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II. Electric Field
[Physics 2702]
Dr. Bill Pezzaglia
Updated 2015Feb09
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II. Electric Field
A. Faraday Lines of Force
B. Electric Field
C. Gauss’ Law (very lightly)
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A. Lines of Force
1) Action at a Distance
2) Faraday’s Lines of Force
3) Principle of “Locality”
1. “Action at a Distance”
• Newton proposes gravity must act
instantaneously, regardless of
distance (else angular momentum
not conserved).
• “actio in distans” (action at a
distance), no mechanism
proposed to transmit gravity
"...that one body may act upon another at a
distance through a vacuum without the
mediation of anything else, by and through
which their action and force may be conveyed
from one to another, is to me so great an
absurdity that, I believe no man, who has in
philosophic matters a competent faculty of
thinking, could ever fall into it." -Newton
Sir Isaac Newton
(1643-1727)
How does moon “know”
the earth is there to fall
towards it?
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2a. Sir Humphry Davy 1778 - 1829
•1807 Electrolysis, used to
separate salts. Founds
science of electrochemistry.
•His greatest discovery was
Michael Faraday.
•1813-15 takes Faraday with
him on grand tour visiting
Ampere and Volta.
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2b. Michael Faraday 1791 - 1867
•1821 First proposes ideas
of “Lines of Force”
• Example: iron filings over a
magnetic show field lines
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2c. Electric Lines of Force
•Electric charges create “electric field lines”
•Field lines start on + charges, end on –
•A plus charge will tend to move along these lines
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2d. Other Properties
•Field Lines can’t cross (else physics would not be
deterministic, ambiguity which way to go)
•Density of lines is proportional to the “strength” of
the force
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3. Principle of Locality
I cannot conceive curved lines of force without
the conditions of a physical existence in that
intermediate space. (Michael Faraday)
• Argues that the field lines have
independent reality
•Force fields exist as distortions in the
“aether” of space
•Alternative to “action at a distance”,
charges Locally interact with force lines
•Ideas rejected by others. He can’t put
them into mathematical form.
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B. Electric Field
1) Definition of Field
2) Sources of Field
3) Electrodynamics
1a. James Maxwell (1831-1879)
•1855 essay On Faraday's
Lines of Force, suggests
lines are like an imaginary
incompressible fluid (obeying
hydrodynamic equations)
•1861 paper On Physical
Lines of Force, proposes
“real” physical model of
vortices for magnetic field
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1b. Definition of Field
• Definition: force per unit test charge
(i.e. don’t want test charge to affect field)


F
E  Lim 
q 0 q
 
q
+
• Units of Newton/Coul (or Volts/meter)
• So force on charge is: F=qE
F
E
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1c. Analogy to Gravity
• Gravitational Force Field:
force per unit test mass

F

g  Lim  
m 0 m
 
• i.e. its an “acceleration of gravity” field
• Mass is the “charge” of gravity: F = mg
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2. Sources of E Field
(a) Point Charge Source (monopoles
(b) Dipoles
(c) Field of Dipole (incomplete)
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2.a Monopole Sources
•
A positive charge is a “source” of
electric field. Field radiates outward
from a point source
•
A negative charge is a “sink” of
electric field. Field radiates inward
•
Field strength: E=kQ/r2
2.b Dipole Sources
• An “electric dipole” is a “stick”
of length “L” with + charge on
one end and equal – charge on
other.
• Dipole moment: p=QL
• The vector “p” points along axis
from – to + charge
• Units (SI) is Cm
• Standard in Chemistry is the
Debye: 1D=3.33564x10-30 Cm
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2.c Field of Dipole
• Derivation will be done on board.
Basically you use “superposition” of
fields of two monopoles.
• Field of dipole along its axis drops off like the
cube of the distance!
kQ
kQ
p
E( z) 

 2k 3
2
2
1
1
z
z  2 L  z  2 L 
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3. Electrodynamics
a) Force on monopole
b) Torques on Dipoles
c) Van der Waal Forces
B.3.a: Force on a Charge (monopole)
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

F  qE
• Force on positive charge
is in direction of field
• Force on negative charge
is opposite direction of
field
q
+
F
E
F
q
E
B.3.a Point Charge Electrodynamics
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•
Force between
monopoles is hence
Coulomb’s law


Q
F  q E  qk 2 rˆ
R
•
Force between dipole “p”
and monopole “q”
decreases cubically:
2kpq
F qE 3
z
B.3.b Torque on Dipole
•
An electric dipole will
want to twist and line up
with the electric field
•
Torque on a dipole in an
electric field is:
•
Recall dipole moment
p=qL
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  
  p E
  pE cos
B.3.c Gradient Forces on Dipole
(Van-der-Waal’s forces between molecules,
e.g. Hydrogen Bonding in water)
•
If field is not constant (has a “gradient”)
then there will be a force on a dipole
E
F  qE ( x  L / 2)  qE ( x  L / 2)  p
x
•
Forces between dipoles (along a line)
can be shown to be:
p1 p2
F  6k 4
z
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C. Gauss’s Law (Lightly)
Ignoring the mathematics,
Gauss’s law (1813) has the
following results:
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Spherical Symmetry:
Electric field of a spherical ball of charge the
same as a point charge:
E (r ) 
Q
40 r
2
Where “r” is measured from
center of ball.
Note that the result is INDEPENDENT of radius of ball!
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Field is zero inside a conductor
Consider a solid conducting sphere.
Electric charge will be pushed to surface
Electric field inside conductor is zero
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Electric Field inside a
conductor is ZERO
Example of
Faraday
Cage: An
external
electrical
field
causes the
charges to
rearrange
which
cancels the
field inside.
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Cylindrical Symmetry:
Electric field of a charge “Q” spread out on a
long cylinder (length “L”) is:spherical ball of
charge the same as a point charge:
E (r ) 
Q
20 Lr
e.g. a line charge, or charge on a wire
Note that the result is INDEPENDENT of radius of
cylinder.
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c. Plane Geometry
Consider a large flat sheet (area “A”) with charge “Q”
spread out uniformly. The electric field outside is
constant [Laplace 1813].

Q
E 
A 2 0 A
With the application of superposition principle, you can
show that parallel plates of opposite charge have a
constant field between (and zero outside).

Q
E 
A 0 A
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References
•http://maxwell.byu.edu/~spencerr/phys442/node4.html
•http://en.wikipedia.org/wiki/Timeline_of_Fundamental_Physics_Discoveries
•http://www.oneillselectronicmuseum.com/index.html