PROFESSOR: An artificial dielectric
made from an array of conducting spheres demonstrates
how polarization of media gives rise
to the properties of a linear dielectric.
When the region between electrodes
is filled with a dielectric material,
the capacitance is increased.
This increase is due to polarization
of molecules of the material.
We form an appreciation for how this happens
by replacing the molecules with macroscopic spheres suspended
in air.
This artificial dielectric is composed
of what we can think of as molecules
that are actually essentially perfectly conducting spheres.
Each has radius R, and they're in a cubic array
with spacing S.
Application of voltage to the electrodes
results in the spheres acquiring positive and negative surface
charges on their poles.
In addition to the uniform field due to the applied voltage,
the field outside the spheres also includes the dipole fields
from the array of spheres.
The spheres, like the molecules of a material,
are polarized by an applied field.
The artificial dielectric is composed
of an array of ping-pong balls with conducting coatings.
We're going to measure the effective connectivity
by measuring the change in capacitance
as the array is placed between the plates of this plane
parallel plate capacitor.
The cage is grounded for shielding
and to keep us from touching the bottom electrode.
It's driven to 400 volts RMS at 250 Hertz
by this transformer, which is itself driven
by an oscillator and amplifier.
Here's the top electrode.
To avoid fringing effects, only the charge
induced on this central section will
be measured when we measure the capacitance.
Here's how the dielectric is inserted between the plates.
Before balancing the bridge, we remove
the array of ping-pong balls.
We've already set the driving voltage to about 400 volts RMS.
Here are the resisters in the two upper legs of the bridge.
They shunt the scope differentiable amplifier.
So the scope signal is the voltage V0.
The balancing capacitance, C2, is here.
This is the capacitor C1, which is there for fine tuning.
We can balance the signal with this capacitor.
So we tune C2 to know the bridge voltage and C1
to fine tune the null.
We're ready to insert the artificial dielectric.
As the array is inserted, the bridge
becomes unbalanced, indicating that the capacitance has
changed.
We measure a voltage of 135 millivolts peak.
Remember, what we predicted was a change
of 133 millivolts peak.
The agreement is perhaps better than we should expect.
Has the capacitance actually been
increased by the insertion of the spheres?
Let's try the experiment again.
We can see that it has by looking at the balancing
capacitor.
Here, the array is out and we balance the capacitor.
Now, we insert the array.
Note the position of the tuning capacitor plates.
If the capacitance has been increased,
to balance the bridge, the knob must
be turned so that they have greater area of overlap.
The balance in capacitance is increased.
So the artificial dielectric does
increase the capacitance of the plane parallel plate capacitor.