Transcript 幻灯片 1

1.8. Relative Motion
A
B
Z
Y
X
C
Galilean coordinate transformation
S’ motorial reference system
S static reference system
z
  
r  r0  r '
S

r
z' 
S'

r0
P

r'
O'
x'
O
y
x
Relative motion, in nature, is the transformation of
reference frame.
y'




 dr dr0 dr ' 
v
 v0  v '


dt dt
dt



vabsol ut e  vconvect ed  vr el at i ve
z
S

r
z'  P
S'

r0

r'
O'
x'
O
x
y
y'
aabsolute  aconvected  arelative
z
S

r
S'

r0

r'
O'
x'
Extreme case:
O
y
x
relative to S , S system does uniform motion
aconvected  0
z'  P
aabsolute  arelative
 
a  a'
y'
 
a  a'
The acceleration of the particle measured by an observer in
one frame of reference is the same as that measured by any
other observer moving with constant velocity relative to the
first frame.
 Galilean Experiment
Exercise
A Boat Crossing a River
A boat heading due north crosses a wide river with a speed
of 10.0 km/h relative to the water. The water in the river has
a uniform speed of 5.00 km/h due east relative to the Earth.
Determine the velocity of the boat relative to an observer
standing on either bank.

 is
vBE

v
RE
the velocity of the boat relative to Earth .
is the velocity of the river relative to Earth.

 v is the velocity of the boat relative to Earth.
BE



vBE  vBR  vRE
vBE  v  vRE
2
BR
2
 11.2 (km / h)
Look at the examples given in
P65 to 67!
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Charles Augustin Coulomb (1736-1806) invented an
instrument called the torsion balance - which later showed
great utility for measuring very small electrical forces.
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Coulomb stated that the electrical force between two
electrified objects is proportional to the inverse square of
the distance between them and to the product P of their
electrical masses.
q1q2
f  2
r
This achievement marked the point where electricity
became thoroughly open to mathematical analysis.
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Orsted (1777-1851) was remembered as the man
responsible for discovering the first experimental evidence
for the relationship between electricity and magnetism.
I
the Magnetic Effect of Electrical Currents
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Just over a month after the discovery, Jean-Baptise Biot
(1774-1862) and Felix Savart (1791-1841) were the first to
provide a precise analysis of the effect. Biot and Savart
announced the Biot-Savart Law which can be used to
calculate the magnetic field for a segment of current
carrying wire.
Idl  r
dB 
3
r
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Andre-Marie Ampere (1775-1836) was the first person
to develop a technique for measuring electricity. he built
an instrument which later refined being known as the
galvanometer.
Ampere’s theories became fundamental for 19th
century developments in electricity and magnetism.
Ampere’s law
Ampere’s circulation theorem
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Michael Faraday (1791-1867) made one of the most
important discoveries in the sciences of electricity and
magnetism; namely, electromagnetic induction.
James Clerk Maxwell (1831-1879) . His most
important contribution was the extension and
mathematical formulation of previous works on
electricity and magnetism by Faraday, Ampere ad others
into a linked set of partial differential equations. These
equations, now collectively known as Maxwell’s
Equations.
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Maxwell ’ s equations
predicted that the
phenomenon of light was
electromagnetic in nature.
Maxwell ’ s equations
summarized a series of
experimental laws in the
field of electromagnetics.
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In 1888 the German physicist Hertz (H. Hertz, 18571894) firstly discovered the electromagnetic wave
predicted by the Maxwell equations, thus the
theoretical system of the classical electromagnetism
was finally established.
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Outline of Chapter 2
Electrostatic Field
Two Important
Physical Quantities
Two Fundamental
Theorems
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The field distributed round a static charge
is called the electrostatic field.
Force

E
Work
U
Field with sources
conservative field
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Gauss’s Law
Circulation Theorem
Main Contents
Coulomb’s Law，Superposition Principle of Coulomb Force

 Definition and computation of E
Electric Flux, Gauss’s Law
Circulation Theorem of electrostatic field, Electric Potential

The relationship of E
and potential gradient
Motion of charged particles in electric field
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Requirements
Master the Calculation of Field Intensity
Find the Field Intensity with Gauss Law
Find Electric Potential
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§2.1 Point Charge, Coulomb’s Law
1. Properties of Electric Charges
A charged body without size and shape, i.e., a charged
geometrical point.
(1) Two Kinds of Electric Charge
Positive Charge, Negative Charge
Like charges repel each other, and unlike
charges attract each other. Where “like”
means two charges with the same sign.
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When the girl touches
a Van de Graaff
generator, she received
an excess of positive
charge, causing her hair
to stand on end.
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(2) Quantization of Electric Charge
Electric Quantity
e  1.6  10 19 C
(3) Conservational Low of Charge
The net charge in an isolated system is always conserved.
Or : total charge is constant in any process.
Conserved quantities: energy, momentum, angular
momentum, charge……
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(4) Relativistic Invariability of Electric Quantity
The electric quantity is independent
of the velocity and acceleration. This
characteristics is not identical with
mass.
Q
+++
Q
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2. Coulomb’s Law in the Vacuum
French physicist. His major
contributions to science were
in the areas of electrostatics
and magnetism.
Coulomb’s Law gives the
force between two charged
particles at rest.
Charles Coulomb (1736-1806)
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Coulomb Law in the Vacuum
The direction of interaction force between two
small charged balls at rest is along the line connected
them, the magnitude F of interaction force is direct
proportional to the product of charges q1 and q2 , and
is opposite proportional to the square of distance r
separated them, like charges repel each other, and
unlike charges attract each other.
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Attention
“vacuum” means that, except the charges
considered suppose there is no any others.
This law applies exactly only to particles.
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Mathematics Expression

f 12q1
Vector form,

q1q
q12q2 
f12  K
r12
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4 0rr

r12
q2
r

 r21is a vector directed from the charge q2 toward the q1.
Permittivity of vacuum,
 0  8.85  10 12 C 2 / Nm 2 
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Coulomb constant,
k
1
40
The interaction force between point charges at rest
is usually called electrostatic force or Coulomb force.
When dealing with Coulomb law, remember that
force is a vector quantity and must be treated
accordingly.
Discussion
r 0
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F 
?
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Example
The Hydrogen Atom
Find the ratio of Coulomb force and the universal gravitation
between electron and nucleus in a hydrogen atom.
Solution
The electron and proton of a hydrogen atom are
separated (on average) by a distance of
approximately 5.3 10 11 m,and the masses are
M  1840me
me  9.11  10 31 kg
From Coulomb’s law, we find that the magnitude of the
attractive electric force is
F
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e2
40 r 2
 8.2 10 8 N
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Using Newton’s law of universal gravitation, we
find that the magnitude of the gravitational force is
Mme
f  G 2  3.6 10  47 N
r
The ratio
f
 4 0 GMme  e 2  4.4  10  40
F
Thus the gravitational force between charged atomic
particles is negligible compared with the electric force.
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3. Superposition Principle of Electrostatic Force
The resultant force on any one particle equals the
vector sum of the individual forces due to all other
particles.
The resultant force on particle 1 due to particles
2 and 3 is given by the vector sum

f1 


f 12

f 1i
i
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
f1
33
q1
q2
+
+

f13
-
q3
4. Find Electrostatic Force
(1). Force Due to the System of Point Charges.
The resultant force on particle 0 due to the other
particles is given by the vector sum
N
q0 qi ri
F 
3
i 1 4 0 ri
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Quick Quiz
 There is a point charge q at
every tip of the isosceles right
triangle as shown in figure,
AC=BC=a . Find Coulomb force
on the point charge at tip C.
Y
+A
a
+
B
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a
+
C
X
Key:
F
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q
2
40 a
2
(i  j )
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(2). Force Due to Continuous Charge Distributions
dq
Strategy
Q
1. Divide the charge distribution into
small elements, each of which
contains a small amount of charge dq.

r
q0
+
P

2. Model the element as a point charge, and find the dF at the
point P due to one of these elements.
3. Evaluate the total electrostatic force at P due to the charge
distribution by performing a vector sum of the contributions
of all the charge elements. (i.e., by applying the superposition
principle.)
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Charge Density
If a total charge Q is uniformly distributed along a
line of length l ,the linear charge density  is defined by
Q
=
l
If Q is uniformly distributed on a surface of area A,
the surface charge density  is defined by

Q
A
If Q is uniformly distributed throughout a volume V,
the volume charge density  is defined by
Q

V
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How to Represent dq
lin e a r c h a rg e d e n s ity  ，
dq   dl
s u rfa c e c h a rg e d e n s ity  ， d q   d S
v o lu m e c h a rg e d e n s id ity  ， d q   d V
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Element Analysis
Method
dq
Q
  dl

dq  ds
 dV

Q
q0dq r
dF 
4 0 r 3

r
q0
+
P
q0dq r
3
4


r
0

F
The integral covers the whole system of charged body.
Symmetry: with both distributions of point charges and
continuous charge distributions, take advantage of any
symmetry in the system to simplify your calculations.
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Example
As shown in figure, Electric quantities Q
distribute uniformly on a fine bar of length
L .Find the electrostatic force acting on the
point charge q0 .
Q,L
b
+
q0
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q0 Q 1
1
f 
( 
)
4πε0 L b b  L
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Sum-up
– Physical model
Point charge
– Coulomb law
– Calculate the electrostatic force
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