Any other mutual alignments of the steel strip and the magnet poles are characterized by intermediate values
of the magnetic flux. Because of the demagnetizing effect of the edges of a steel strip in the case of transverse
magnetization, the magnetic flux and magnetic induction depend considerably on the pipe thickness.
If the required magnetic field strength is reached for transverse magnetization (Fig. 3a), the magnetic
field strength for longitudinal magnetization (Fig. 3b) is substantially higher than the required value. Therefore,
from the practical point of view, it suffices to solve the problem of transverse magnetization of a pipe
edge with a U-shaped magnet.
Figure 4 shows a scheme of the formation of a magnetic field of a steel strip in the magnetic field of a
U-shaped magnet. Magnetic charges whose field is opposite to the field of the U-shaped magnet are formed
at the strip surfaces. Because of this, the field within the strip is substantially lower than the magnetic field
in air. The magnetic field of the strip also decreases the external field at the strip face where magnetic particles
are deposited.
To calculate the magnetic field within a strip, equations obtained for a rectangular crack existing within
a ferromagnetic half-space can be used, with the only difference being that the opposite direction of the
magnetic field should be taken; the depth of the crack is equal to the pole half-width b and the crack width
is equal to the strip thickness d.
Then, as a first approximation, the density of magnetic charges σ at the strip surface (µ = const) is