Table 8.1 Magnetic quantities and their units. Magnetic quantity Symbol Definition Units Comment

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1 Table 8.1 Magnetic quantities and their units. Magnetic quantity Symbol Definition Units Comment Magnetic field; magnetic induction B F = qv! B T = tesla = webers m -2 Produced by moving charges or currents and acts on moving charges or currents. Magnetic flux "# $" = B normal $A Wb = $" is flux through $A and B normal is normal weber to $A. Total flux through any closed surface is zero. Magnetic dipole % m # % m = I A A m 2 Experiences a torque in B and a net force in moment a nonuniform B. Bohr magneton &# & = e!/2m e. A m 2 or Magnetic moment due to the spin of the J T -1 electron. & = 9.27!10-24 A m 2 Magnetization vector M Magnetic moment per unit volume A m -1 Net magnetic moment in a material per unit volume Magnetizing field; H H = B/% o M A m -1 H is due to external conduction currents Magnetic field only and is the cause of B in a material. intensity Magnetic ' m M = ' m H None Relates the magnetization of a material to susceptibility the magnetizing field H. Absolute % o c = [( o % o ] -1/2 H m -1 = A fundamental constant in magnetism. In permeability Wb m -1 A -1 free space % o = B/H. Relative % r % r = B / (% o H). None permeability Magnetic %# % = % o % r H m -1 Not to be confused with magnetic moment. permeability Inductance L L = " )otal / I H (henries) Total flux threaded per unit current. Magnetostatic E vol de vol = H db J m -3 de vol is the energy required per unit volume energy density in changing B by db.

2 Table 8.2 Classification of magnetic materials. Type ' m (typical values) ' m vs. T Comment and examples Negative and small T independent Atoms of the material have closed shells. Organic materials, e.g. many polymers; covalent solids, Diamagnetic ( 10-6 ) e.g. Si, Ge, diamond; some ionic solids, e.g. alkalihalides, some metals e.g. Cu, Ag, Au. Negative and Below a critical Superconductors Paramagnetic Ferromagnetic Antiferromagnetic Ferrimagnetic large ( 1) small, * ) small (10-5 ) very large small very large temperature Independent of T Curie or Curie-Weiss law ' m = C / (T T C ) Ferromagnetic below and paramagnetic above the Curie temperature Antiferromagnetic below and paramagnetic above the Neel temperature Ferrimagnetic below and paramagnetic above the Curie temperature Due to the alignment of spins of conduction electrons. Alkali and transition metals. Materials in which the constituent atoms have a permanent magnetic moment, e.g. gaseous and liquid oxygen, ferromagnets (Fe), antiferromagnets (Cr) and ferrimagnets (Fe 3 O 4 ) at high temperatures. May possess a large permanent magnetization even in the absence of an applied field. Some transition and rare earth metals, Fe, Co, Ni, Gd, Dy Mainly salts and oxides of transition metals e.g. MnO, NiO, MnF 2, and some transition metals, + Cr, Mn. May possess a large permanent magnetization even in the absence of an applied field. Ferrites.

3 Table 8.3 Properties of the ferromagnets Fe, Co, Ni and Gd. Fe Co Ni Gd Crystal structure BCC HCP FCC HCP Bohr magnetons per atom M sat (0) (MA m -1 ) B sat = % o M sat T C 770,C 1043 K 1127,C 1400 K 358,C 631 K 16,C 289 K

4 Table 8.4 Selected soft materials and some typical values and applications (W h is the hysteresis loss, energy dissipated per unit volume per cycle in hysteresis losses, J m -3 cycle -1, typically at B m = 1 T). Magnetic Material IDEAL SOFT Iron (commercial grade, 0.2% impurities) Silicon iron (Fe: 2-4%Si) Supermalloy (79Ni-15Fe- 5Mo-0.5Mn) 78 Permalloy (78.5%Ni- 21.5%Fe) Glassy metals Fe-Si-B Ferrites Mn-Zn ferrite % o H c B sat B r % ri % rmax W h Typical applications 0 Large 0 Large Large 0 Transformer cores, inductors, electrical machines, electromagnet cores, relays, magnetic recording heads etc. < < Large eddy current losses. Generally not preferred in electrical machinery except in some specific applications (e.g., some electromagnets and relays) < Higher resistivity and hence lower eddy 4!10 5 current losses. Wide range of electrical machinery (e.g., transformers etc.) 2! < <0.5 High permeability, low loss electrical devices, e.g. specialty transformers, magnetic amplifiers 5! <0.1 8! <0.1 Low-loss electrical devices, audio transformers, HF transformers, recording heads, filters etc. 2! < Low-loss transformer cores <0.01 2!10 3 5!10 3 <0.01 HF low-loss applications. Low conductivity ensures negligible eddy current losses. HF transformers, inductors (pot cores, E and U cores etc.), recording heads.

5 Table 8.5 Hard magnetic materials and typical values. Magnetic Material % o H c B r (BH) max (kj m -3 ) Examples and Uses IDEAL HARD Large Large Large Permanent magnets in various applications Alnico (Fe-Al-Ni- Co-Cu) Wide range of permanent magnet applications Alnico (Columnar)) Strontium ferrite (anisotropic) dc motors, starter motors, loudspeakers, telephone receivers, various toys Rare earth cobalt e.g. Sm 2 Co 17 (sintered) Servo motors, stepper motors, couplings, clutches, quality audio headphones etc. NdFeB magnets Wide range of applications, small motors (e.g. in hand tools), walkman equipment, CD motors, MRI body scanners, computer applications Hard particles --Fe 2 O Audio and video tapes, floppy disks

6 Table 8.6 Selected examples of Type I and Type II superconductors. Critical fields are close to absolute zero (obtained by extrapolation). Type I for pure and clean elements. Type I Sn Hg Ta V Pb Nb T c (K) B c Type II Nb 3 Sn Nb 3 Ge Ba 2 x Br x CuO 4 Y-Ba-Cu-O YBa 2 Cu 3 O 7 Bi-Sr-Ca-Cu-O (Bi 2 Sr 2 Ca 2 Cu 3 O 10 ) Hg-Ba-Ca-Cu-O T c (K) B c2 (Tesla) at 0 K ~150 ~300 J c (A cm -2 ) at 0 K ~

7 Table 8.7 Selected examples of flexible magnetic storage media based on coatings of particulate mat Typical values. Particulate matter Typical application % o M r % o H c Comment --Fe 2 O 3 Audio tapes (Type I) Widely used particles --Fe 2 O 3 Floppy disk Co(--Fe 2 O 3 ) Video tape Cobalt impregnated --Fe 2 O 3 particles CrO 2 Audio tapes (Type II) More expensive than --Fe 2 O 3 CrO 2 Video tape Fe Audio tape (Type IV) High coercivity and magnetization. To avoid corrosion, the particles have to be treated (expensive)

8 Table 8.8 Selected examples of thin films in magnetic storage media; typical values. Thin Film Deposition % o M s % o H c Comment and typical or potential application Co-(Rare earth) Co-Cr alloys Co(--Fe 2 O 3 ) Sputtering in vacuum Sputtering in vacuum Sputtering in vacuum Longitudinal magnetic recording media. Hard disks Perpendicular magnetic recording media Longitudinal magnetic recording media. Co-Ni-P Electroplating Longitudinal magnetic recording media.