INSTRUCTOR: Skin effect describes
the tendency for high frequency currents
to be near surfaces of conductors.
Here's the experiment.
The section were essentially one dimensional magnetic diffusion
occurs is here.
By making the conductor long in the y direction,
we provide enough length for the current distribution
to become primarily dependent on x over the middle cross
section.
To avoid an influence of the magnetic core on the field
distribution here at the center, we've placed it to one end.
This transverse probe can be inserted
so that it samples the vertical magnetic field intensity
over the span of the conductor.
The field component normal to the flat phase as measured.
The slit is little more than large enough for the probe.
The top trace is the current in the primary of the transformer,
the driving current.
The bottom trace is the probe signal, the magnetic flux
density.
As we pull the probe out, we see the field distribution with x.
The frequency is 60 hertz.
Here, we're at 3 centimeters, half the slab thickness.
It appears that the decay is somewhat more
rapid than linear.
So it looks like the skin depth at 60 hertz
is less than the thickness of the aluminum.
Here's a prediction of the field decay,
with distance from the left edge of the conductor.
This curve is for 60 hertz.
In going from 0 to 1 centimeter here on the 60 hertz curve,
we should see the field decay by 40%.
What we measure decays to about 50% of its original value.
Remember, the skin depth is inversely
proportional to the square root of the frequency.
So if we increase the frequency to 240 hertz,
4 times the frequency, the skin depth is 1/2 as much,
and the decay should be more rapid.
This is the decay at 60 hertz.
Here, we're at 1 centimeter.
Here, we're at 3 centimeters.
Now we raise the frequency to 240 hertz.
This is the decay at 240 hertz--
1 centimeter, 3 centimeters.
The decay at 1 centimeter and 240 hertz plots like this.
These are additional data points.
Here's the major decay at 240 hertz, here at 60 hertz.
The discrepancy is probably due to the finite length
of the aluminum in the direction of current circulation.
Our one dimensional theory strictly
applies only where the currents have had sufficient development
length.
When the skin depth is short compared to the conductor
thickness, the current distribution
takes the form of a wave.
We've been observing the decay of this wave.
There's also a phase shift with x,
caused by the propagation of this diffusion wave
under the conductor.
By looking at the probe's signal on an oscilloscope,
we can see this phase shift as the probe is withdrawn.
The top trace is the excitation current, the bottom one
the probe current.
Sync to the excitation current.
The frequency is 240 hertz.
So as the probe is withdrawn, the field decays rapidly.
To see the phase shift associated
with the propagation, let's put the probe signal
on top of the driving signal.
Watch the position of a peek in the probe signal,
relative to that of the driving current,
as the probe is withdrawn.
As the probe is pulled into the conductor,
it measures a field that is increasingly delayed in phase.
The magnitude of the magnetic diffusion wave
decays exponentially into the conductor,
with a decay length that is the skin depth.
The phase shift shows that the wave has phases that
propagate into the conductor.