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Electric Fields and Matter
Read: Chapter 15
The Net Charge of an object is the sum of all the charges of its constituent particles.
The statement of Conservation of Charge says that the net charge of a system plus its surroundings cannot change.
Question: If a Helium atom is struck by a photon and an electron is ejected,
γ + He −→ He+ + e− ,
is charge conservation violated? Why or why not?
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Electric Fields and Matter
An insulator is a material in which all charges are bound and therefore free to move only very short distances (on the scale
of an atomic diameter).
A conductor is a material in which some of the charged particles are free to move throughout the material, but are still
bound within the material as a whole.
An insulator may become charged through transfer of charged particles, either ions or electrons — protons are not transferred.
Since charges in insulators are tightly bound, only surface charges can be transferred.
Question: Why are protons not transferred?
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Electric Fields and Matter
Polarization
Charged objects are attracted or repelled by other charged objects, but they are also attracted to electrically neutral objects.
This is possible because of a process known as polarization.
The polarization of an electrically neutral object describes the separation of the positive and negative centers of charge due
to the influence of an external electric field.
~ ext = 0
E
~ ext = E x̂
E
−
+
x
s
Note that a polarized neutral atom becomes an induced dipole with dipole moment p
~ = Z~s where Z is the number of protons.
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Electric Fields and Matter
Polarization
The polarizability α for materials is an experimentally determined quantity that relates the polarization of the material to
the applied external field:
~ ext .
p~ = αE
Now we turn our attention to describing the process of polarization mathematically by investigating the effect of a point
charge on a neutral atom.
q1
~1
E
+
r
Figure 1: The instantaneous moment before polarization
s
q1
~1
E
+
-
q2
q2
~2
E
r
Figure 2: The instantaneous moment after polarization
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+
Electric Fields and Matter
Polarization
Question: Will polarization ever result in a neutral object being repelled by a charged object? Why or why not?
Intervening matter does not “block” electric fields, but does have an effect on the strength of the field through polarization
and the superposition principle.
~Q
E
~ induced
E
+
-
+
-
+
-
+
-
+
-
+
+
-
Q
+
-
+
-
+
-
The presence of charge Q to the right polarizes the neutral insulator to the left, leading to an induced electric field. So,
~ =E
~Q + E
~ induced .
according to the superposition principle, the field to the left of the material is given by E
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Electric Fields and Matter
Polarization and Conductors
Consider an ionic solution such as Sodium Chloride, in which the solution contains
mobile Na+ and Cl− ions. In the absence of an external field, the electric effects of
the ions in the solution cancels on a macroscopic scale and motion of the ions in the
solution is primarily thermal .
-
-
+
+
-
+
+
+
-
~ ext is applied, the ions begin to polarize, moving
When an external electric field E
~ ind is
toward either side of the container. As they do so, an induced electric field E
generated inside the solution that opposes the applied field.
+
-
-
+
~ ext E
+
-
+
+
-
~ ind
E
+
-
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+
Electric Fields and Matter
Polarization and Conductors
This process proceeds until the net electric field inside the solution drops to 0 —
~ ind | = |E
~ ext |. At this point, the charges in the solution no longer experience any
|E
electric force, and the system is said to be in equilibrium.
+
+
+
+
~ ext
E
-
+
~ ind
E
+
Charges in a conductor under the influence of an external field quickly reach a constant velocity known as their drift velocity,
~ net ,
~vdrif t = uE
~ net = E
~ ext + E
~ ind . At equilibrium,
where u is an experimentally determined constant of the conductor called mobility and E
~vdrif t = 0. (Why?)
~ net /dt,
Question: Consider the polarization process just described. Without doing any calculation, determine the sign of dE
the rate of change of the net electric field with time.
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Electric Fields and Matter
Polarization and Conductors
Figure 3: metal lattice model
A simple model of a metal consists of a regular lattice of atoms (green balls) containing free electrons (black balls) that are
~ = 0 in equilibrium and the
not bound to any particular lattice site, commonly called the “electron sea.” Inside a metal, E
electrons may be treated as an ideal gas.
Question: Why may we ignore the repulsion between the free electrons in a metal?
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Electric Fields and Matter
Polarization and Conductors
Derivation of electron mobility u in a metal.
Since we assume a finite time between collisions for this calculation, we express the momentum principle as ∆~
p/∆t = F~net .
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Electric Fields and Matter
Polarization and Conductors
Polarization in metal can be visualized as a very small shift in the “electron sea,”
leading to an excess of negative charge at one end of the sample and an excess of
positive charge at the other.
-
-
+
+
+
+
A simplified diagram of a conductor neglects the neutral interior details, concentrating
only on the the charges at the surface.
+
+
+
+
+
+
+
+
+
-
+
~ ext
E
+
+
+
+
+
+
+
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+
+
+
+
+
+
-
-
+
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Electric Fields and Matter
Polarization and Conductors
+
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+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
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+
+
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+
In the case of a charged conductor, all the excess charge is found on the surface. The excess charge is not necessarily evenly
distributed.
~ = 0 still true inside of a charged
Question: Why is all the excess charge located on the surface of a charged conductor? Is E
conductor?
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Electric Fields and Matter
Polarization and Conductors
Example: Ball and Wire, from pg. 604 of text.
r
R
L
−Q
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Electric Fields and Matter
Additional Concepts
Charged objects can be discharged by contact and grounding.
A water molecule is a permanent dipole, allowing it to bind to many things. High humidity causes a thin film of water to
collect on surfaces — free ions in this film neutralize excess charge. You’ve seen this effect in static electricity demonstrations.
The field concept is somtimes problematic. Consider a test charge +Q placed near a conducting sphere of charge −Q0 where
Q ∼ Q0 .
-
-
-
-
−Q0
-
-
-
+Q
-
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