Transcript Equipotential Lines

-Atomic View of Dielectrics
-Electric Dipole in an Electric Field
-Partially Filled Capacitors
AP Physics C
Mrs. Coyle
Atomic View of Dielectrics: The molecules of
the dielectric are modeled as dipoles
External E-Field
No External E-Field
Random orientation of molecules
Partial Alignment of Molecules
Force Acting by a Uniform External
Field on the Dipole




Note: E is not the field
produced by the dipole
The force acting on each
charge is
F = Eq
The net force on the dipole is
zero
The forces produce a net

torque on the dipole
p=2aq
2a
= 2Fa sin  = pE sin 
 =pxE
Electric Dipole Moment, p

The electric dipole
moment (p) is a vector
directed along the line
joining the charges from –
q to +q ,

A dipole has two equal but
opposite sign charges

Assume the distance
between the charges is 2a
p=2aq
Work Required to Rotate the Dipole will result
in an Increase in the Potential Energy of the
Dipole-External Field System
dW   d
f
W  U f  U i    d
i
U f -U i = pE(cos i - cos  f )
Assume i  90o , U i  0
 = pE sin 
U f -Ui = - pE cos 
U= - p · E
An external field can polarize the dielectric
whether the molecules are polar or nonpolar

The charged edges of the
dielectric act as a second
pair of plates producing
an induced electric field
in the direction opposite
the original electric field
The degree of alignment of the molecules with the
field depends on temperature and the magnitude of
the field.
Generally:

the alignment increases with increasing field
strength

the alignment increases with decreasing
temperature
Non Polar Dielectrics

The electric field produces some charge
separation

This produces an induced dipole moment

The effect is then the same as if the
molecules were polar
Induced Charge and Field



The electric field due to the
plates is directed to the right
and it polarizes the dielectric
The net effect on the
dielectric is an induced
surface charge that results
in an induced electric field
If the dielectric were
replaced with a conductor,
the net field between the
plates would be zero
Geometry of Some Capacitors
Example – Partially Filled Capacitor
o A
Co 
, Capacitance without dielectric
d
+Q
d
3
d
-Q
A
What is the capacitance in terms of Co?
Hint: Two capacitors in series.
Ans:
 3 
C 
 C0
 2  1 