When electrical resistivity (mohmscm) and relative permeability are known.
or
Where:
d 
= 
Standard Depth of Penetration (mm or inch) 
r 
= 
Electrical Resistivity (mohmcm) 
f 
= 
Test Frequency (Hz) 
m_{r} 
= 
Relative Magnetic Permeability (dimensionless) 

Eddy currents are more concentrated at the surface and decrease in intensity with distance below the surface of the metal. This effect is known as the "skin effect." 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). Although eddy currents penetrate deeper than one standard depth of penetration, they decrease rapidly with depth. At two standard depths of penetration (2d), the 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.
The depth of penetration is dependent of test drive frequency, the test material's conductivity and magnetic permeability. The depth of penetration decreases with increasing frequency, conductivity and permeability. It is important to know the standard depth of penetration because for some testing (like flaw detection) the inspection should be conducted at a frequency that places the depth of any likely flaws at 1d or less where eddy currents are strong. When making conductivity tests, the sample should be at least 3d thick so that changes in the thickness of the sample do not affect the measurements. When electrical conductivity in % IACS and permeability in H/mm are known, the standard depth of penetration can be calculated using the equation to the right.
Working with this Equation
In many places, magnetic permeability is presented as relative permeability. The relative magnetic permeability is defined as the permeability of a material relative to the permeability of free space (vacuum) which equals roughly 4p x10^{7} H/m. Since the magnetic permeability of nonmagnetic materials is close to that of free space, the value of one is used as the relative permeability.
Example 1
What is the standard depth of penetration when performing an eddy current inspection on a piece of 304 Corrosion Resistant Steel? The material has a relative permeability of 1.05 and a conductivity of 2.5% IACS. The frequency used to drive the eddy current probe is 50 kHz.
Since conductivity in %IACS is known, it must be converted to resistivity in mohmscm.
Then plugin the values and solve the equation.
Example 2
Determine the frequency needed to achieve a depth of penetration of 2mm in 7075T76 aluminum plate.
Aluminum is nonmagnetic so its relative permeability is one. With a measurement or from the Electrical Conductivity and Resistivity Property Tables, determine the resistivity value for the material. The value given in the table is 4.48x10^{8} ohmmeters, which is 4.48 mohmcm.
The depth of penetration equation must be rearranged to solve for frequency (f).
Plug in the known values and solve.