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PROFESSOR: The force on a liquid dielectric results
in a visual evidence for molecular polarization.
A pair of capacitor plates are going
to be dipped into a dielectric fluid.
With the application of a voltage,
the fluid is drawn upward, into the region between.
To be sure that the displacement is
due to the polarization induced in the fluid by the field,
care must be taken to avoid having
an electrically induced force density associated
with unpaired or free charges.
Such a force density is the result
of the force transmitted to the liquid
by unpaired charges, each subject to an electric force.
Each transfer is a force equal to its charge
times the average electric field.
This force is transmitted to the liquid
in which it is entrained.
The positive charge is transferring
a force in the direction of the electric field.
The negative charge is transmitting a force
in the opposite direction.
For there to be a net force density
due to these unpaired charges, there
must be a net unpaired charge density, rho sub u.
In our experiment, the applied voltage is AC.
The source has a sufficiently high frequency
that the unpaired charge density throughout the liquid
is negligible.
The polarization force density is
proportional to the square of the applied field.
Thus, the AC field produces a force density
that has time average and second harmonic parts.
The frequency is high enough and the liquid viscous enough
that the fluid only responds to the time average force.
It responds to the root mean square of the applied field.
Even with essentially no net charge density anywhere
in the liquid, there is a force density
due to molecular dipoles induced by the applied field.
The dipole can be modeled as a pair of equal charges
of opposite sign.
In a non-uniform electric field, the force
on one of these charges differs from that on the other.
Thus, in a non-uniform electric field,
there is a net force on the dipole.
When there's a distribution of such dipoles in a material,
this force is transmitted to the surrounding material.
Rather than having particles carrying a net charge transfer
their force to the material, it is the dipoles
which transfer their force.
The result is a polarization force density
that is proportional to the gradient and E.
With P, the polarization density,
it is P dot del E. In our experiment,
the non-uniform electric field experienced by the liquid
is the fringing field.
Thus, dipoles in the fringing field
are attracted into the field region.
For example, this one is attracted upward.
The vertical fields on each charge are of opposite sign.
But then so are the charges.
So the net force is up.
Here's the experiment.
The plates are made from tin oxide coated glass
so that they are conducting and yet transparent.
So we'll be able to see the liquid through the front plate.
The plates used to apply the field
are closer together at the left, so the field
will be more intense there.
They're set in a shallow dish of corn oil, which is then placed
in a nitrogen pressure chamber.
25-kilovolt AC is applied.
Polarization forces push the fluid
upward between the plates.
The field intensity is greatest at the left, about
100 kilovolts per centimeter.
The polarization force density that pushes the liquid upward
between the plates is also responsible
for the net upward force on this dielectric slab.
This upward electrical force on the slab
can be derived using the principle of energy
conservation.
Here, we've divided the force by the area ca of the top slab.
The force per unit area is 1/2 of the square
of the electric field intensity between the plates multiplied
by the difference in permativity between the slab
and free space.
In our experiment, this force per unit area
is equal to the gravitational force acting
on a column of a liquid having the height c, mass density
rho, where g is the gravitational constant.
Also, in our experiment, the distance between plates
is a function of radial distance.
The spacing a is equal to the angle alpha times the distance
r from the imaginary line where the plates would join.
Thus, the height of rise is inversely
proportional to the square of the radial distance.
The height of rise is inversely proportional to the square
of the radial distance.
This experiment teaches an important lesson.
The force density associated with polarization
is not equal to the polarization charge
density times the electric field intensity.
In our experiment, this is particularly evident.
Because the permittivity is uniform throughout the liquid
volume, the polarization charge density
is 0 throughout the volume of the liquid.
The only place where there could be a polarization charge giving
rise to a vertical force density is at the gas-liquid interface.
But the field is tangential to the gas-liquid interface.
And so the surface polarization charge density is 0 there.
So rho sub p is 0 throughout the liquid, even at the interface.
And it's clear that the force density rho sub pE cannot be
the force density that accounts for what we've seen.
The rise of the liquid between the plates
is due to the force on the dipoles, a force that
can exist even where there is no net unpaired charge, a force
that is proportional to the dipole polarization density
P and the gradient of E.