## Ohms Law

According to Ohms Law, the voltage is the product of current and resistance.

i.e., V = I x R

Where V = Voltage in volts, I = Current in Amps and R = Resistance in Ohms

## Phase Angle and Impedance

Phase angle is expressed as follows:

TanΦ = X_{L}/R

Where Φ = Phase Angle in degrees, X_{L} = Inductive Reactance in ohms and R = Resistance in ohms.

Impedance is defined as follows:

Where Z = Impedance in ohms, R = Resistance in ohms and X_{L} = Reactance in ohms.

## Magnetic Permeability and Relative Magnetic Permeability

Magnetic permeability is the ratio between magnetic flux density and magnetizing force.

i.e., μ =B/H

Where μ = Magnetic Permeability in Henries per meter (mu), B = Magnetic Flux Density in Tesla, H = Magnetizing Force in Amps/meter.

Relative magnetic permeability is expressed as follows:

μ _{r} = μ/ μ_{o}

Where μ_{r} = Relative magnetic permeability (mu) and μ_{o} = Magnetic permeability of free space (Henries per meter = 1.257 * 10^{-6}). μ_{r} = 1 for non-ferrous materials.

## Conductivity and Resistivity

Conductivity and resistivity is related as follows:

σ =1/ρ

Where σ = Conductivity (sigma) and ρ =Resistivity (rho). Conductivity can be quantified in Siemens per m (S/m) or in Aerospace NDT in % lACS (International Annealed Copper Standard). One Siemen is the inverse of an ohm. Another common unit used for conductivity measurement is Siemen per cm (S/cm).

## Resistance and Conductivity

Resistance can be defined as follows:

R = l/Aσ or R = ρl/A

Where R = the resistance of a uniform cross section conductor in ohms (Ω), l = the length of the conductor in the same linear units as the conductivity or resistivity is quantified, A=Cross Sectional area, σ = conductivity in S/m and ρ = Resistivity in Ωm.

## Standard Depth of Penetration

Standard depth of penetration is given as follows:

Where δ = standard depth of penetration in m; f = frequency (Hz); μ = Magnetic Permeability (Henries per meter); and σ = conductivity in S/m.

The influence of frequency and conductivity on standard depth of penetration is illustrated in Figure 1.

**Figure 1. **Influence of frequency and conductivity on standard depth of penetration.

## Current Density Change with Depth

The change in current density with depth is expressed as follows:

Where J_{x} = Current Density at distance x below the surface (amps/m^{2}); J_{0} = Current Density at the surface (amps/m^{2}); e = the base of the natural logarithm (Euler's number) = 2.71828; x = Distance below the surface; and δ = standard depth of penetration in meters.

## Depth of Penetration and Probe Size

Smith et al have introduced the idea of spatial frequency.

Where D = the effective diameter of the probe field in meters, limiting the depth of penetration to D/4. The probe effective diameter is considered to be infinite in the usual equation.

## Phase change with Depth

Phase change with depth is expressed as follows:

θ = 57.3x/δ

Where, θ = Phase lag (degrees); 57.3 = 1 radian expressed in degrees; x = Distance below the surface; and δ = standard depth of penetration.

The change in phase and current density with depth of penetration is depicted in Figure 2.

**Figure 2. **Phase and current density change with depth of penetration.

## Frequency

Frequency is expressed as follows:

Where f = frequency (Hz); x= material thickness in meters; μ = Magnetic Permeability (Henries per meter); and σ = conductivity in S/m.

Conductivity of some common non-ferrous metals is listed in Table 1:

**Table 1**. Conductivity of Some Common Non-Ferrous Metals

Types and/or Description |
Conductivity % lACS |
Mega Siemen per m (MSm-1) |

Aluminium |

Pure Aluminium (A1) |
65.86% |
38.20 |

Aluminium Alloy 1100-0 |
59.45% |
34.48 |

Aluminium Alloy 1100-H18 |
57.47% |
33.33 |

Aluminium Alloy 2024-0 |
50.71% |
29.41 |

Aluminium Alloy 2024-T4 |
30.25% |
17.55 |

Nickel and Alloys |

Nickel - (Pure) (Ni) |
25.00% |
14. 50 |

Nickel - (Wrought) |
18.00% |
10.44 |

Nickel - (Dura) 301 |
4.06% |
2.35 |

Monel 400 |
3.38% |
1.96 |

Monel K-500 |
2.83% |
1.64 |

Stainless Steels |

Stainless Steel Type 420 |
3.13% |
1.82 |

Stainless Steel Type 403, 410 & 416 |
3.02% |
1.75 |

St Steel Type 430, 430-F, 434 & & 436 |
2.87% |
1.66 |

Stainless Steel Type 405 & 409 |
2.83% |
1.64 |

Stainless Steel Type 442 |
2.69% |
1.56 |

Copper |

99.995% Min (Vacuum Cast Pure Copper) (Cu) |
102.00% |
59. 16 |

C10100 99.99% Min |
101.00% |
58.58 |

C10200 99.95% Cu+Ag |
100.00% |
58.00 |

C10400, C10500 & C10700 +0.5 to 0.15% Ag |
100.00% |
58.00 |

C10300 +0.001 to 0.005% P |
98.20% |
56.96 |

Miscellaneous |

Brass 95% Cu + 5% Zn |
55.00% |
31.90 |

95.7% Cu + 4.3% Ti |
10.00% |
5.80 |

Barium (Ba) |
2.76% |
1.60 |

Beryllium (Be) |
38.50% |
22.33 |

C17300 Cu+Be+Pb |
22.00% |
12.76 |

C34000 65% Cu; 34%Zn |
26.00% |
15.08 |

C85200 (Yellow Brass) |
18.00% |
10.44 |

C86200 (Manganese Bronze) |
7.50% |
4.35 |

Cobalt (Co) (99.8% Pure) |
17.80% |
10.32 |

Cobalt (Co) (Pure) |
27.60% |
16.01 |

Lead Alloy +0.07% Ca |
7.91% |
4.59 |

Lead Alloy +0.07% Ca +0.7% Sn |
7.87% |
4.56 |

Molybodenum (Annealed) |
41.00% |
23.78 |

Molybodenum (Hard Drawn) |
35.20% |
20.42 |

Rhodium (Rh) |
38.20% |
22.16 |

Rubidium (Rb) |
14.90% |
8.64 |

Uranium (U) |
5.86% |
3.40 |

Vanadium (Va) |
6.90% |
4.00 |

Zircalloy2 |
2.40% |
1.39 |

Zirconium (Zr) |
4.13% |
2.40 |

## About Ether NDE

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