Bate, G, Kryder, M.H. Magnetism and Magnetic Fields The Electrical Engineering Handbook Ed. Richard C. Dorf Boca raton crc Press llc. 2000
Bate, G., Kryder, M.H. “Magnetism and Magnetic Fields” The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000
36 Magnetism and Magnetic Fields 36.1 Magnetism Static Magnetic Fields. Time-Dependent Electric and Magnetic Fields. Magnetic Flux Density. Relative Permeabilities. Forces on a Moving Charge. Time-Varying Magnetic Fields. Maxwell ' Equations. Dia- and Paramagnetism.Ferromagnetism and Geoffrey Bate Ferrimagnetism. Intrinsic Magnetic Properties. Extrinsic Magnetic Properties. Amorphous Magnetic Materials 6.2 Magnetic Recording Fundamentals of Magnetic Recording. The Recording Mark H. Kryder Process. The Readback Process. Magnetic Recording Carnegie Mellon University Meda· Magnetic Recording heads· Conclusions 36.1 Magnetism Geoffrey bate Static Magnetic Fields To understand the phenomenon of magnetism we must also consider electricity and vice versa. A stationary electric charge produces, at a point a fixed distance from the charge, a static(i.e, time-invariant)electric field A moving electric charge, i.e., a current, produces at the same point a time-dependent electric field and a magnetic field, dH, whose magnitude is constant if the electric current, L, represented by the moving electric charge, is constant Fields from Constant Currents Figure 36. 1 shows that the direction of the magnetic field is perpendicular both to the current I and to the line, R, from the element dL of the current to a point, P where the magnetic field, dH, is being calculated or measured. dh =I dL x r/4Tr3 A/m when I is in amps and dL and r are in meters If the thumb of the right hand points in the direction of the current, then the fingers of the hand curl in the direction of the magnetic field. Thus, the stream lines of H, i.e. the lines representing at any point the direction of the H field, will be an infinite set of circles having the current as center. The magnitude of the field Ho /2R A/m. The line integral of H about any closed path around the current is H dL= I. This relationship lown as Ampere's circuital law) allows one to find formulas for the magnetic field strength for a variety of symmetrical coil geometries, e.g c 2000 by CRC Press LLC
© 2000 by CRC Press LLC 36 Magnetism and Magnetic Fields 36.1 Magnetism Static Magnetic Fields • Time-Dependent Electric and Magnetic Fields • Magnetic Flux Density • Relative Permeabilities • Forces on a Moving Charge • Time-Varying Magnetic Fields • Maxwell’s Equations • Dia- and Paramagnetism • Ferromagnetism and Ferrimagnetism • Intrinsic Magnetic Properties • Extrinsic Magnetic Properties • Amorphous Magnetic Materials 36.2 Magnetic Recording Fundamentals of Magnetic Recording • The Recording Process • The Readback Process • Magnetic Recording Media • Magnetic Recording Heads • Conclusions 36.1 Magnetism Geoffrey Bate Static Magnetic Fields To understand the phenomenon of magnetism we must also consider electricity and vice versa. A stationary electric charge produces, at a point a fixed distance from the charge, a static (i.e., time-invariant) electric field. A moving electric charge, i.e., a current, produces at the same point a time-dependent electric field and a magnetic field, dH, whose magnitude is constant if the electric current, I, represented by the moving electric charge, is constant. Fields from Constant Currents Figure 36.1 shows that the direction of the magnetic field is perpendicular both to the current I and to the line, R, from the element dL of the current to a point, P, where the magnetic field, dH, is being calculated or measured. dH = I dL 2 R/4pR3 A/m when I is in amps and dL and R are in meters If the thumb of the right hand points in the direction of the current, then the fingers of the hand curl in the direction of the magnetic field. Thus, the stream lines of H, i.e., the lines representing at any point the direction of the H field, will be an infinite set of circles having the current as center. The magnitude of the field Hf = I/2pR A/m. The line integral of H about any closed path around the current is rH · dL = I. This relationship (known as Ampère’s circuital law) allows one to find formulas for the magnetic field strength for a variety of symmetrical coil geometries, e.g., Geoffrey Bate Consultant in Information Storage Technology Mark H. Kryder Carnegie Mellon University
FIGURE 36.1 a current I flowing through a small segment dl of a wire produces at a distance r a magnetic field whose direction dH is perpendicular both to R and dL. At a radius, P, between the conductors of a coaxial cable I12πpA/ 2. Between two infinite current sheets in which the current, K, flows in opposite directions H=K×an where a. is the unit vector normal to the current sheets 3. Inside an infinitely long, straight solenoid of diameter d, having N turns closely wound h= Nilda/m 4. Well inside a toroid of radius p, having N closely wound turns H=N2rp·aA/m Applying Stokes' theorem to Ampere's circuital law we find the point form of the latter. V×H where J is the current density in amps per square meter. Time-Dependent Electric and Magnetic Fields A constant current I produces a constant magnetic field H which, in turn, polarizes the medium containing H. While we cannot obtain isolated magnetic poles, it is possible to separate the" poles"by a small distance to reate a magnetic dipole (i. e, to polarize the medium), and the dipole moment(the product of the pole strength and the separation of the poles) per unit volume is defined as the magnetization M. The units are emu/cc in the cgs system and amps per meter in the SI system of units. Because it is usually easier to determine the ma of a sample than to determine its volume, we also have a magnetization per unit mass, o, whose units are emu/g or Am /kg. The conversion factors between cgs and SI units in magnetism are shown in Table 36.1 The effects of the static and time-varying currents may be summarized as follows Static I。→[H]。→[M]。 Time-varying 山→[H]→[M]r where the suffixes"o"and"t"signify static and time-dependent, respectively e 2000 by CRC Press LLC
© 2000 by CRC Press LLC 1. At a radius, r, between the conductors of a coaxial cable Hf = I/2pr A/m 2. Between two infinite current sheets in which the current, K, flows in opposite directions H = K 2 an where an is the unit vector normal to the current sheets 3. Inside an infinitely long, straight solenoid of diameter d, having N turns closely wound H = NI/d A/m 4. Well inside a toroid of radius r, having N closely wound turns H = NI/2pr · af A/m Applying Stokes’ theorem to Ampère’s circuital law we find the point form of the latter. ¹ 2 H = J where J is the current density in amps per square meter. Time-Dependent Electric and Magnetic Fields A constant current I produces a constant magnetic field H which, in turn, polarizes the medium containing H. While we cannot obtain isolated magnetic poles, it is possible to separate the “poles” by a small distance to create a magnetic dipole (i.e., to polarize the medium), and the dipole moment (the product of the pole strength and the separation of the poles) per unit volume is defined as the magnetization M. The units are emu/cc in the cgs system and amps per meter in the SI system of units. Because it is usually easier to determine the mass of a sample than to determine its volume, we also have a magnetization per unit mass, s, whose units are emu/g or Am2 /kg. The conversion factors between cgs and SI units in magnetism are shown in Table 36.1. The effects of the static and time-varying currents may be summarized as follows: where the suffixes “o” and “t ” signify static and time-dependent, respectively. FIGURE 36.1 A current I flowing through a small segment dL of a wire produces at a distance R a magnetic field whose direction dH is perpendicular both to R and dL
TABLE 36.1 Units in Magnetism Symbol cgs Units x Factor SI units B=H+4TM Magnetic flux density B tesla(T), wb/m2 maxwell (Mx) webers(wb) magnetomotive force) UHM 10/4兀 (Oe) Magnetization(per volume) Magnetization(per mass Magnetic moment xKμμ sss xxxxxxxx dimensionless dimensionless 4π Wb/A·m Permeability(material) Wb/A Bohr m =0.927×10erg/Oex103 Am Demagnetizing factor n dimensionless 14 dimensionless tic flux density In the case of electric fields there is in addition to E an electric flux density field d, the lines of which be on positive charges and end on negative charges. D is measured in coulombs per square meter and is associated with the electric field E(V/m)by the relation D=EE E where e, is the permittivity of free space(E,=8.854 x 10-12 F/m)and E, is the(dimensionless)dielectric constant. For magnetic fields there is a magnetic flux density B(Wb/m2)=A,u, H, where u, is the permeability of free space(u,=4T X 10 H/m) andu, is the(dimensionless)permeability. In contrast to the lines of the D field, lines of B are closed, having no beginning or ending. This is not surprising when we remember that while lated positive and negative charges exist, no magnetic monopole has yet been discovered Relative permeabilities The range of the relative permeabilities covers about six orders of magnitude(Table 36. 2)whereas the range of dielectric constants is only three orders of magnitude Forces on a Moving Charge A charged particle, g, traveling with a velocity v and subjected to a magnetic field experiences a force This equation reveals how the Hall effect can be used to determine whether the majority current carriers sample of a semiconductor are(negatively charged) electrons flowing, say, in the negative direction or (positively charged)holes flowing in the positive direction. The(transverse)force( Fig. 36. 2)will be in the same direction in either case, but the sign of the charge transported to the voltage probe will be positive for holes and negative for electrons. In general, when both electric and magnetic fields are present, the force experienced by the carriers is given by F=q(E+v×B) The Hall effect is the basis of widely used and sensitive instruments for measuring the intensity of magnetic fields over a range of 10to2×10°A/m. e 2000 by CRC Press LLC
© 2000 by CRC Press LLC Magnetic Flux Density In the case of electric fields there is in addition to E an electric flux density field D, the lines of which begin on positive charges and end on negative charges. D is measured in coulombs per square meter and is associated with the electric field E (V/m) by the relation D = er eoE where eo is the permittivity of free space (eo = 8.854 ¥ 10–12 F/m) and er is the (dimensionless) dielectric constant. For magnetic fields there is a magnetic flux density B(Wb/m2 ) = mrmoH, where mo is the permeability of free space (mo = 4p 2 10–7 H/m) and mr is the (dimensionless) permeability. In contrast to the lines of the D field, lines of B are closed, having no beginning or ending. This is not surprising when we remember that while isolated positive and negative charges exist, no magnetic monopole has yet been discovered. Relative Permeabilities The range of the relative permeabilities covers about six orders of magnitude (Table 36.2) whereas the range of dielectric constants is only three orders of magnitude. Forces on a Moving Charge A charged particle, q, traveling with a velocity v and subjected to a magnetic field experiences a force F = qv 2 B This equation reveals how the Hall effect can be used to determine whether the majority current carriers in a sample of a semiconductor are (negatively charged) electrons flowing, say, in the negative direction or (positively charged) holes flowing in the positive direction. The (transverse) force (Fig. 36.2) will be in the same direction in either case, but the sign of the charge transported to the voltage probe will be positive for holes and negative for electrons. In general, when both electric and magnetic fields are present, the force experienced by the carriers is given by F = q (E + v 2 B) The Hall effect is the basis of widely used and sensitive instruments for measuring the intensity of magnetic fields over a range of 10–5 to 2 2 106 A/m. TABLE 36.1 Units in Magnetism Quality Symbol cgs Units 2 Factor = SI units B = H + 4pM B = mo(H + M) Magnetic flux density B gauss (G) 2 10–4 = tesla (T), Wb/m2 Magnetic flux F maxwell (Mx) 2 10–8 = webers (Wb) G · cm2 Magnetic potential difference (magnetomotive force) U gilbert (Gb) 2 10/4p = ampere (A) Magnetic field strength H oersted (Oe) 2 103 /4p = A/m Magnetization (per volume) M emu/cc 2 103 = A · m Magnetization (per mass) s emu/g 2 1 = A · m2 /kg Magnetic moment m emu 2 10–3 = A · m2 Susceptibility (volume) c dimensionless 2 4p = dimensionless Susceptibility (mass) k dimensionless 2 4p = dimensionless Permeability (vacuum) mo dimensionless 2 4p.10–7 = Wb/A · m Permeability (material) m dimensionless 2 4p.10–7 = Wb/A · m Bohr magneton mB = 0.927 2 10–20 erg/Oe 2 10–3 = Am2 Demagnetizing factor N dimensionless 2 1/4p = dimensionless
TABLE 36.2 Relative Permeability, H, of Some Diamagnetic, Material Na cygan(s t.p.) permalloy: 79% Ni, 15% Fe Permendur: 49% Fe, 49% Ca, 2%6V Source: F Brailsford, Physical Principles of Magnetism, London: Van Nos- and, 1966. With permission. (b) FIGURE 36.2 Hall effect. A magnetic field B applied to a block of semiconducting material through which a current I is flowing exerts a force F=VX B on the current carriers(electrons or holes)and produces an electric charge on the right face of the block. The charge is positive if the carriers are holes and negative if the carriers are electrons Time-Varying Magnetic Fields In 1831, 11 years after Oersted demonstrated that a current produced a magnetic field which could deflect a compass needle, Faraday succeeded in showing the converse effect-that a magnetic field could produce a current. The reason for the delay between the two discoveries was that it is only when a etic field is anging that an emf is produce dΦ e 2000 by CRC Press LLC
© 2000 by CRC Press LLC Time-Varying Magnetic Fields In 1831, 11 years after Oersted demonstrated that a current produced a magnetic field which could deflect a compass needle, Faraday succeeded in showing the converse effect—that a magnetic field could produce a current. The reason for the delay between the two discoveries was that it is only when a magnetic field is changing that an emf is produced. TABLE 36.2 Relative Permeability, mr , of Some Diamagnetic, Paramagnetic, and Ferromagnetic Materials Material mr Ms , A/m2 Diamagnetics Bismuth 0.999833 Mercury 0.999968 Silver 0.9999736 Lead 0.9999831 Copper 0.9999906 Water 0.9999912 Paraffin wax 0.99999942 Paramagnetics Oxygen (s.t.p.) 1.000002 Air 1.00000037 Aluminum 1.000021 Tungsten 1.00008 Platinum 1.0003 Manganese 1.001 Ferromagnetics Purified iron: 99.96% Fe 280,000 2.158 Motor-grade iron: 99.6% Fe 5,000 2.12 Permalloy: 78.5% Ni, 21.5% Fe 70,000 2.00 Supermalloy: 79% Ni, 15% Fe, 5% Mo, 0.5% Mn 1,000,000 0.79 Permendur: 49% Fe, 49% Ca, 2% V 5,000 2.36 Ferrimagnetics Manganese–zinc ferrite 750 0.34 1,200 0.36 Nickel–zinc ferrite 650 0.29 Source: F. Brailsford, Physical Principles of Magnetism, London: Van Nostrand, 1966. With permission. FIGURE 36.2 Hall effect. A magnetic field B applied to a block of semiconducting material through which a current I is flowing exerts a force F = V ¥ B on the current carriers (electrons or holes) and produces an electric charge on the right face of the block. The charge is positive if the carriers are holes and negative if the carriers are electrons. emf d d = - V F t