Download Lecture #12 09/23/05

Conductors shield charges
+Q
Charge q
Charge -q
Charge +q+Q
Reading Quizzes: Problems
Several people are having difficulties presenting good answers:
Why is always assumed in a question:
“The capacitance decreases” is not a good answer
The answer should be in your own words:
Taking a sentence from the book and switching the subject
and object is not acceptable.
Physical explanations are really what I am after.
A wrong answer that answers the question with your reasoning in
your own words is okay on a reading quiz!
What is a Dipole
-
+
A positive and negative charge separated by some distance
The dipole moment is the vector connecting the charges times
the positive charge.
Dipoles in an field
-
+
In a uniform field, the force on each end is equal but opposite;
no net force [as the charges are connected!]
In a nonuniform field, the force on each end is not equal but opposite;
So a net force
Dipoles in an field
-
In a uniform field, the force on
each end is equal but opposite;
no net force [as the charges are
connected!]
+
There can be a torque!!
If the dipole moment makes an angle with the field, t=dFsinq,
where F is the force on 1 charge, and so t=dqEsinq=pEsinq
 
t  p E

What is the lever
Capacitors and Dielectrics
-dq
-Q
Q
dq
•Charges are aligned and/or induced in the diectric are from
microscopic dipoles
Dielectrics and Dipoles
When a dielectric is placed inside a capacitor, it is polarized
That is the dipole moments of polar molecules partially align
Nonpolar molecules have dipoles induced and partially aligned
Surface charges are created and fields generated (e. g. induced) which
lowers the field inside the capacitor, and hence reduces the potential
difference and raises the capacitance.
Note: being in the capacitor is not the key feature; rather its being
subjected to an external electric field, and having dipoles that can be
aligned or induced and aligned.
Dielectrics and Dipoles
Dielectrics exist because molecules have dipole moments and can
reorient to align with fields.
So the dielectric constant depends on:
1) The magnitude of the dipole moment {permanent or induced}
2) The ability of the dipoles to move
3) The density of the material
Gauss’ law with a dielectric
Original formulation:
~ ~
 o  E  dA  q
Flux is proportional to the charge
More General formulation:
~
~
D   0E
~ ~
 D  dA  q
The integral of the
electric displacement equals the charge
Types of Electric Dipoles
There are two types of dipoles:
Permanent dipoles (always a charge separation):
-
Water!
+
+
Temporary Dipoles: (Induced Dipoles):
+
-
CO2 and water
+
+
Coulomb’s Law with a dielectric
q1q2
Fe 
rˆ
2
4 0 r

F
q1q2
rˆ
2
40r
•Original formulation
•In the presence of a
dielectric
•This is more general than
just in a capacitor!
Coulomb’s Law with a dielectric
•Suppose I have a pair of charges:
-
-
+
+
+
+
-Q
+
+

q11q
q22
q
FFe 4 r 22rˆrˆ
400r
+
+
+Q
•Suppose I have a pair of charges in a dielectric now. The
intervening dipoles weaken the interaction of the two
charges.