
0 Lecture 1 Slide 2
15
W
Refraction and Lenses
17
F*
Telescopes and Microscopes
Apr 20
M
Review
22
W
Seeing Atoms
24
F
The really BIG & the really small
INTRODUCTION TO Modern Physics PHYX 2710
May
1
F
Final Exam: 09:30-11:20am
Chapter
No Class
8
5-8
5-8
9
9
9
10
10
10
No Classes
11
11
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12
13
9-12
13
14
9-12
14
15
15
16
17
17
17
1-17
18 (not on test)
21 (not on test)
Homework Due
-
6
7
8
-
9
10
11
No test week
12
Fall 2004
* = Homework Handout
*Homework Handout
Physics of Technology—PHYS 1800
Spring 2009
Electric Fields and Potential
Lecture 29 Slide 2
Physics of Technology
PHYS 1800
Lecture 29
Electric Fields and Potentials
Introduction
Section 0
Lecture 1
Slide 3
Electrostatic Force
INTRODUCTION TO Modern Physics PHYX 2710
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Electric Fields and Potential
Lecture 29 Slide 3
The Electrostatic Force: Coulomb’s Law
• Coulomb measured how the
electrostatic force varies with
distance and quantity of charge.
– Since the electrostatic force is so
weak, he had to develop special
techniques, involving a torsion
balance.
– The degree of twist of the wire
measures the repulsive force
between the two charges.
• Determining the amount of charge
on the balls was more difficult.
Introduction
Section 0
Lecture 1
Slide 4
INTRODUCTION TO Modern Physics PHYX 2710
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Lecture 29 Slide 4
Historical Perspective on Gravity
Cavendish
Developed a clever way to measure
the weak gravitational force between
small masses.
Confirmed Newton’s Law of Universal
Gravitation (and in essence measured
the mass of the Earth in comparison
GmM earth
Fgravity 
to the kg mass standard).
r2
The effect the 320 kg balls of the 1.5 kg
balls was about
that of a grain of sand!
Introduction Section 0 Lecture 1 Slide 5
That’s 20 parts per billion precision!!!
INTRODUCTION TO Modern Physics PHYX 2710
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Wikeapedia has a nice description
of the experiment.
Physics of Technology—PHYS 1800
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Electric Fields and Potential
Lecture 29 Slide 5
Coulomb’s Law: Amounts of Charge
•
Although he could not measure absolute quantities of charge
on the balls, Coulomb was able to measure the effects due to
different relative amounts of charge.
– By bringing two identical metal balls into contact, one charged
and the other initially uncharged, Coulomb knew he had equal
amounts of charge on both balls.
– By repeating the process, he could get a ball with exactly half that
charge, or one-fourth, etc.
– He could then measure
how the strength of the
electrostatic force varied
when the amount of
charge was doubled,
quadrupled, etc., in
addition to how the force
varied
with distance
Introduction
Section 0 Lecture 1 Slide 6
between the balls.
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Lecture 29 Slide 6
Coulomb’s Law
• The electrostatic force between two charged objects is
proportional to the quantity of each of the charges and
inversely proportional to the square of each distance
between the charges.
kq1q2
F 2
r
Introduction
Section 0
Lecture 1
7
inSlide
units
of coulombs (C)
Coulomb' s constant k  9 10 9 N  m2 /C 2
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Lecture 29 Slide 7
Two positive charges, one 2 C and the other 7 C,
are separated by a distance of 20 cm. What is
the magnitude of the electrostatic force that each
charge exerts upon the other?
a)
b)
c)
d)
e)
q1  2 C
0.32 N
0.63 N
0.70 N
2.02 N
3.15 N
F
Introduction
Section 0
INTRODUCTION TO Modern Physics PHYX 2710
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r  20 cm  0.2 m
kq1q2
r2
9 10


Lecture 1
q2  7 C
Slide 8
9
N  m2 /C 2 2 106 C7 106 C
0.2 m
2
0.126 N  m2

 3.15 N
0.04 m2
Electric Fields and Potential
Lecture 29 Slide 8
The Electrostatic and Gravitational Forces
• The electrostatic force has the same inverse-square
dependence on distance as Newton’s law of gravitation.
Gm1m2
Fg 
r2
kq1q2
and Fe  2
r
– If we double the distance between the charges, the force falls
to one-fourth of the original.
– The gravitational force depends on the masses, and the
electrostatic force depends on the charges.
– Gravity is always attractive; there is no such thing as negative

mass.
– Gravity is much weaker than the electrostatic force.
– Introduction
Physicists
are still trying to understand the reasons for the
Section 0 Lecture 1 Slide 9
relative strengths of the fundamental forces.
– The search for a unified field theory that would explain the
relationships between all of the fundamental forces is a major
area of research in modern theoretical physics.
INTRODUCTION TO Modern Physics PHYX 2710
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Lecture 29 Slide 9
Three positive charges are located along a line as shown.
What is the magnitude of the force exerted on the 0.02-C
charge by the 0.10-C charge?
a)
b)
c)
d)
e)
q1  0.02 C
106
2.25 x
N
4.5 x 106 N
9.0 x 106 N
1.8 x 107 N
2.7 x 108 N
F
q2  0.10 C
r2m
kq1q2
r2
9 10


9
N  m2 /C 2 0.02 C0.10 C
2 m
2
 4.5 10 6 N (to the right)
Introduction
Section 0
Lecture 1
Slide 10

INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
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Spring 2009
Electric Fields and Potential
Lecture 29 Slide 10
Three positive charges are located along a line as shown.
What is the magnitude of the force exerted on the 0.02-C
charge by the 0.04-C charge?
a)
b)
c)
d)
e)
q1  0.02 C
1.8 x 106 N
3.6 x 106 N
7.2 x 106 N
1.44 x 107 N
2.88 x 107 N
q2  0.04 C
r 1m
kq1q2
F 2
r
9 10


9
N  m2 /C 2 0.02 C0.04 C
1 m
2
 7.2 10 6 N (to the left)
Introduction
Section 0
Lecture 1
Slide 11

INTRODUCTION TO Modern Physics PHYX 2710
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Spring 2009
Electric Fields and Potential
Lecture 29 Slide 11
Three positive charges are located along a line as shown. What is
the net force exerted on the 0.02-C charge by the other two
charges?
a)
b)
c)
d)
e)
2.25 x 106 N
4.5 x 106 N
9.0 x 106 N
1.8 x 107 N
2.7 x 108 N
F  F1  F2
 7.2 10 6 N  4.5 10 6 N
 2.7 10 6 N (to the left)
Introduction
Section 0

Lecture
1
Slide 12
INTRODUCTION TO Modern Physics PHYX 2710
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Electric Fields and Potential
Lecture 29 Slide 12
Physics of Technology
PHYS 1800
Lecture 29
Electric Fields and Potentials
Introduction
Section 0
Lecture 1
Slide 13
Electric Fields
INTRODUCTION TO Modern Physics PHYX 2710
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Electric Fields and Potential
Lecture 29 Slide 13
The Electric Field
• How do the charges exert forces on each other, when
they are not even touching?
– The concept of an electric field describes how one
charge affects the space around it, which then exerts a
force on another charge.
– The electric field at a given point in space is the electric
force per unit positive charge that would be exerted on
a charge if it were placed at that point.
F
kq
E electric  electric  22 r̂12
q1
r
– It is a vector having the same direction as the force on
a positive charge placed at that point.
E
Introduction
Section 0
Lecture 1
Slide 14
– Compare this to the gravitational field
INTRODUCTION TO Modern Physics PHYX 2710
E gravity 
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Electric Fields and Potential
Fgravity
m1
Gm2
 2 rˆ12  g rˆ12
r
Lecture 29 Slide 14
Two point charges, 3 C and 2 C, are separated by a distance of
30 cm. A third charge q0 is placed between them as shown. The
force exerted by q1 on q0 is 10.8 N, and the force exerted by q2
on q0 is 1.8 N.
What is the net electrostatic force acting on q0?
a)
b)
c)
d)
e)
1.8 N to the left
9 N to the right
10.8 N to the right
12.6 N to the right
12.6 N to the left
Introduction
Section 0
Lecture 1
F  F1  F2
 10.8 N 1.8 N
 9 N (to the right)

Slide 15
INTRODUCTION TO Modern Physics PHYX 2710
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Electric Fields and Potential
Lecture 29 Slide 15
What is the electric field at the location of the charge
q0 due to the other two charges?
a)
b)
c)
d)
e)
f)
2.25 N/C to the left
3.0 N/C to the left
4.5 N/C to the left
2.25 N/C to the right
3.0 N/C to the right
4.5 N/C to the right
E

F
q0
9N
4 10 -6 C
 2.25 10 6 N/C (to the right)

Introduction
Section 0
Lecture 1
Slide 16
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Lecture 29 Slide 16
Forces and the Electric Field
• We can then use the electric field to find the force
on any other charge placed at that point:
– If the charge q is negative, the minus sign indicates that
the direction of the force on a negative charge is opposite
to the direction of the field.
– The direction of the electric field is the direction of the
force exerted on a positive test charge.
– We can talk about the field at a point in space even if there
Introduction
Section 0at Lecture
1 Slide 17
is
no charge
that point.
– The electric field can exist even in a vacuum.
– The field concept can also be used to define a
gravitational field or a magnetic field, as well as others.
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Electric Fields and Potential
Lecture 29 Slide 17
Electric Field and Field Lines
• Although Maxwell was the major contributor to the electric
field concept, Faraday also developed the idea of field lines
as a means of visualizing both the direction and strength of
the field.
• The direction of the electric
field lines around a positive
charge can be found by
imagining a positive test
charge q0 placed at various
points around the source
charge.
• The field has the same
Section 0on Lecture
directionIntroduction
as the force
a
positive test charge.
1
Slide 18
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Electric Fields and Potential
Lecture 29 Slide 18
Electric Field and Field Lines
• Although Maxwell was the major contributor to the
electric field concept, Faraday also developed the
idea of field lines as a means of visualizing both
the direction and strength of the field.
• The electric field lines
associated with a
positive charge are
directed radially outward.
Introduction
Section 0
Lecture 1
Slide 19
INTRODUCTION TO Modern Physics PHYX 2710
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Electric Fields and Potential
Lecture 29 Slide 19
Electric Field and Field Lines
• Although Maxwell was the major contributor to the
electric field concept, Faraday also developed the
idea of field lines as a means of visualizing both
the direction and strength of the field.
• A positive test charge is
attracted to a negative
charge.
• The electric field lines
associated with a
negative charge are
directed
inward,
as0 Lecture
Introduction
Section
indicated by the force on
a positive test charge, q0.
1
Slide 20
INTRODUCTION TO Modern Physics PHYX 2710
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Electric Fields and Potential
Lecture 29 Slide 20
Dipole Electric Field and Field Lines
• An electric dipole is two charges of equal magnitude but
opposite sign, separated by a small distance.
– You just add the vectors!!!
– Electric field lines originate on positive charges and end
on negative charges.
• The field lines point
away from the positive
charge, and in toward the
negative charge.
• Near each charge, the
electric
field
Introduction Section 0 Lecture 1
approximates the field
due to a single point
charge of the same sign.
Slide 21
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Electric Fields and Potential
Lecture 29 Slide 21
Two charges, of equal magnitude but opposite sign, lie
along a line as shown. What are the directions of the
electric field at points A, B, C, and D?
a)
b)
c)
d)
e)
A:left, B:left, C:right, D:right
A:left, B:right, C:right, D:right
A:left, B:right, C:right, D:left
A:right, B:left, C:left, D:right
A:right, B:left, C:right, D:right
Introduction
Section 0
Lecture 1
Slide 22
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Lecture 29 Slide 22
Physics of Technology
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Lecture 29
Electric Fields and Potentials
Introduction
Section 0
Lecture 1
Slide 23
Electrostatic Potential
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Lecture 29 Slide 23
Electric Potential
• The electrostatic force is a conservative force, which means we
can define an electrostatic potential energy.
– We can therefore define electric potential or voltage.
• Two parallel metal
plates containing equal
but opposite charges
produce a uniform
electric field between the
plates.
Introduction
Section 0
• This arrangement is an
example of a capacitor, a
device to store charge.
Lecture 1
Slide 24
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Lecture 29 Slide 24
Electric Potential
• A positive test charge placed in the uniform electric field will
experience an electrostatic force in the direction of the
electric field.
• An external force F, equal in magnitude to the electrostatic
force qE, will move the charge q a distance d in the uniform
field.
• The external force does work
on the charge and increases the
potential energy of the charge.
• The work done by the external
force is qEd, the force times the
distance.
• This is equal to the increase in
potential energy of the charge:
Introduction Section 0 Lecture 1 Slide
PE = qEd.
• This is analogous to what
happens when a mass m is lifted
against the gravitational force.
25
INTRODUCTION TO Modern Physics PHYX 2710
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Electric Fields and Potential
Lecture 29 Slide 25
Electric Potential
• Electric potential is related to electrostatic potential energy in
much the same way as electric field is related to electrostatic
force.
• The change in electric potential is equal to the change in
electrostatic potential energy per unit of positive test charge:
PEelectric
q
1 J/C  1 V
PEelectric  qV
V 
PEgravity m g h
in units of volts (V)
Pgravity 

gh
m
1 J/kg  1 m 2 /s 2
PEgravity  m Pgravity
m
in units of (m 2 /s 2 )
• Electric potential and potential energy are closely related, but
they are NOT the same.
– If the charge q is negative, its potential energy will decrease
Introduction
0 Lecture
1 direction
Slide 26
when
it is Section
moved
in the
of increasing electric
potential.
• It is the change in potential energy that is meaningful.
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Electric Fields and Potential
Lecture 29 Slide 26
Two plates are oppositely charged so that they have a uniform electric
field of 1000 N/C between them, as shown. A particle with a charge
of +0.005 C is moved from the bottom (negative) plate to the top
plate. What is the change in potential energy of the charge?
a)
b)
c)
d)
e)
0.15 J
0.3 J
0.5 J
0.8 J
1.5 J
PE  W  Introduction
Fd  qEdSection 0
Lecture 1
Slide 27
 (0.005 C)(1000 N/C)(0.03m)
INTRODUCTION TO Modern Physics PHYX 2710
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 0.15 J
Physics of Technology—PHYS 1800
Spring 2009
Electric Fields and Potential
Lecture 29 Slide 27
What is the change in electric potential from the bottom
to the top plate?
a)
b)
c)
d)
e)
0.15 V
0.3 V
5V
30 V
150 V
Introduction
V 
Section 0
Lecture 1
Slide 28
PE
0.15 J

 30 V
q
0.005 C
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Lecture 29 Slide 28
Relation between Electric Potential and Electric Field
• The potential energy of a positive charge increases
when we move it against the field.
– For a uniform electric field, there is a simple relationship
between the magnitude of the electric field and the change
in electric potential: V = Ed.
• For non-uniform fields, the
relationship is more
complicated, but the electric
potential always increases
most rapidly in the direction
opposite to the electric field.
Introduction
Section 0
Lecture 1
• For a positive point charge,
the electric potential
increases as we move closer
to the charge.
Slide 29
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Lecture 29 Slide 29
What is lightning?
• Most thunderclouds generate a separation of charge
resulting in a net positive charge near the top and a net
negative charge near the bottom.
• The charge separation produces strong electric fields in
the cloud as well as between the cloud and earth.
• Since moist earth is a reasonably good conductor, a
positive charge is induced on the surface of the earth
below the cloud.
Introduction
Section 0
Lecture 1
Slide 30
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Lecture 29 Slide 30
Circuits and Electric Potential and Electric Field
Moving a charge in an
electric field changes the
electric PE and electric
potential (the voltage!).
Thus moving charge
(current) is directly
related to change in
voltage.
V= 30 V
Sounds like circuits to
me!!!
Introduction
Section 0
Lecture 1
Slide 31
V= 0 V
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Electric Potential and Electric Field of Lightning
• The electric field generated can be several thousand volts per
meter; the potential difference between the cloud’s base and the
earth can easily be several million volts!
• This creates an initial flow of charge (the “leader”) along a path
that offers the best conducting properties over the shortest
distance.
• The leader ionizes some of
the atoms in the air along that
path.
• The following strokes all take
place along this same path in
rapid succession.
• The heating and ionizing
produce the lightning we see.
• The thunder
Introduction (sound
Section 0 waves)
Lecture 1 isSlide
produced at the same time, but
takes longer to reach us since
sound travels slower than
light.
32
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Electric Fields and Potential
Lecture 29 Slide 32
Physics of Technology
Next Lab/Demo:
Electric Charge
Electric Circuits
Thursday 1:30-2:45
ESLC 46
Ch 12 and 13
Next Class:
Wednesday 10:30-11:20
BUS
Slide 33318 room
Read Ch 13
Introduction
Section 0
Lecture 1
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Electric Fields and Potential
Lecture 29 Slide 33