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  1. 1. Designation: A 340 – 03a Standard Terminology of Symbols and Definitions Relating to Magnetic Testing1 This standard is issued under the fixed designation A 340; the number immediately following the designation indicates the year of original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A superscript epsilon (e) indicates an editorial change since the last revision or reapproval. INTRODUCTION In preparing this glossary of terms, an attempt has been made to avoid, where possible, vector analysis and differential equations so as to make the definitions more intelligible to the average worker in the field of magnetic testing. In some cases, rigorous treatment has been sacrificed to secure simplicity, but it is believed that none of the definitions will prove to be misleading. It is the intent of this glossary to be consistent in the use of symbols and units with those found in ANSI/IEEE 260-1978 and USA Standard Y 10.5-1968. Part 1—Symbols Used in Magnetic TestingSymbol Term Hb biasing magnetic field strength Hc coercive field strengtha cross-sectional area of B coil Hci intrinsic coercive field strengthA cross-sectional area of specimen Hcs coercivityA8 solid area Hd demagnetizing field strengthB H magnetic induction magnetic flux density HD Hg HL incremental magnetic field strength air gap magnetic field strength ac magnetic field strength (from an assumedDB excursion range of induction peak value of magnetizing currentBb · biased induction Hm maximum magnetic field strength in a hyster-Bd remanent induction esis loopBdm remanence Hmax maximum magnetic field strength in a flux-BdHd energy product current loop(BdHd)m maximum energy product Hp ac magnetic field strength (from a measuredBD incremental induction peak value of exciting current)Bi intrinsic induction Ht instantaneous magnetic field strength (coinci-Bm maximum induction in a hysteresis loop dent with Bmax)Bmax maximum induction in a flux current loop Hz ac magnetic field strength force (from an as-Br residual induction sumed peak value of exciting current)Brs retentivity I ac exciting current (rms value)Bs saturation induction Ic ac core loss current (rms value)cf crest factor Idc constant currentCM cyclically magnetized condition Im ac magnetizing current (rms value)d lamination thickness J magnetic polarizationDB demagnetizing coefficient k8 coupling coefficientdf distortion factor , flux path lengthDm magnetic dissipation factor ,1 effective flux path lengthE exciting voltage ,g gap lengthE1 induced primary voltage + (also f N) flux linkageE2 induced secondary voltage +m mutual flux linkageEf flux volts L self inductancef cyclic frequency in hertz L1 core inductance^ magnetomotive force LD incremental inductanceff form factor Li intrinsic inductanceH magnetic field strength Lm mutual inductanceDH excursion range of magnetic field strength L0 initial inductance Ls series inductance Lw winding inductance m magnetic moment 1 This terminology is under the jurisdiction of ASTM Committee A06 on M magnetizationMagnetic Properties and is the direct responsibility of Subcommittee A06.92 on m total mass of a specimenTerminology and Definitions. m1 active mass of a specimen Current edition approved June 10, 2003. Published July 2003. Originally ND demagnetizing factorapproved in 1949. Last previous edition approved in 2003 as A 340 – 03. N1 turns in a primary windingCopyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States. 1
  2. 2. A 340 – 03aN2 turns in a secondary winding Gm magnetic constantN1I/,1 ac excitation d densityp magnetic pole strength k susceptibility3 permeance ac Permeabilities:P active (real) power µa ideal permeabilityPa apparent power µL inductance permeabilityPa (B;f) specific apparent power µDL incremental inductance permeability µ0d initial dynamic permeabilityPc total core loss µp peak permeabilityPc (B;f) specific core loss µDp incremental peak permeability µi instantaneous permeabilityP cD incremental core loss µz impedance permeabilityPe normal eddy current core loss µDz incremental impedance permeabilityPD e incremental eddy current core loss dc Permeabilities:Ph normal hysteresis core loss µ normal permeabilityPD h incremental hysteresis core loss µabs absolute permeabilityPq reactive (quadrature) power µd differential permeabilityPr residual core loss µD incremental permeabilityPw winding loss (copper loss) µeff effective circuit permeabilityPz exciting power µi intrinsic permeabilityPz (B;f) specific exciting power µDi incremental intrinsic permeability µm maximum permeabilityQm magnetic storage factor µ0 initial permeability5 reluctance µr relative permeabilityR1 core resistance µv (also Gm) space permeabilityRw winding resistance µrev reversible permeabilityS lamination factor (stacking factor) µ8/cot g figure of meritSCM symmetrically cyclically magnetized condition n reluctivityTc Curie temperature p the numeric 3.1416w lamination width r resistivityWh hysteresis loop loss f magnetic fluxa linear expansion, coefficient (average) fN flux linkage (see +)Dx incremental tolerance x mass susceptibilityb hysteretic angle x0 initial susceptibilityg loss angle v angular frequency in radians per secondcos g magnetic power factorgp proton gyromagnetic ratio Part 2—Definition of Terms Used in Magnetic Testingac excitation, N1I/¯1—the ratio of the rms ampere-turns of point in a nonmagnetic gap in a magnetic circuit. exciting current in the primary winding of an inductor to the effective flux path length of the inductor. NOTE 4—In the cgs-emu system of units, Hg is numerically equal to the induction existing at such a point and exceeds the magnetic field strengthactive (real) power, P—the product of the rms current, I, in an in the magnetic material. electrical circuit, the rms voltage, E, across the circuit, and the cosine of the angular phase difference, u between the amorphous alloy—a semiprocessed alloy produced by a rapid current and the voltage. quenching, direct casting process resulting in metals with P 5 EI cosu noncrystalline structure. ampere (turn), A—the unit of magnetomotive force in the SI NOTE 1—The portion of the active power that is expended in a system of units. The symbol A represents the unit of electricmagnetic core is the total core loss, Pc. current, ampere, in the SI system of units.aging coefficient—the percentage change in a specific mag- ampere per metre, A/m—the unit of magnetic field strength in netic property resulting from a specific aging treatment. the SI system of units. anisotropic material—a material in which the magnetic prop- NOTE 2—The aging treatments usually specified are: erties differ in various directions. (a) 100 h at 150°C or (b) 600 h at 100°C. anisotropy of loss—the ratio of the specific core loss measured with flux parallel to the rolling direction to the specific coreaging, magnetic—the change in the magnetic properties of a loss with flux perpendicular to the rolling direction. material resulting from metallurgic change due to a normal Pc ~B;f! l or specified aging condition. anisotropy of loss 5 P c ~B;f! t NOTE 3—This term implies a deterioration of the magnetic properties ofmagnetic materials for electronic and electrical applications, unlessotherwise specified. where:air-gap magnetic field strength, Hg—the magnetic field Pc (B;f) l = specific core loss value with flux parallel to the strength required to produce the induction existing at some rolling direction, W/lb [W/kg], and 2
  3. 3. A 340 – 03aPc (B;f) t = specific core loss value with flux perpendicular to zero after the material has been symmetrically cyclically to the rolling direction, W/lb [W/kg]. magnetized. coercivity, Hcs—the maximum value of coercive field strength NOTE 5—This definition of anisotropy normally applies to electrical that can be attained when the magnetic material is symmetri-steels with measurements made in an Epstein frame at a flux density of 15kG [1.5 T] and a frequency of 60 Hz (see Test Method A 343). cally cyclically magnetized to saturation induction, BS. core, laminated—a magnetic component constructed byanisotropy of permeability—the ratio of relative peak perme- stacking suitably thin pieces of magnetic material which are ability measured with flux parallel to the rolling direction to stamped, sheared, or milled from sheet or strip material. the relative peak permeability measured with flux perpen- Individual pieces usually have an insulating surface coating dicular to the rolling direction. to minimize eddy current losses in the assembled core. µprl core, mated—two or more magnetic core segments assembled anisotropy of permeability 5 µ with the magnetic flux path perpendicular to the mating prt surface. core, powder (dust)—a magnetic core comprised of smallwhere: particles of electrically insulated metallic ferromagneticµprl = relative peak permeability value with flux parallel to material. These cores are characterized by low hysteresis and the rolling direction, and eddy current losses.µprt = relative peak permeability value with flux perpen- core, tape-wound—a magnetic component constructed by the dicular to the rolling direction. spiral winding of strip material onto a suitable mandrel. The NOTE 6—This definition of anisotropy normally applies to electrical strip material usually has an insulating surface coating whichsteels with measurements made in an Epstein frame at a flux density of 15 reduces interlaminar eddy current losses in the finished core.kG [1.5 T] and a frequency of 60 Hz (see Test Method A 343). core loss, ac eddy current, incremental, PDe—the power loss caused by eddy currents in a magnetic material that isantiferromagnetic material—a feebly magnetic material in cyclically magnetized. which almost equal magnetic moments are lined up antipar- core loss, ac eddy current, normal, Pe—the power losses as allel to each other. Its susceptibility increases as the tem- a result of eddy currents in a magnetic material that is perature is raised until a critical (Neél) temperature is symetrically cyclically magnetized. reached; above this temperature the material becomes para- magnetic. NOTE 7—The voltage is generally assumed to be across the parallelapparent power, Pa—the product (volt-amperes) of the rms combination of core inductance, L1, and core resistance, R1. exciting current and the applied rms terminal voltage in an core loss, ac, incremental, PcD—the core loss in a magnetic electric circuit containing inductive impedance. The compo- material when the material is subjected simultaneously to a nents of this impedance as a result of the winding will be dc biasing magnetizing force and an alternating magnetizing linear, while the components as a result of the magnetic core force. will be nonlinear. The unit of apparent power is the volt- core loss, residual, Pr—the portion of the core loss power, Pc, ampere, VA. which is not attributed to hysteresis or eddy current lossesapparent power, specific, Pa(B;f)—the value of the apparent from classical assumptions. power divided by the active mass of the specimen, that is, core loss, ac, specific, Pc(B;f)—the active power (watts) ex- volt-amperes per unit mass. The values of voltage and pended per unit mass of magnetic material in which there is current are those developed at a maximum value of cycli- a cyclically varying induction of a specified maximum value, cally varying induction B and specified frequency f. B, at a specified frequency, f.area, A—the geometric cross-sectional area of a magnetic path core loss, ac, (total), Pc—the active power (watts) expended in which is perpendicular to the direction of the induction. a magnetic circuit in which there is a cyclically alternatingBloch wall—a domain wall in which the magnetic moment at induction. any point is substantially parallel to the wall surface. See NOTE 8—Measurements of core loss are normally made with sinusoi- also domain wall. dally alternating induction, or the results are corrected for deviations fromBohr magneton—a constant that is equal to the magnetic the sinusoidal condition. moment of an electron because of its spin. The value of the core loss density—the active power (watts) expended in a constant is (9 274 078 3 10 −21 erg/gauss or magnetic core in which there is a cyclically varying induc- 9 274 078 3 10−24 J/T). tion of a specified maximum value, B, at a specifiedcgs-emu system of units—the system for measuring physical frequency, f, divided by the effective volume of the core. quantities in which the base units are the centimetre, gram, and second, and the numerical value of the magnetic NOTE 9—This parameter is normally used only for non-laminated cores constant, Gm, is unity. such as ferrite and powdered cores.coercive field strength, Hc—the (dc) magnetic field strength core plate—a generic term for any insulating material, formed required to restore the magnetic induction to zero after the metallurigically or applied externally as a thin surface material has been symmetrically cyclically magnetized. coating, on sheet or strip stock used in the construction ofcoercive field strength, intrinsic, Hci—the (dc) magnetic field laminated and tape wound cores. strength required to restore the instrinsic magnetic induction coupling coefficient, k8—the ratio of the mutual inductance 3
  4. 4. A 340 – 03a between two windings and the geometric mean of the demagnetizing factor, ND—defined as 4p times the demag- individual self-inductances of the windings. netizing coefficient, DB.crest factor, cf—the ratio of the maximum value of a periodi- demagnetizing field strength, Hd—a magnetic field strength cally alternating quantity to its rms value. applied in such a direction as to reduce the induction in a magnetized body. See demagnetization curve. NOTE 10—For a sinusoidal variation the crest factor is =2 . density, d—the ratio of mass to volume of a material. In theCurie temperature, Tc—the temperature above which a fer- cgs-emu system of units, g/cm3. In SI units, kg/m3. romagnetic material becomes paramagnetic. diamagnetic material—a material whose relative permeabil-current, ac core loss, Ic—the rms value of the in-phase ity is less than unity. component (with respect to the induced voltage) of the NOTE 14—The intrinsic induction, Bi, is oppositely directly to the exciting current supplied to a coil which is linked with a applied magnetizing force H. ferromagnetic core.current, ac exciting, I—the rms value of the total current dissipation factor, magnetic, Dm—the tangent of the hyster- supplied to a coil that is linked with a ferromagnetic core. etic angle that is equal to the ratio of the core loss current, Ic, to the magnetizing current, Im. Thus: NOTE 11—Exciting current is measured under the condition that anyother coil linking the same core carries no current. Dm 5 tan b 5 cot g 5 Ic/Im 5 vL1/R1 5 I/Qmcurrent, ac, magnetizing, Im—the rms value of the magnetiz- NOTE 15—This dissipation factor is also given by the ratio of the energy ing component (lagging with respect to applied voltage) of dissipated in the core per cycle of a periodic SCM excitation (hysteresis the exciting current supplied to a coil that is linked with a and eddy current heat loss) to 2p times the maximum energy stored in the ferromagnetic core. core.current, dc, Idc—a steady-state dc current. A dc current flowing in an inductor winding will produce a unidirectional distortion, harmonic—the departure of any periodically vary- magnetic field in the magnetic material. ing waveform from a pure sinusoidal waveform.customary units—a set of industry-unique units from the NOTE 16—The distorted waveform that is symmetrical about the zero cgs-emu system of units and U.S. inch-pound systems and amplitude axis and is most frequently encountered in magnetic testing units derived from the two systems. contains only the odd harmonic components, that is fundamental, 3rd harmonic, 5th harmonic, and so forth. Nonsymmetrical distorted wave- NOTE 12—Examples of customary units used in ASTM A06 standards forms must contain some even harmonic components, in addition to theinclude: fundamental and, perhaps, some odd harmonic components. Quantity Quantity Name Symbol Unit Name Unit Symbol distortion factor, df—a numerical measure of the distortion in any ac nonsinusoidal waveform. For example, if by FourierMagnetic field strength H oersted OeMagnetic induction (magnetic B gauss G analysis or direct measurement E1, E2, E3, and so forth are flux density) the effective values of the pure sinusoidal harmonic compo-Specific core loss Pc(b;f) watt/pound W/lb nents of a distorted voltage waveform, then the distortioncyclically magnetized condition, CM—a magnetic material is factor is the ratio of the root mean square of the second and in a cyclically magnetized condition when, after having been all higher harmonic components to the fundamental compo- subjected to a sufficient number of identical cycles of nent. magnetizing field, it follows identical hysteresis or flux- df 5 @E22 1 E32 1 E42 1 ···# 1/2 E1 current loops on successive cycles which are not symmetri- cal with respect to the origin of the axes. NOTE 17—There are no dc components (E0) in the distortion factor.demagnetization curve—the portion of a flux versus dc current plot (dc hysteresis loop) that lies in the second or domains, ferromagnetic—magnetized regions, either macro- fourth quadrant, that is, between the residual induction point, scopic or microscopic in size, within ferromagnetic materi- Br, and the coercive force point, Hc. Points on this curve are als. Each domain, in itself, is magnetized to intrinsic designated by the coordinates, Bd and Hd. saturation at all times, and this saturation induction isdemagnetizing coefficient, DB—is defined by the equation: unidirectional within the domain. DB 5 @Gm~Ha 2 H!#/Bi domain wall—a boundary region between two adjacent do- mains within which the orientation of the magnetic moment of one domain changes into a different orientation of thewhere: magnetic moment in the other domain.Ha = applied magnetic field strength, eddy current—an electric current developed in a material as aH = magnetic field strength actually existing in the mag- result of induced voltages developed in the material. netic material, effective circuit permeability, µeff—when a magnetic circuitBi = intrinsic induction, and consists of two or more components, each individuallyGm = 1 in the cgs system and 4p 3 10−7, henry/metre in homogeneous throughout but having different permeability the SI system. values, the effective (overall) permeability of the circuit is NOTE 13—For a closed, uniform magnetic circuit, the demagnetizing that value computed in terms of the total magnetomotivecoefficient is zero. force, the total resulting flux, and the geometry of the circuit. 4
  5. 5. A 340 – 03aelectrical steel—a term used commercially to designate strip of the magnetic core only. When the core has a secondary winding, the or sheet used in electrical applications and historically has induced primary voltage is obtained from the measured open-circuit referred to flat-rolled, low-carbon steels or alloyed steels secondary voltage multiplied by the appropriate turns ratio. with silicon or aluminum, or both. Common types of exciting power, specific, Pz(B;f)—the value of the ac rms electrical steels used in the industry are grain-oriented exciting power divided by the active mass of the specimen electrical steel, nonoriented electrical steel, and magnetic (volt-amperes/unit mass) taken at a specified maximum lamination steel. value of cyclically varying induction B and at a specifiedelectrical steel, grain oriented—a flat-rolled silicon-iron alloy frequency f. usually containing approximately 3 % silicon, having en- exciting voltage, E—the ac rms voltage across a winding hanced magnetic properties in the direction of rolling and linking the flux of a magnetic core. The voltage across the normally used in transformer cores. winding equals that across the assumed parallel combinationelectrical steel, nonoriented—a flat-rolled silicon-iron or of core inductance L1, and core resistance, R1. silicon-aluminum-iron alloy containing 0.0 to 3.5 % silicon feebly magnetic material—a material generally classified as and 0.0 to 1.0 % aluminum and having similar core loss in “nonmagnetic,” whose maximum normal permeability is all directions. less than 4.emu—the notation emu is an indicator of electromagnetic ferrimagnetic material—a material whose atomic magnetic units. When used in conjunction with magnetic moment, m, moments are both ordered and anti-parallel but being un- it denotes units of ergs per oersted, erg/Oe. A moment of 1 equal in magnitude produce a net magnetization in one erg/Oe is produced by a current of 10 amperes (1 abampere) direction. flowing in a loop of area 1 cm2. The work done to rotate a ferrite—a term referring to magnetic oxides in general, and moment of 1 erg/Oe from parallel to perpendicular in a especially to material having the formula M O Fe2 O3, where uniform field of 1 Oe is 1 erg. The conversion to the SI units M is a divalent metal ion or a combination of such ions. of magnetic moment J/T (joule/tesla) or A m2 is given by Certain ferrites, magnetically “soft” in character, are useful erg/Oe ~cgs2emu! 10 amperes cm2 ~cgs2emu! for core applications at radio and higher frequencies because J/T ~SI! [ 5 1023 (1) of their advantageous magnetic properties and high volume A m2 ~SI! resistivity. Other ferrites, magnetically “hard” in character, have desirable permanent magnet properties. Magnetization, M, the magnetic moment per unit volume, ferromagnetic material—a material whose magnetic mo-has units erg/(Oe-cm3), often expresssed as emu/cm3. ments are ordered and parallel producing magnetization inenergy product, BdHd—the product of the coordinate values one direction. of any point on a demagnetization curve. figure of merit, magnetic, µ8/cot g—the ratio of the real partenergy-product curve, magnetic—the curve obtained by of the complex relative permeability to the dissipation factor plotting the product of the corresponding coordinates, Bd and of a ferromagnetic material. Hd, of points on the demagnetization curve as abscissa against the induction, Bd, as ordinates. NOTE 21—The figure of merit index of the magnetic efficiency of the core in various ac electromagnetic devices. NOTE 18—The maximum value of the energy product, (BdHd)m, corre-sponds to the maximum value of the external energy. flux-current loop, incremental (biased)—the curve devel- NOTE 19—The demagnetization curve is plotted to the left of the oped by plotting magnetic induction, B, versus magneticvertical axis and usually the energy-product curve to the right. field strength, H, when the magnetic material is cyclicallyenergy product, maximum (BdHd)m—for a given demagneti- magnetized while under dc bias condition. This loop will not zation curve, the maximum value of the energy product. be symmetrical about the B and H axes.equipment test level accuracy—(1) For a single test equip- flux-current loop, normal—the curve developed by plotting ment, using a large group of test specimens, the average magnetic induction, B, versus magnetic field strength, H, percentage of test deviation from the correct average value. when the magnetic material is symmetrically cyclically magnetized. (2) The average percentage deviation from the average NOTE 22—The area of the loop is proportional to the sum of the static value obtained from similar tests, on the same test specimen hysteresis loss and all dynamic losses. or specimens, when measured with a number of other test flux linkage, +—the sum of all flux lines in a coil. equipments that have previously been proven to have both suitable reproducibility of measurement and test level, and whose calibrations and quality have general acceptance for + 5 f 1 1 f2 1 f3 1 ···fN standardization purposes and where better equipment for establishing the absolute accuracy of test is not available. where:exciting current, ac, I—See current, ac exciting. f1 = flux linking turn 1;exciting power, rms, Pz—the product of the ac rms exciting f2 = flux linking turn 2, and so forth; and current and the rms voltage induced in the exciting (primary) fN = flux linking the Nth turn. winding on a magnetic core. NOTE 23—When the coupling coefficient, k8, is less than unity, the flux NOTE 20—This is the apparent volt-amperes required for the excitation linkage equals the product of the average flux linking the turns and the 5
  6. 6. A 340 – 03atotal number of turns. When the coupling coefficient is equal to unity, the where:flux linkage equals the product of the total flux linking the coil and the f = resonance frequency in cycles per second (hertz) andtotal number of turns. g p = gyromagnetic ratio (the accepted value at present for water is 2.675 12 3 104 gauss−1 s−1).flux linkage, mutual, +m—the flux linkage existing between two windings on a magnetic circuit. Mutual linkage is henry (plural henries), H—the unit of self- or mutual maximum when the coupling coefficient is unity. inductance. The henry is the inductance of a circuit in whichflux path length, ¯—the distance along a flux loop. a voltage of 1 V is induced by a uniform rate of change 1 A/sflux path length, effective, ¯1—the calculated length of the in the circuit. Alternatively, it is the inductance of a circuit in flux paths in a magnetic core, which is used in the calcula- which an electric current of 1 A/s produces a flux linkage of tions of certain magnetic parameters. one weber turn (Wb turn) or 108 maxwell-turns. See induc-flux volts, Ef—the voltage induced in a winding of a magnetic tance, mutual, and inductance, self. component when the magnetic material is subjected to hertz, Hz—the unit of cyclic frequency, f. repeated magnetization under SCM or CM conditions. hysteresis loop, biased—an incremental hysteresis loop that lies entirely in any one quadrant. NOTE 27—In this case, both of the limiting values of H and B are in theEf = 4.443 BmaxA8Nf 3 10−8 V (SCM excitation) same direction.Ef = 2.221 D BA8 Nf 3 108 V (CM excitation)Ef = 1.1107 Eavg hysteresis loop, incremental—the hysteresis loop, nonsym- metrical with respect to the B and H axes, exhibited by awhich ferromagnetic material in a CM condition.A8 = solid cross-sectional area of the core in cm2,N = number of winding turns, and NOTE 28—In this case, both of the limiting values H may have oppositef = the frequency in hertz. polarity, but definitely have different absolute values of Hm. An incremen- tal loop may be initiated at either some point on a normal hysteresis loop or at some point on the normal induction curve of the specimen.form factor, ff—the ratio of the rms value of a periodically alternating quantity to its average absolute value. hysteresis loop, intrinsic—a hysteresis loop obtained with a ferromagnetic material by plotting (usually to rectangular NOTE 24—For a sinusoidal variation, the form factor is: coordinates) corresponding dc values of intrinsic induction, p/ 2=2 5 1.1107 Bi, for ordinates and magnetic field strength H for abscissae. hysteresis loop, normal—a closed curve obtained with a ferromagnetic material by plotting (usually to rectangularfrequency, angular, v—the number of radians per second coordinates) corresponding dc values of magnetic induction traversed by a rotating vector that represents any periodically (B) for ordinates and magnetic field strength (H) for abscissa varying quantity. when the material is passing through a complete cycle NOTE 25—Angular frequency, v, is equal to 2p times the cyclic between equal definite limits of either magnetic fieldfrequency, f. strength, 6Hm, or magnetic induction, 6Bm. In general, the normal hysteresis loop has mirror symmetry with respect tofrequency, cyclic, f—the number of hertz (cycles/second) of a the origin of the B and H axes, but this may not be true for periodic quantity. special materials.gap length, ,g—the distance that the flux transverses in the hysteresis loop loss, Wh—the power expended in a single slow central region of a gap in a core having an “air” (nonmag- excursion around a normal hysteresis loop. The energy is the netic) gap in the flux path may be considered unity in the integrated area enclosed by the loop measured in gauss- gap. oersteds. Using the cgs-emu system of units:gauss (plural gausses), G—the unit of magnetic induction in Wh 5 ~* HdB/4p! ergs the cgs-emu system of units. The gauss is equal to 1 maxwell per square centimetre of 10−4 tesla. See magnetic induction (flux density). where the integrated area enclosed by the loop is measured in gauss-oersteds.gilbert, Gb—the unit of magnetomotive force in the cgs-emu hysteresis loss, incremental, PDh—the power (watts) as a system of units. The gilbert is a magnetomotive force of result of hysteresis expended in a ferromagnetic material 4p/10 ampere-turns. See magnetomotive force. while being driven through an incremental flux-current loopgyromagnetic ratio, proton, gp—the ratio of the magnetic by a CM-type of excitation. moment of a hydrogen nucleus to its angular momentum. hysteresis loss, normal, Ph—(1) the power expended in a NOTE 26—The gyromagnetic ratio is used to calculate the magnetic ferromagnetic material, as a result of hysteresis, when thefield from a measured resonance frequency when using the nuclear material is subjected to a SCM excitation.magnetic resonance technique.The relationship is: (2) The energy loss/cycle in a magnetic material as a result of magnetic hysteresis when the induction is cyclic (but not B 5 ~2pf/gp! gausses 5 ~2pf/gp! 3 1024 teslas necessarily periodic). hysteresis loss, rotational—the hysteresis loss that occurs in a 6
  7. 7. A 340 – 03a body when subjected to a constant magnetizing force, the Lm 5 ~+2/I1! 3 1028 direction of which rotates with respect to the body, either in a continuously cyclic or in a repeated oscillatory manner. NOTE 34—If the linkage is proportional to the current (no ferromag-hysteresis, magnetic—the property of a ferromagnetic mate- netic material present), the inductance is constant and may be obtained from the equation: rial exhibited by the lack of correspondence between the changes in induction resulting from increasing magnetic field strength and from decreasing magnetic field strength. e2 5 Lm~di1/dt!hysteretic angle, magnetic, b—the mean angle by which the fundamental component of exciting current leads the funda- where: mental component of magnetizing current, Im, in an inductor e2 = instantaneous induced emf in the secondary and having a ferromagnetic core. di1/dt = time rate of change of the current in the primary. NOTE 35—If ferromagnetic materials or eddy currents are present, the NOTE 29—Because of hysteresis, the instantaneous value of the hyster- mutual inductance must be regarded as a function of the primary current,etic angle will vary during the cycle of SCM excitation. However, b is its rate of change, and the magnetic history of the material. Thus:taken to be the mean effective value of this angle. e2 5 2~d~Lmi1!/dt! 5 2 @Lm~di1/dt! 1 i1~dLm/dt!#inductance, core, L1—the effective parallel circuit inductance of a ferromagnetic core based upon a hypothetical nonresis- inductance, self, L—that property of an electric circuit that tive path that is exclusively considered to carry the magne- determines the flux linkage produced by a given current in tizing current, Im. the circuit. The self-inductance, L, is defined by the equa- NOTE 30—The product Im2vL1 equals the quadrature power delivered tion:to the core. L 5 +/Iinductance, incremental, LD—the self-inductance of an elec- trical circuit when the ferromagnetic core has an ac cyclic where: magnetization produced by specified values of both ac and + = flux linkage and dc components of the exciting current. I = current.inductance, initial, L0—the limiting value of the core induc- tance, L1 reached in a ferromagnetic core when, under ac NOTE 36—If + is in maxwell-turns and I in amperes, then the self-inductance in henries is defined by the equation: symmetrical cyclic excitation, the magnetizing current has been progressively and gradually reduced from a compara- L 5 ~+/I! 3 1028 tively high value to a zero value. NOTE 37—If the linkage is proportional to the current (no ferromag- NOTE 31—Initial inductance may be obtained by highly sensitive netic material present), the inductance is constant and may be obtainedASTM bridge methods working in the range in which µL is a linear from the equation:function of H. A series of decreasing values of µL is measured and plottedversus corresponding values of magnetizing current, Im (or other suitable e2 5 2 Lm~di/dt!excitation parameter), and the data extrapolated to zero excitation. Seepermeability, initial dynamic. where:inductance, intrinsic (ferric), Li—that portion of the self- e = instantaneous induced emf and di/dt = time rate of change of the current. inductance which is due to the intrinsic induction in a NOTE 38—If ferromagnetic material or eddy currents are present, the ferromagnetic core. self-inductance must be regarded as a function of the circuit current, its NOTE 32—It is determined at a specified value of the magnetizing rate of change, and the magnetic history of the material. Thus:current.inductance, mutual, Lm—the common property of two elec- e 5 2~d~Li!/dt! 5 2 @L ~di/dt! 1 i~dL/dt!# trical circuits that determines the flux linkage in one circuit (the secondary) produced by a given current in the other inductance, series, Ls—the effective series ac self-inductance circuit (the primary). The mutual inductance, Lm, is defined exhibited by an inductor having a ferromagnetic core and by the equation: subjected to an SCM excitation after the core has been demagnetized. Lm 5 +2I1 NOTE 39—The value of series inductance is a function of the level of excitation.where: inductance, winding, Lw—the linear inductance of the mag-+2 = flux linkage in the secondary and netizing winding as a result of the flux caused by the acI1 = current in the primary, assuming no current in the symmetrical cyclic magnetization exciting current, I. The secondary. flux linking the winding is that flux outside of the ferromag- NOTE 33—If +2 is in maxwell-turns and I1 is in amperes, then the netic core material.mutual inductance in henries is defined by the equation: induction, B—See magnetic induction (flux density). induction, biased, Bb—the value of the apparent dc magnetic 7
  8. 8. A 340 – 03a induction around which the ac cyclic changes are occurring tion and corresponding ascending values of magnetic field in a magnetic material resulting from the biasing magnetiz- strength. This curve starts at the origin of the B and H axes. ing field. This value is a function of the incremental insulation resistance—the apparent resistance between adja- magnetizing field and is not determined by the normal cent contacting laminations, calculated as a ratio of the induction curve. applied voltage to conduction current. This parameter isinduction, incremental, BD—one half the algebraic difference normally a function of the applied force and voltage. of the extreme values of the magnetic induction during a International System of Units, SI—a complete coherent cycle in a magnetic material that is subjected simultaneously system of units whose base units are the metre, kilogram, to a biasing magnetizing field and a symmetrically cyclically second, ampere, kelvin, mole, and candela. Other units are varying magnetizing field. Twice the incremental induction derived as combinations of the base units or supplementary is indicated by the symbol DB, thus: units. iron-silicon alloys—a material composition containing up to BD 5 DB/2 5 % silicon with balance iron. isotropic material—material in which the magnetic propertiesinduction, intrinsic, Bi—the vector difference between the dc are the same for all directions. magnetic induction in a magnetic material and the magnetic Jordan diagram—a graph showing the variation of some induction that would exist in a vacuum under the influence of magnetic parameter versus frequency when the excitation is the same magnetic field strength. This is expressed by the within the Rayleigh range. equation: joule, J—the unit of energy in the SI system of units. One joule is one watt-second. Bi 5 B 2 GmH lamination factor, (space factor, stacking factor), S—a numeric, less than unity and usually expressed as a percent- NOTE 40—In the cgs-emu system of units, Bi/4p is often called age, which is defined as the ratio of the uniform solid heightmagnetic polarization. h of the magnetic material in a laminated core to the actual height h8 (core buildup) when measured under a specifiedinduction, maximum: pressure. S is thus equal to the ratio of the volume of (1) Bm—the maximum value of induction, B, in a dc magnetic material in a uniform laminated core to the overall hysteresis loop. The tip of this loop has the magnetostatic geometric volume of the core. coordinates Hm, Bm, which exist simultaneously. lamination stack resistance—the electrical resistance mea- sured in the direction perpendicular to the plane of lamina- (2) Bmax—the maximum value of induction, B, in an ac tion in a stack of laminations. flux-current loop. lamination surface insulation—the insulation between core NOTE 41—In a flux-current loop, the magneto-dynamic values Bmax and laminations produced by a surface condition or layer eitherHmax do not exist simultaneously; Bmax occurs later than Hmax. formed or applied for this purpose.induction, normal, B—the maximum induction, in a magnetic NOTE 43—In commercial practice, this insulating layer is frequently material that is in a symmetrically cyclically magnetized designated as core plate. condition. lamination thickness, d—the active thickness of a singleinduction, remanent, Bd—the magnetic induction that re- lamination cut from sheet stock, including any core plate mains in a magnetic circuit after the removal of an applied material. magnetic field. lamination width, w—the width of a core lamination perpen- NOTE 42—If there are no air gaps or other inhomogeneities in the dicular to the direction of the induction therein.magnetic circuit, the remanent induction, Bd, will equal the residual leakage flux—the flux outside the boundary of the practicalinduction, Br; if air gaps or other inhomogeneities are present, Bd will be magnetic circuit.less than Br. linear expansion, coefficient of, a —the change in length per unit length per degree change in temperature orinduction, residual, Br—the value of magnetic induction corresponding to zero magnetizing field when the magnetic L1 2 L0 a 5 L ·DT material is subjected to symmetrically cyclically magnetized 0 conditions. where:induction, saturation, Bs—the maximum intrinsic induction L1 = length of specimen at the higher temperature, possible in a material. L0 = length at lower temperature, andinduction curve, intrinsic (ferric)—a curve of a previously DT = difference between temperatures. demagnetized specimen depicting the relation between in- loss angle, magnetic, g—the mean angle by which the trinsic induction and corresponding ascending values of fundamental component of core loss current leads the magnetic field strength. This curve starts at the origin of the fundamental component of exciting current, I, in an inductor Bi and H axes. having a ferromagnetic core.induction curve, normal—a curve of a previously demagne- NOTE 44—The loss angle, g, is the complement of the hysteretic angle, tized specimen depicting the relation between normal induc- b. 8
  9. 9. A 340 – 03a NOTE 45—Because of hysteresis, the instantaneous value of the loss current and the geometry of certain magnetizing circuits. For example, inangle will vary during the cycle of SCM excitation; however, g is taken to the center of a uniformly wound long solenoid.be the mean effective value of this angle.magnet—a body that produces a magnetic field external to H 5 C ~NI/I! itself. NOTE 46—By convention, the north-seeking pole of a magnet is marked where:with an N, + , or is colored red. H = magnetic field strength, NOTE 47—Natural magnets consist of certain ores such as magnetite H = constant whose value depends on the system of units,(loadstone); artificial (permanent) magnets are made of magnetically hard N = number of turns,materials; electromagnetics have cores made of magnetically soft materi- I = current, andals which are energized by a current carrying winding. l = axial length of the coil. If I is expressed in amperes and l is expressed in centimetres, thenmagnetic circuit—a region at whose surface the magnetic C = 4p/10 to obtain H in the cgs-emu system of units, the oersted. induction is tangential. If I is expressed in amperes and l is expressed in metres, then C = 1 to obtain H in the SI units, ampere-turn per metre. NOTE 48—A practical magnetic circuit is the region containing the flux NOTE 53—The magnetic field strength, H, at a point in air may beof practical interest, such as the core of a transformer. It may consist of calculated from the measured value of induction at the point by dividingferromagnetic material with or without air gaps or other feebly magnetic this value by the magnetic constant Gm.materials such as porcelain, brass, and so forth. magnetic field strength, ac—the value of one of threemagnetic constant (permeability of space), Gm—the dimen- dynamic magnetic field strength parameters in common use. sional scalar factor that relates the mechanical force between They are: two currents to their intensities and geometrical configura- (a) HL—an assumed peak value computed in terms of peak tions. That is: magnetizing current (considered to be sinusoidal). dF 5 GmI1I2dl1 3 ~dl2 3 r1!/nr2 (b) Hz—an assumed peak value computed in terms of measured rms exciting current (considered to be sinusoidal).where: (c) Hp—computed in terms of a measured peak value ofGm = magnetic constant when the element of force, dF, of exciting current, and thus equal to the value H8max. a current element I1dl1 on another current element magnetic field strength, biasing, Hb—the algebraic mean I2dl2 is at a distance r, value of the magnetic field strength in a magnetic materialr1 = unit vector in the direction from dl1 to dl2, and that is subjected simultaneously to a constant magnetizingn = dimensionless factor. The symbol n is unity in field and a periodically varying magnetizing field. unrationalized systems and 4p in rationalized sys- NOTE 54—The biasing magnetizing field and the biased magnetic tems. induction are corresponding coordinates of a single point on the B-H plane but not necessarily on the normal induction curve. NOTE 49—The numerical values of Gm depend upon the system of unitsused. In the cgs-emu system of units, Gm = 1, in the SI system, NOTE 55—The biasing magnetic field strength, Hb, is equal to theGm = 4p 3 10−7 H/m. applied constant magnetizing field only when the applied periodically NOTE 50—The magnetic constant expresses the ratio of magnetic varying magnetizing field is symmetrical.induction to the corresponding magnetizing force at any point in a vacuumand therefore is sometimes called the permeability of space, µv. magnetic field strength, incremental, HD—a value equal to NOTE 51—The magnetic constant times the relative permeability is one half the algebraic difference of the maximum andequal to the absolute permeability. minimum values of the magnetic field strength during a cycle in a magnetic material that is subjected simultaneously µabs 5 Gmµr to a biasing magnetic field strength and a symmetrical periodically varying magnetic field strength.magnetic excursion range, DB, DH—the excursion ranges Twice the incremental magnetic field strength is indicated equaling the algebraic differences between the upper and by the symbol DH. lower values of B, and between the upper and lower values Thus: of H, in a hysteresis or flux-current loop. HD 5 DH/2magnetic field of induction—the magnetic flux field induced in a region such that a conductor carrying a current in the magnetic field strength, maximum—(a) Hm—the maxi- region would be subjected to a mechanical force, and an mum value of H in a dc hysteresis loop. electromotive force would be induced in an elementary loop (b) Hmax—the maximum value of H in an ac flux-current rotated with respect to the field in such a manner as to loop. change the flux linkage. magnetic flux, f—the product of the magnetic induction, B,magnetic field strength, H—the magnetic vector quantity at a and the area of a surface (or cross section), A, when the point in a magnetic field which measures the ability of magnetic induction B is uniformly distributed and normal to electric currents or magnetized bodies to produce magnetic the plane of the surface. induction at the given point. f 5 BA NOTE 52—The magnetic field strength, H, may be calculated from the 9
  10. 10. A 340 – 03awhere: of magnetic nonuniformity associated with the magneticf = magnetic flux, discontinuities or inhomogeneities.B = magnetic induction, and NOTE 64—Magnetic particle inspection is an accepted method for theA = area of the surface. detection of defects. NOTE 56—If the magnetic induction is not uniformly distributed overthe surface, the flux, f, is the surface integral of the normal component of magnetic polarization, J—in the cgs-emu system of units, theB over the area. intrinsic induction divided by 4p is sometimes called mag- netic polarization or magnetic dipole moment per unit f5 ** B • dA s volume. NOTE 57—Magnetic flux is a scalar and has no direction. magnetic pole—the magnetic poles of a magnet are thosemagnetic flux density, B—that magnetic vector quantity portions of the magnet toward which or from which the which at any point in a magnetic field is measured either by external magnetic induction appears to converge or diverge, the mechanical force experienced by an element of electric respectively. current at the point, or by the electromotive force induced in NOTE 65—In the hypothetical case of a uniformly magnetized body of an elementary loop during any change in flux linkages with constant cross-sectional area, the poles would be located at its ends. the loop at the point. NOTE 66—By convention, the north-seeking pole is marked with an N, or + , or is colored red. NOTE 58—If the total flux, f is uniformly distributed and normal to asurface or cross section, then the magnetic induction is: magnetic pole strength, p—the magnetic moment divided by B 5 f/ A the distance between the poles. p 5 m/l where: B = magnetic induction, f = total flux, and where: A = area. p = pole strength, NOTE 59—Bin is the instantaneous value of the magnetic induction and m = magnetic moment, andBm is the maximum value of the magnetic induction. l = distance between the poles. magnetics (magnetism)—that branch of science which dealsmagnetic induction, B—an alternate term for magnetic flux with the laws of magnetic phenomena and their application density. to practice.magnetic lamination steel—a flat-rolled, low-carbon (usually below 0.06 %) steel containing 0.0 to 1.0 % silicon and up to magnetician—one skilled in the theory and practice of mag- 0.4 % aluminum and having similar core loss in all direc- netics. tions. magnetization, M—the component of the total magnetizingmagnetic line of force—an imaginary line in a magnetic field force that produces the intrinsic induction in a magnetic which at every point has the direction of magnetic induction material. at that point. M 5 ~B 2 GmH!/Gmµr 5 Bi/µabs NOTE 60—Extended lines of force must always form nonintersectingclosed loops. where:magnetic moment, m—a measure of the magnetic field M = magnetization, strength, H, produced at points in space by a plane current H = applied magnetizing force, Gm = magnetic constant, loop or a magnetized body. B = total magnetic induction, NOTE 61—The magnetic moment of a plane current loop is a vector, the µr = relative permeability,magnitude of which is the product of the area of the loop and the current; µabs = absolute permeability, andthe direction of the vector is normal to the plane of the loop in that Bi = intrinsic induction.direction around which the current has a clockwise rotation when viewedalong the vector. NOTE 67—The magnetization can be interpreted as the volume density NOTE 62—The magnetic moment of a magnetized body is the volume of magnetic moment.integral of the magnetization, M. NOTE 63—In the cgs-emu system of units, magnetic moment is usually magnetizing current, ac, Im—See current, ac magnetizing.defined as the pole strength multiplied by the distance between poles. This magnetizing force, H—an alternate term for magnetic fieldis sometimes called the magnetic dipole moment. strength.magnetic ohm—the unit of reluctance sometimes used in the magnetodynamic—the magnetic condition when the values of cgs-emu system of units. One magnetic ohm equals one magnetic field strength and induction vary, usually periodi- gilbert/maxwell or 4p/109 ampere-turns/weber. cally and repetitively, between two extreme limits.magnetic particle inspection method—a method for detect- magnetomotive force, ^—the line integral of the magnetizing ing magnetic discontinuities or inhomogeneities on or near field around any flux loop in space. the surface in suitably magnetized materials that uses finely ^ 5 *H·dl divided magnetic particles that tend to congregate in regions 10
  11. 11. A 340 – 03awhere: nonoriented electrical steel—a flat-rolled electrical steel^ = magnetomotive force, which has approximately the same magnetic properties in allH = magnetic field strength, and directions.dl = unit length along the loop. oersted, Oe—the unit of magnetic field strength in the cgs- emu system of units. One oersted equals a magnetic field NOTE 68—The magnetomotive force is proportional to the net currentlinked with any closed loop of flux or closed path. strength of 1 Gb/cm of flux path. One oersted equals 1000/4p or 79.58 ampere-turns per metre. See magnetic ^ 5 CNI field strength. paramagnetic material—a material having a relative perme-where: ability which is slightly greater than unity, and which is^ = magnetomotive force, practically independent of the magnetizing force.N = number of turns linked with the loop, permeability, ac, magnetic—a generic term used to representI = current in amperes, and a dynamic material property. It is expressed as the ratio ofC = constant whose value depends on the system of units. In the cgs-emu system of units, C = 4p/10. In the SI system, C = 1. the magnetic induction, B, to the magnetic field strength, H, that produced the induction. The value of H may bemagnetostatic—the magnetic condition when the values of calculated from several different component values of the magnetic field strength and induction are considered to exciting current. (See magnetic field strength, ac, and remain invariant with time during the period of measure- various permeabilities.) ment. This is often referred to as a dc (direct current) NOTE 71—The numerical value for any permeability is meaningless condition. unless the corresponding B or H excitation level is specified. Formagnetostriction—the change in dimensions of a body result- incremental permeabilities not only the corresponding dc B or H excitation ing from magnetization. level must be specified, but also the dynamic excursion limits of dynamicmass, active, m1—the effective value of mass, which may be excitation range (DB or DH). used with values of ,1, and A8 to evaluate a magnetic core as permeability, ac, rms, impedance, µz—the ratio of the though it has an equivalent uniform flux path having the measured peak value of magnetic induction, B, to the same induction at all points. apparent magnetic field strength, Hz, calculated from the rmsmass, total, m—the actual mass of a magnetic core. value of the total exciting current.maxwell, f—the unit of magnetic flux in the cgs-emu system NOTE 72—The value of the current used to compute Hz is obtained by of units. One maxwell equals 10−8 weber. See magnetic multiplying the measured value of rms exciting current by 1.414. This flux. assumes that the total exciting current is magnetizing current and is NOTE 69— sinusoidal. e 5 2Ndf/dt 3 1028 permeability, ac, inductance, µL—the value developed from the measured inductive component of the electrical circuitwhere: for a material in an SCM condition, the permeability ise = induced instantaneous emf in volts, evaluated from the measured inductive component of thedf/dt = time rate of change of flux in maxwells per second, electrical circuit representing the magnetic specimen. This and circuit is assumed to be composed of paralleled linearN = number of turns surrounding the flux, assuming inductive and resistive elements, vL1 and R1. each turn is linked with all the flux. permeability, ac, peak, µp—the ratio of the measured peak value of magnetic induction to the peak value of themeasurement accuracy—the numerical or percentage devia- magnetic field strength, Hp, calculated from the measured tion of a measured value (or a value computed from one or peak value of the exciting current. more measurements) from its true value or from some permeability, ideal, µa—the ratio of the magnetic induction to absolute or standardized value. This deviation may depend the corresponding magnetic field strength after the material upon the procedures used and is caused chiefly by systematic has been simultaneously subjected to a value of ac magne- errors in the calibrations of the equipment used, which tizing field approaching saturation superimposed on a given errors, if known, may be removed from the measured data to dc magnetizing field, and the ac magnetizing field has enhance the accuracy of the measured or computed value. thereafter been gradually reduced to zero. The resulting idealNéel wall—in a thin magnetic film (less than about 10−6 cm permeability is thus a function of the incremental field and thick for iron), a domain wall in which the magnetic moment residual strongly polarized domains that remain after the ac at any point is substantially parallel to the film surface. See field is reduced to zero. also domain wall. NOTE 73—Ideal permeability, sometimes called anhysteretic permeabil-nonmagnetic—a relative term describing a material which, for ity, is principally significant to feebly magnetic material and to the practical purposes, may be considered to have a relative Rayleigh range of soft magnetic material. permeability close to unity. permeability, ac, impedance, incremental, µD z—the value of NOTE 70—Certain materials may be nonmagnetic only under limited impedance permeability obtained when ac excitation isconditions. superimposed on a dc excitation. 11
  12. 12. A 340 – 03apermeability, ac, inductance, incremental, µDL—the value of change in magnetic field strength when the mean induction inductance permeability, µL, obtained when the ac excitation differs from zero. is superimposed on a dc excitation. permeability, incremental, µD—the ratio of the change ofpermeability, initial dynamic, µ0d—the limiting value of each magnetic induction, B, to the corresponding change in of the various ac permeabilities reached in a magnetic magnetic field strength, H, under dc biasing conditions and material as the magnetizing current is first raised to a when B is not equal to zero. This value is also the slope of moderate value then is progressively and gradually reduced a straight line joining the excursion limits of an incremental to a zero value. See initial inductance. hysteresis loop. NOTE 74—This same value, µ0d, is also equal to the initial values of NOTE 81—When the change in H is reduced to zero, the incrementalboth impedance permeability, µz, and peak permeability, µp. permeability, µD, becomes the reversible permeability, µrev.permeability, instantaneous—(Coincident with Bmax), µt— permeability, initial, µ0—the limiting value approached by with SCM excitation, the ratio of the maximum induction the normal permeability as the applied magnetic field Bmax to the instantaneous magnetic field strength, Ht, which strength, H, is reduced to zero. The permeability is equal to is the value of apparent magnetic field strength, H8, deter- the slope of the normal induction curve at the origin of linear mined at the instant when B reaches a maximum. B and H axes.permeability, dc, µ—a generic term used to represent a permeability, intrinsic, µi—the ratio of the calculated value of number of magnetostatic material properties. The value intrinsic induction Bi, to the corresponding magnetic field represented is the ratio of the induction, B, to the dc strength, H. magnetic field strength, H, producing magnetic flux under NOTE 82—See definition of susceptibility. the specific magnetizing conditions. permeability, maximum, µm—the highest value of permeabil- NOTE 75—The magnetic constant Gm is a scalar quantity differing invalue and uniquely determined by each electromagnetic system of units. ity achieved when the magnetic material is subjected to aIn the cgs–emu system of units, Gm is 1 gauss/oersted, and in the SI symmetrically cyclically magnetized condition.system, Gm = 4p 3 10−7 H/m. NOTE 83—Under dc test conditions the maximum permeability, µm, is NOTE 76—Relative permeability is a pure number which is the same in the highest value of normal permeability µ, developed by the magneticall unit systems. The value and dimension of absolute permeability material.depends on the system of units used. NOTE 84—Under ac test conditions, the maximum permeability is the NOTE 77—For any ferromagnetic material permeability is a function of highest value of ac permeability achieved under symmetrically cyclicallythe degree of magnetization. However, initial permeability, µ0, and magnetized conditions and with no biasing magnetic field in the magneticmaximum permeability, µm, are unique values for a given specimen under material.specified conditions. NOTE 78—Except for initial permeability, µ0, a numerical value for any permeability, normal, dc, µ—the ratio of any magneticof the dc permeabilities is meaningless unless the corresponding B or H induction, B, to the corresponding dc magnetic field strength,excitation level is specified. H, when the magnetic material has been subjected to SCM NOTE 79—For the incremental permeabilities, µD and µDi, a numerical conditions.value is meaningless unless both the corresponding values of meanexcitation level (B or H) and the excursion range (DB or DH) are specified. permeability, relative, µr—the ratio of the absolute perme- ability of a material to the magnetic constant Gm, giving apermeability, dc, absolute, µabs—the ratio of the total induc- pure numeric parameter. tion, DB, to the dc magnetic field strength, DH, which NOTE 85—In the cgs-em system of units, the relative permeability is produced it. Also described as: numerically the same as the absolute permeability. µabs 5 Gm 1 µi 5 Gm·µr permeability, dc, reversible, µrev—the ratio of magneticpermeability, differential, µd—the ratio of an increment of induction, DB, to the dc magnetic field strength increase, induction, DB, to an increment of magnetic field strength, DH, when the magnetic field strength is first established at a DH, for any point on a dc hysteresis loop. It is also the value, H, then reduced by a small increment H, and then absolute slope (DB/DH) of the curve at any point on the reestablished to the value, H. normal magnetizing curve. permeability, unoccupied space, µv—the permeability of space (vacuum), identical with the magnetic constant, Gm. NOTE 80—For a symmetrical series circuit in which each componenthas the same cross-sectional area, reluctance values add directly giving: permeance, 3—the reciprocal of the reluctance of a magnetic circuit. ,1 1 ,2 1 ,3 1 ···· power factor, magnetic, cos g—(a) the cosine of the angle µeff 5 , ,2 ,3 1 between vectors representing the rms values of the applied µ 1 µ 1 µ 1 ···· 1 2 3 voltage of a circuit and the current in circuit. For a symmetrical parallel circuit in which each component has thesame flux path length, permeance values add directly giving: (b) the ratio of the active (real) power to the apparent power in an ac circuit. µ1A1 1 µ2A2 1 µ3A3 1 ···· µeff 5 power, reactive (quadrature), Pq—the product of the rms A1 1 A2 1 A3 1 ···· current in an electrical circuit, the rms voltage across thepermeability, incremental intrinsic, µDi—the ratio of the circuit, and the sine of the angular phase difference between change in the intrinsic induction Bi to the corresponding the current and the voltage. 12