Magnetic Permeability

5 Key excerpts on "Magnetic Permeability"

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  Balanis' Advanced Engineering Electromagnetics

  • Constantine A. Balanis(Author)
  • 2023(Publication Date)
  • Wiley

    (Publisher)

  For diamagnetic material, this vector M is very small, opposes the applied magnetic field, leads to a negative magnetic susceptibility χ m , and results in values of relative permeability that are slightly less than unity. For example, copper is a diamagnetic material with a magnetic susceptibility χ =− × − 9 10 m 6 and a relative permeability µ r = 0 999991 . . In paramagnetic material, the magnetic moments associated with the orbiting and spinning electrons of an atom do not quite cancel each other in the absence of an applied magnetic field. Therefore each atom possesses a small magnetic moment. However, because the orientation of the magnetic moment of each atom is random, the net magnetic moment of a large sample (macro- scopic scale) of dipoles, and the magnetization vector M, are zero when there is no applied field. When the paramagnetic material is subjected to an applied magnetic field, the magnetic dipoles align slightly with the applied field to produce a small nonzero M in its direction and a small increase in the magnetic flux density within the material. Thus the magnetic susceptibilities have small positive values and the relative permeabilities are slightly greater than unity. For example, aluminum possesses a susceptibility of χ = × − 2 10 m 5 and a relative permeability of µ r = 1 00002 . . The individual atoms of ferromagnetic material possess, in the absence of an applied magnetic field, very strong magnetic moments caused primarily by uncompensated electron spin moments. The magnetic moments of many atoms (usually as many as five to six) reinforce one another and form regions called domains, which have various sizes and shapes. The dimensions of the domains depend on the material’s past magnetic state and history, and range from µ 1 m to a few millime- ters.

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  Non-Destructive Testing

  And Testability of Materials and Structures

  • Gilles Corneloup, Cécile Gueudré, Marie-Aude Ploix(Authors)
  • 2021(Publication Date)
  • PPUR

    (Publisher)

  Fig. 5.1 Principle of magnetic testing 68 Non-Destructive Testing 5.1 PHYSICAL PRINCIPLES 5.1.1 Electromagnetic phenomena Magnetic testing is based on the magnetization of the materials and parts to be inspected. When a medium is subjected to magnetic excitation H (unit: A · m –1 ), gener- ally obtained from a current, it takes on a magnetic condition called induction field B: B = μ 0 μ r H in Tesla, where μ 0 is the absolute Magnetic Permeability of vacuum, constant and equal to 4 · π · 10 –7 Henry · m –1 and μ r is the relative Magnetic Permeability of the medium. The latter is the reaction of the medium to the magnetic excitation, that is, its capac- ity to modify a magnetic field and thus the magnetic flux lines. Materials are dis- tinguished between ferromagnetic materials (iron, nickel, cobalt, etc.), diamagnetic materials (copper, water, gold, zinc, etc.), and paramagnetic materials (aluminum, magnesium, air, etc.). For a ferromagnetic material, μ r depends on excitation and can reach large values. Materials that can be inspected by magnetic testing belong to this category. Fig. 5.2 Distribution of field lines according to material permeability 1 1 1 f H The channeling of the magnetic field in a conductive material is all the more effi- cient when field variation frequency, permeability, and conductivity are high, result- ing from the presence of induced currents. Ferromagnetic materials: curve of initial magnetization When a ferromagnetic material is subjected to an increasing excitation H, the curve representing the relation between the induction field B and this excitation H shows several zones (Fig. 5.3 curve from a to b, then c, d, etc.). 5. Magnetic Testing 69 The curve (ab), from a to b, is called the initial magnetization curve. It first shows a quasi-linearity between B and H. So, the more the excitation H increases, the more the material reacts. The magnetic state B increases proportionally with H.

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  Handbook of Magnetic Measurements

  • Slawomir Tumanski(Author)
  • 2016(Publication Date)
  • CRC Press

    (Publisher)

  density. B .and.the.polarization. J .is.negligibly.small . .In. the.case.of.hard.magnetic.materials,.this.difference.can. be.significant.and.often.both.relationships. B .=. f ( H ).and. J .=. f ( H ).are.presented . 2.2.4 Permeability μ The. relationship. between. the. flux. density. B . and. the. magnetic.field.strength. H .of.a.magnetized.material.is . B H = μ . (2 .18) This. way. of. describing. properties. of. a. material. is. not. convenient. in. practice. and. usually. the. permeability. of.material.is.described.in.relation.to.the.permeability. of. free. space,. that. is,. relative permeability . μ r .=. μ / μ 0 . . The. dependence.(2 .18) .can.be,.therefore,.written.as . B H = μ μ r 0 . (2 .19) Theoretically,.permeability. μ .could.be.the.best.factor.for. describing.the.properties.of.magnetic.materials.because. TABLE 2.1 Conversion.Factors.for.Common.Magnetic.Units Tesla (T) (A/m) Gauss (G) Oersted (Oe) A/m 1.256 .×.10 −6 1 12.56 .×.10 −3 12.56 .×.10 −3 Oe 10 −4 79.6 1 1 T 1 7.96 .×.10 5 10 4 10 4 γ 10 −9 7.96 .×.10 −5 10 −5 10 −5 G 10 −4 79.6 1 1 Fundamentals of Magnetic Measurements 9 it.informs.directly.about.the.relationship.between.two. main. material. parameters:. the. flux. density. B . and. the. magnetic.field.strength. H . .But.in.practice,.the.situation. is.much.more.complex,.because: •. The. relationship. between. B . and. H . is. almost. always. nonlinear,. and. therefore. permeabil-ity. depends. on. the. working. point. (value. of. magnetic.field.strength) . .Figure.2 .5 .presents.a. curve. μ .=. f ( H ).determined.for.a.typical.electri-cal.steel . .We.can.see.that.the.maximum.value. of. relative. amplitude. permeability. reaches. about. 40,000,. but,. at. higher. flux. density,. it. is. much. lower. (for. deep. saturation. it. is. very. small—the. material. practically. is. not. ferro-magnetic). . Similarly,. the. initial. permeability. (for.very.small.magnetic.field).is.also.signifi-cantly.smaller .

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  Magnetic Sensors

  Principles and Applications

  • Kevin Kuang(Author)
  • 2012(Publication Date)
  • IntechOpen

    (Publisher)

  (2001). This last point remains a common denominator of many magnetic sensors. When a magnetic field is applied on a ferromagnetic material, this one becomes magnetised. This magnetization, linked to the magnetic field as expressed by eq. 3, implies an increase of flux density (eq. 4). −→ M = χ −→ H (3) −→ B = μ 0 parenleftBig −→ H + −→ M parenrightBig (4) The magnetic susceptibility χ can vary from unity up to several tens of thousands for certain ferromagnetic materials. When magnetic field line exit from the ferromagnetic core, a magnetic interaction appears Aharoni (1998) which is opposite to the magnetic field. This interaction, designed as demagnetizing field, is related to the shape of the core through the demagnetizing coefficient tensor || N || and magnetization (cf. eq. 5). −→ H d = −|| N || −→ M (5) By combining, eq. 3, 4 and 5 we can express the ratio between flux density outside of the ferromagnetic body ( B n ) and inside ( B ext ). This ratio, designed as apparent permeability ( μ app , cf. eq. 6), depends on the relative permeability of the ferromagnetic core ( μ r ) and the demagnetizing field factor ( N x , y , z ) in the considered direction ( x , y or z ). μ app = B n B ext = μ r 1 + N z ( μ r − 1 ) (6) Under the apparent simplicity of the previous formulas is hidden the difficulty to get the demagnetizing field factor. Some empirical formulas and abacus are given for rods in 47 Induction Magnetometers Principle, Modeling and Ways of Improvement 4 Will-be-set-by-IN-TECH Fig. 3. Ferromagnetic core using flux concentrators. Bozorth & Chapin (1942) while analytic formulas for general ellipsoids, where demagnetizing coefficient is homogeneous into the volume, are computed in Osborn (1945). However in common shapes of ferromagnetic cores demagnetizing coefficients are inhomogenenous and numerical simulation could be helpfull to guide the design.

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  Engineering Electromagnetics

  Pergamon Unified Engineering Series

  • David T. Thomas, Thomas F. Irvine, James P. Hartnett, William F. Hughes(Authors)
  • 2013(Publication Date)
  • Pergamon

    (Publisher)

  We find, (8.70) For fi > /¿o, which is the case here, we can approximate this as Inserting values to find out how well we did, So a great reduction in the magnetic field surrounding the wire is possible by sim-ply using a magnetic shielding pipe. If we had completed solving for the coeffi-cients and computed the fields, they would appear as shown in Fig. 8-38. The suction of field lines into the magnetic material is characteristic of highly magne-tic materials. In that manner the region of strong fields is diverted into the steel pipe and away from the wire. The force on the wire is therefore greatly reduced. SUMMARY The macroscopic influence of magnetic materials is best seen through use of the magnetization, M, defined by the equation, Exercises 281 Fig. 8-38. Magnetic shielding by pipe. In terms of M, the equivalent magnetic currents, J m , are J m = V X M, and the equivalent magnetic surface currents, J,^, are J ms = MXn. Once J m and J m are known, the problem is worked in conventional fashion as outlined in Chapter 7. Magnetic materials generally fall into three groups, diamagnetic, paramagnetic and ferromagnetic. Of these diamagnetic and paramagnetic are weak effects where the atomic magnetic dipole energy is less than the thermal energy of the atom. Ferromagnetic materials on the other hand exhibit strong magnetization even without external magnetic fields (as in a permanent magnet). EXERCISES 8-1. A small bar magnet (m = 200 amps/m 2 ) is placed parallel to a very long current carry-ing wire (/= 100amps). The bar magnet is 1 m from the wire. Find the force and/or torque on the bar magnet. 8-2. A permeable sphere (permeability /JL = 3/x 0 ) is placed in a uniform magnetic field B = zB 0 . Find B, H, M inside and outside the sphere. 8-3. An iron ring is constructed of iron whose permeability, /¿, is 300 /x 0 when B = 0.5 Webers/m 2 . The toroidal ring has uniform cross-sectional area 1 cm 2 and mean radius 10 cm.

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