Where:
Jx 
= 
Current Density (amps/m^{2}) 
J_{o} 
= 
Current Density at Surface (amps/m^{2)} 
e 
= 
Base Natural Log = 2.71828 
x 
= 
Distance Below Surface 
d 
= 
Standard Depth of Penetration 

Eddy currents induced in a material by a changing magnetic field from a coil concentrate near the surface of the material adjacent to the coil. The strength of the eddy currents decays with depth because eddy currents produce their own magnetic field that opposes the primary field. Therefore, the eddy currents that form first at the surface, weaken the magnetic field that induces the next deeper layer of eddy currents. This weakening of the magnetic field and the resulting eddy currents continues with increasing depth into the material. The decay of the eddy current density is exponential and is described by the equation to the right.
This equation shows that the eddy current density (J) at some depth (x) is a function of the density at the surface (J_{o}) and decays exponentially with increasing distance from the surface and decreasing standard depth of penetration. The standard depth of penetration term takes into account the magnetic permeability and electrical resistivity of the material, and the drive frequency of the test coil. An increase in these three values will result in a decrease in the standard depth of penetration and this will result in weaker eddy currents at the given depth.
In practice the actual eddy current density is rarely calculated but it is important to know how the density or strength relates to the standard depth of penetration. From the table below it can be seen that at a distance below the surface of one standard depth of penetration, the strength of the eddy currents will be 37% the strength of those at the surface. At a distance equal to three standard depths of penetration the strength of the eddy currents are only 5% the strength as those at the surface. As the distance below the surface increase, the strength of the eddy currents continue to decay exponentially.
Number of Standard Depth of Penetrations 
Relative Strength of the Eddy Currents at the Indicated Depth 
0

e^{0}=100%

d

e^{1}=37%

2d

e^{2}=14%

3d

e^{3}=5%

4d

e^{4}=2%

5d

e^{5}=0.7%
