Recommended problems: FGT 26.62, 22.65, 22.69
Recommended reading for Lecture 14: Chap. 27 FGT
Dielectric materials ()
In order to treat the effect of materials' structure on the
electrostatic response of materials, we need to know
two properties of the materials. The first and
most important is the dielectric constant
and the second is the threshold field at which the material
``fails'' and begins to conduct, Ec. For insulators Ec>0while for conductors Ec=0. Insulators which are used
in capacitors and other applications requiring electrical
insulation are often called dielectrics. In practice, there
is a simple way to include the effect of dielectric properties of
materials on electrostatic response we simply make the
all of our electrostatic formula. For example
Coulomb's law is now,
Example: 26-7 of FGT
A parallel plate capacitor has area A=20cm2 and plate separation d=4mm.
Find its capacitance if the gap is filled with: a) Air ()
b) Teflon (
). Now consider the following experiment.
Use a battery to apply a voltage of 24V to the capacitor with an air gap. Now
disconnect the battery. Then insert the Teflon dielectric into the
gap. Find the stored potential energy before and after insertion of the Teflon.
Where has the energy gone?
c) The amount of charge on the plates of the capacitor is
Q = Ca Va.
This capacitor with the air gap thus stores energy Q2/2Ca.
When the battery is disconnected and the Teflon inserted, the charge
remains the same, but the voltage is now given by, Q=Cb Vb.
This capacitor stores energy Q2/2Cb. Since Cb>Ca the
stored potential energy decreases when the teflon
replaces the air gap. In practice, this means that the
dielectric material is ``sucked into'' the gap between the plates.
Negative external work is required. This means that the capacitor
itself does positive work.
Example: 26.8 of FGT
A parallel plate capacitor is disconnected
and carries a charge of q=1nC. It has a gap
which is d=4mm wide and contains
a teflon sheet which is 2mm=d/2 thick. What is the
electric field between the gap a) inside the
teflon. b) inside the air within the gap. Now
calculate the potential drop across the
air gap and the teflon. Finally, find the capacitance of the
a) The charge on each plate is q. The
electric field is still
b) Inside the teflon, the electric
field has magnitude
c) The potential drop across the air
potential drop across the teflon is
d) The capacitance of the system is
found from the definition q = CV.
Dielectric materials - It's the dipoles stupid!
Dielectric materials can be considered to be composed of dipoles, either permanent dipoles or induced dipoles. We shall discuss the case of two plates which carry equal and opposite charges Q. These plates have a dielectric material between them and we want to understand the behavior of the dipoles in this material in the presence of the electric field produced by the plates of charge.
The dipoles in the dielectric material align
with the electric field produced by the plates.
This screens the charge on each of the plates of the
capacitor. If Q is the true magnitude of charge
on each plate, we introduce Qi to be the
screening charge of the dipoles produced by
the electric field. The charge
that remains to generate the electric field
between the plates is Q-Qi. The
electric field between the plates is then,
More on dielectrics
1. Polar (those with permanent dipole
moments) dielectrics should line up more
readily as the temperature is reduced. In
many cases they obey
K = 1 + c/T, where cis a constant. Polar dielectrics can
sometimes show ferroelectricity. This
is like magnetism but the spins are
replaced by electric dipoles. In that
case there is a critical temperature
at which the dipoles spontaneously align.
2. The polarization of solids with permanent
dipoles can sometimes be changed by applied stress.
This can lead to a detectable electrical signal.
Materials with this property are called
piezoelectrics. Sometimes this property is
used in reverse, ie. an electrical signal applied
to piezo-electric can lead to a change in the
shape of the material (e.g. quartz, BaTiO3...).
This can be used
to provide very sensitive control of movement
and devices of this sort are called piezo-actuators.
Piezo actuators are very important in nano-engineeing.