Magnetic measurements are made in the air adjacent to the pipe wall. The magnetic field H and flux density B are related by material permeability:

B = µH

Since sensor measurements are made in air and the permeability of air is nearly constant, µ is nearly a constant at the sensor. The output of a sensor is a voltage. With knowledge of sensor parameters, this voltage can be converted directly to the leakage field or flux density.

The leakage field is a function of the applied magnetic field in the pipe. The conversion between the field in air and the field or flux density in the pipe itself is not simple. In the pipe material, the permeability is a nonlinear function of the field. So, one cannot easily derive the field of flux density in the pipe from the field or flux density in the air. Conversion between the air field and the pipe field is discussed later.

Sensor Orientation. The magnetic field H (w/ right vector) and the flux density B (w/ right vector) are vector quantities; that is, they have both magnitude and direction. Sensors read only one vector component of the field or flux density. Since these measurements are dealing with pipe, a cylindrical coordinates system is often used:

• Axial Components H_z, B_z
• Radial Components H_r, B_r
• Circumferential Components H_f, B_f

A second conversion uses the terms tangential and normal and ignores the circumferential orientation as follows:

• Tangential (Axial) Component H_t, B_t
• Normal (Radial) Component H_n, B_n

In MFL tools, the radial (normal) and axial (tangential) components are most commonly measured. The third component in the circumferential direction is not as commonly examined as the other two. Each of these field components contains information that is useful for estimating the geometry of an imperfection.

Boundary Conditions. As discussed above, the field or flux density in the pipe cannot be easily derived from the field or flux density in the air. Although measurements cannot be made in the pipe itself, two specific relationships exist at the interface between the pipe and the air. These relationships, or boundary conditions, are as follows:

1. The tangential component of the magnetic field (H_z or H_t) is equal at the interface between the pipe and the air.
2. The normal component of the flux density (B_r or B_n) is equal at the interface between the pipe and the air.

So, some information on the field level in the pipe can be determined using a sensor that measures the tangential component of the magnetic field or the normal component of the flux density.