PROFESSOR: The steady-state magnetic levitation
of current-carrying conductors over a ground plane
demonstrates magnetic forces due to conduction currents.
Here is the actual experiment with the pancake coil excited
by 60 Hertz current from this variac.
The current is measured with this clip-on ammeter
and indicated on the oscilloscope.
The ground plane is this aluminum sheet.
Its thickness is 1.27 centimeters.
The coil has a thickness of about 1 and 1/2 centimeters.
[COIL HUMMING]
A typical current in the coil is 20 to 30 amperes,
so it's made of large diameter wire to reduce its resistance.
The 250 turns are of number 10 aluminum wire.
Aluminum is chosen for its light weight.
Its density is 2.7 grams per cubic centimeter
so that for a given current and thus magnetic force,
the coil will rise higher than if made of copper.
Although copper is a better conductor
by a factor of about 1.6, its density
is about 3.3 times greater than aluminum.
The scope trace indicates the coil current.
Here again, is what happens as the current is raised.
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The force on the conductor results
in vibrations, which we hear as telltale evidence
that the current is being increased.
The force is proportional to the square of the 60 Hertz current.
These vibrations result from the 120 Hertz second harmonic
component of the force.
When the RMS current is large enough
that the Lorentz force can overcome the coil weight,
the coil lifts off the ground plane.
Increasing the current further results
in an increase in the levitation force at a given altitude,
so the coil rises to make the upwards magnetic force
equal to that of the coil weight.
Let's see if we can estimate how high the pancake coil will
rise for a given coil current.
We're limited in height by the maximum current
before we blow a fuse.
Focusing attention on a single turn of the circular coil
with radius a, with a much larger than the wire diameter,
we can approximately use our inductance formula
for a straight wire of length l if we
take l to just be the coil circumference 2 pi a.
We reconnect the pancake coil to the variac.
The clip-on ammeter measures the current
which is displayed on the oscilloscope.
We raise the current slowly and find the coil lifts off--
[COIL HUMMING]
--at about 15.5 amperes RMS.
What we predicted was 14.3 amperes RMS.
As we raise the current further, the coil height
above the ground plane increases.
Here, the coil center rises by 2.25 centimeters
at 20 amperes RMS.
We take all the data points by increasing the current further.
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The skin depth in aluminum at 60 Hertz is 1.1 centimeters.
At first, one may think that for the assumption of a perfectly
conducting ground plane to be accurate,
the frequency must be high enough
that the ground plane thickness is greater than the skin depth.
For our experiments thus far, the aluminum ground plane
thickness has been 1.27 centimeters.
This thickness is about a skin depth.
To demonstrate the dependence on ground plane thickness,
we can try a ground plane with half the thickness.
This plate has a thickness of 6.35 millimeters.
This is about half the skin depth.
Remember that with 1.27 centimeter thickness,
lift off occurred at 15.5 amperes.
With this half skin depth thick ground plane,
lift off occurs at 16.3 rather than 15.5 amperes RMS.
This current is only slightly higher
than with the 1.27 centimeter thick ground plane.
Even though the ground plane thickness is now
about half the skin depth, it still acts, essentially,
as a perfect conductor.
[COIL HUMMING]
With a one millimeter thick plane,
the coil does not lift up even at 30 amperes RMS.
[COIL HUMMING]
The ground plane is now so thin that most of the magnetic field
penetrates through the ground plane.
We just blew a fuse again, but this time because of an arc.
The enamel insulation on the wires
may not be enough to prevent arcing to the sheet.
We have just seen an example of this.
Let's try it again now with some gaffers tape for better
insulation on the bottom.
Here it is again, with a current of 30 to 40 amperes.
[COIL HUMMING]
The coil doesn't lift off, but the induced current
does make the ground plane very hot.
Our coil has the making of a burner for a stove.
Our thin sheet could be the bottom of a pan.
Our experiment has been turned upside down.
The protective border prevents spillage.
Let's turn the current up and let it heat for a while.
[COIL HUMMING]
It takes a while, but it does cook.
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The experiment demonstrates the magnetic induction
of current in conductors in both the resulting Lorenz
magnetic force of repulsion and the heating.
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