Depth
of Penetration & Current Density
Eddy
currents are closed loops of induced current circulating in planes
perpendicular to the magnetic flux. They normally travel parallel
to the coil's winding and flow is limited to the area of the inducing
magnetic field. Eddy currents concentrate near the surface adjacent
to an excitation coil and their strength decreases with distance
from the coil as shown in the image. Eddy current density decreases
exponentially with depth. This phenomenon is known as the skin
effect.
The skin effect arises when the eddy currents flowing in the test
object at any depth produce magnetic fields which oppose the primary
field, thus reducing the net magnetic flux and causing a decrease
in current flow as the depth increases. Alternatively, eddy currents
near the surface can be viewed as shielding the coil's magnetic
field, thereby weakening the magnetic field at greater depths
and reducing induced currents.
The depth that eddy currents penetrate into a material is affected
by the frequency of the excitation current and the electrical
conductivity and magnetic permeability of the specimen. The depth
of penetration decreases with increasing frequency and increasing
conductivity and magnetic permeability. The depth at which eddy
current density has decreased to 1/e, or about 37% of the surface
density, is called the standard depth of penetration (d).
The word 'standard' denotes plane wave electromagnetic field excitation
within the test sample (conditions which are rarely achieved in
practice). Although eddy currents penetrate deeper than one standard
depth of penetration, they decrease rapidly with depth. At two
standard depths of penetration (2d),
eddy current density has decreased to 1/e squared or 13.5% of
the surface density. At three depths (3d),
the eddy current density is down to only 5% of the surface density.
Since the sensitivity of an eddy current inspection depends on
the eddy current density at the defect location, it is important
to know the strength of the eddy currents at this location. When
attempting to locate flaws, a frequency is often selected which
places the expected flaw depth within one standard depth of penetration.
This helps to assure that the strength of the eddy currents will
be sufficient to produce a flaw indication. Alternately, when
using eddy currents to measure the electrical conductivity of
a material, the frequency is often set so that it produces three
standard depths of penetration within the material. This helps
to assure that the eddy currents will be so weak at the back side
of the material that changes in the material thickness will not
affect the eddy current measurements.
The applet below illustrates how eddy current density changes
in a semiinfinite
conductor. The applet can be used to calculate the
standard depth of penetration. The equation for this calculation
is:
Where: 

d = Standard Depth of Penetration (mm)
p = 3.14
f = Test Frequency (Hz)
m = Magnetic Permeability (H/mm)
s = Electrical Conductivity (% IACS) 
(Note: The applet has an input box for relative permeability since this is often the more readily available value. The applet multiplies the relative permeability of the material by the permeability of free space to get to H/mm units.)
The applet also indicates graphically the phase lag at one and two standard depths of penetration. Phase lag will be discussed on the following page.
