PROFESSOR: Surface currents induced in a ground plane
by an overhead conductor illustrate
the method of images.
Also illustrated is the superposition
of fields due to line currents to satisfy boundary conditions.
Now the situation is magnetoquasistatic, MQS.
Here's the metal cylinder mounted over the metal ground
plane.
The cylinder is driven by a current source at one end,
and is shorter to the ground plane at the other end.
The ground plane consists of an aluminum sheet
having a thickness of about 1 millimeter.
It's resting on a plywood base.
Our magnetic field is the same as that due to a line
current here, just below the center of the conductor,
and its image here, below the ground plane.
When we drive a current from a three kilohertz source
through the circular conductor, the actual currents
are in the metal conductor walls, distributed in just such
a way that there is no magnetic flux normal to every point
on a given conductor surface.
Similarly, these currents are returned
in the ground plane in just such a way
that there is essentially no magnetic flux
density normal to the ground plane either.
We can measure the magnetic field using this induction
coil.
The induced voltage is related through Faraday's law
to the time rate of change of the linked magnetic flux.
With the coil oriented this way, the vertical field component
is recorded.
When oriented this way, the horizontal field component
is measured.
Here at the center line, the tangential field
is horizontal, just because of symmetry.
Let's see if the flux density normal to the conducting
sheet does tend to be zero off the center line.
Here to the side, the normal flux density
appears to remain small compared to that tangential.
So the current is returned in the sheet
with just that distribution required to make
the normal flux density small.
As the sensing coil has moved out from under the conductor,
the tangential flux density decreases.
Because there is little normal flux density just
above the sheet, there is little of either
of the components of magnetic field below the sheet.
So what we see is the distribution
of surface current density returning in the sheet.
At high frequency, the current distributes itself
in the sheet in just such a way as to make the normal flux
density near zero.
Our experiments have shown that the perpendicular
field at the surface of the ground plane
is much smaller than the tangential field.
This is true because the frequency of 3 kilohertz
is high enough that the ground plane behaves
as a perfect conductor.
Let's see what happens if we lower the frequency.
If we reduce the frequency by 10 to 300 hertz,
the induced voltage decreases by 10.
That's just because of Faraday's law.
So let's compensate by turning up the scope gain by 10.
At this lower frequency, we see that the ratio
of normal component to tangential component
is larger than the 3 kilohertz.
At 300 hertz, here's the tangential component.
And here's the normal component.
At 3 kilohertz, here's the normal component.
And here's the tangential component.
At 3 kilohertz, the ground plane is thick enough
to act as a perfect conductor, giving
the tangential field predicted, using the fields of a line
current and its image.