Short Version : 20. Electric Charge, Force,

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Short Version 20. Electric Charge, Force,
Fields ?? 20. ??,?,??
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20.1. Electric Charge ??
2 kinds of charges ?. ???? ??? Total
charge algebraic sum of all charges. ???
?????? Like charges repel. Opposite charges
attract. ????,?????
elementary charge ????
All electrons have charge ?e. ?????? ?e ??.
All protons have charge e. ?????? e ??.
1st measured by Millikan on oil
drops. ?????????????
Theory (standard model) basic unit of charge
(carried by quark) 1/3 e. ?? (????) ??????
(?????) 1/3 e. Quark confinement ? no free
quark can be observed. ???? ? ???????? ?
Smallest observable charge is e. ? ?????????
e?
Conservation of charge total charge in a closed
region is always the same. ????????????????????
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Coulombs law (force between 2 point charges)
???? (???????)
q Coulomb C
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Conceptual Example 20.1. Gravity Electric
Force ?????
The electric force is far stronger than the
gravitational force, ????????, yet gravity is
much more obvious in everyday life. ??????????????
?? Why? ????

• Only 1 kind of gravitational charge ??????
  ?
• forces from different parts of a source tend to
  reinforce.
• ?????????????????
• 2 kinds of electric charges ?????
• forces from different parts of a neutral source
  tend to cancel out.
• ?????????????????????

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Making the Connection ???
Compare the magnitudes of the electric
gravitational forces between an electron a
proton. ??????????????????????
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Point Charges the Superposition
Principle????????
Extension of Coulombs law (point charges) to
charge distributions. ?????? (???) ??????
Superposition principle ??(??)??
Fnet
F23
F13
Independent of each other ????
Task Find net force on q3 . ??? q3 ????
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Example 20.2. Raindrops ??
Charged raindrops are responsible for
thunderstorms. ??????????? Two drops with equal
charge q are on the x-axis at x
?a. ??????????? x ?? x ?a ?? Find the electric
force on a 3rd drop with charge Q at any point on
the y-axis. ?????? y ?????,?? Q ???????????
y
F1
F2
Q
r
r
y
q
q
?
?
x
x1 ?a
x2 a
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20.3. The Electric Field ??
Electric field E at r Electric force on unit
point charge at r. ? r ???? E ? r ??????????
F electric force on point charge q. ??? q
?????
E F/q
E N / C V / m
V Volt
g F/m
Implicit assumption q doesnt disturb E. ?????q
???? E.
Rigorous definition ?????
Gravitational field ???
Electric field ??
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Force approach ???? Charges interact at a
distance (difficult to manage when many charges
are present). ??????? ( ????????? ) ? Fails
when charge distributions are not
known. ??????????? Field approach ????
Charge interacts only with field at its
position. ?????????????? No need to know how
field is generated. ????????????
Given E ?? E
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The Field of a Point Charge ?????
Field at r from point charge q ???? q ?? r ???
Field vectors for a negative point
charge. ?????????
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20.4. Fields of Charge Distributions ??????
(Discrete sources ????)
Superposition principle ? ????
(Point charges ???)
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The Electric Dipole ???
Electric dipole Two point charges of equal
magnitude but opposite charges separated by a
small distance. ??? ??????????????????
Examples ?? Polar molecules ????. Heart muscle
during contraction ????? ?
Electrocardiograph (EKG) ???? Radio TV
antennas ?????????.
H2O ?
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Example 20.5. Modeling a Molecule ??????
A molecule is modeled as a positive charge q at x
a, and a negative charge ?q at x ? a.
??????????? x a ???????? x ? a
????? Evaluate the electric field on the y-axis.
?? y-?????? Find an approximate expression
valid at large distances (y gtgt a). ????? (y gtgt a)
?????
y
E2
Q 1
E
E1
r
r
y
q
?q
?
?
x
x1 ?a
x2 a
(y gtgt a)
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Dipole ( ?q with separation d ) ?? ( ?q ?? d )
for r gtgt d 2a
Typical of neutral, non-spherical, charge
distributions ( d size ). ???????,???????? ( d
??)?
Dipole moment p q d. ???
d vector from ?q to q ? ?q ? q ???
y
On perpendicular bisector ???????
E2
Q 1
E
On dipole axis ?????
E1
r
r
y
q
(Prob ?? 51)
?q
?
?
x
x1 ?d/2
x2 d/2
p
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Continuous Charge Distributions ??????
All charge distributions are ultimately discrete
( mostly protons electrons ). ?????????????
(???????) ? Continuum approximation Good for
macroscopic bodies. ???????????? Volume charge
density ????? ? C/m3 Surface charge
density ????? ? C/m2 Line charge density
????? ? C/m
????
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Example 20.6. Charged Ring ???
A ring of radius a carries a uniformly
distributed charge Q. ????? a ?????????? Q. Find
E at any point on the axis of the ring.
????????? E ?
By symmetry, E has only axial (x-)
component. ?????? E ?? x-????
On axis of uniformly charged ring ?????????
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Example 20.7. Power Line ???
A long electric power line running along the
x-axis carries a uniform charge density ?
C/m. ???x-????????????????? ? C/m. Find E
on the y-axis, assuming the wire to be infinitely
long. ??????,?y-???E?
By symmetry, E has only y- component. ?????? E ??
y-????
y
dEy
dE
dE
P
r
r
y
x
dq
x
dq
Perpendicular to an infinite wire ???????
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20.5. Matter in Electric Fields ??????
Point Charges in Electric Fields ???????
Newtons 2nd law ? ??????
(point charge in field E) (????? E ?)

• Trajectory determined by charge-to-mass ratio
  q/m.
• ????????? q/m ???

Constant E ? constant a. ?E ? ?a.
E.g., CRT, inkjet printer, . ??????,?????,.
Uniform field between charged plates
(capacitors). ??(???)??????
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Example 20.8. Electrostatic Analyzer ????(??)?
Two curved metal plates establish a field of
strength E E0 ( b/r ), where E0 b are
constants. ???????????????? E E0 ( b/r ) ??,??
E0 ? b ???? E points toward the center of
curvature, r is the distance to the center. E
??????,? r ???????? Find speed v with which a
proton entering vertically from below will leave
the device moving horizontally.
????????????,????????,?????????
Too fast, hits outer wall ??,???
For a uniform circular motion ??????
?
???
Too slow, hits inner wall ??,???
???
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Dipoles in Electric Fields ??????
????????
Uniform ?? E
Total force ???
Torque about center of dipole ????????
dipole moment ???
Work done by E to rotate dipole ???? E ???
t // tangent ??
Potential energy of dipole in E (?i ?/2) ??? E
????
( U 0 for p ? E )
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Non-uniform field ????
Total force ??
Example dipole-dipole interaction ? ??-????
F? gt F
c.f. Van der Waals interaction, long range
part. ?? ?????,?????
Force on ? end of B is stronger hence net force
is toward A ? B ??????????? A ?
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Application Microwave Cooking Liquid
Crystals?????????
Microwave oven ??? GHz EM field vibrates
(dipolar) H2O molecules in food ????????????(??)?
?? ? heats up ???.
Liquid Crystal Display ????? (LCD)
????
??
?????
dipolar molecules aligned but positions
irregular ???????????????
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Exploded view of a TN (Twisted Nematic) liquid
crystal cell showing the states in an OFF state
(left), and an ON state with voltage applied
(right) ??????????????????(??) ,??(????)??(??) ?
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Conductors, Insulators, Dielectrics??,???,????
Bulk matter consists of point charges e
p. ???????????
Conductors charges free to move ( ? electric
currents ), ?? ?????? (??? ) e.g., e
(metal), ion ( electrolytes ), eion (plasma).
? e(??) ,??(???) ,e??(??) Insulators
charges are bounded. ??? ???? Dielectrics
insulators with intrinsic / induced dipoles. ???
????????????
internal field from dipoles ??????
Induced dipole ????
Alignment of intrinsic dipoles. ???????