The value (BH)max at which the magnitude of the product of flux density B and field H is greatest on the demagnetization curve of a permanent magnet. In kJ/m³, it measures a magnet's strength.
Japanese name: 最大エネルギー積
Maximum energy product appears in 2 practice questions across 1 topic, including Magnetic materials.
Field: Magnetic materials
Permanent magnets are usually used to create a field in an air gap. Ignoring leakage, the magnet volume needed to create a field of flux density Bg in a gap of volume Vg is Vm = Bg²Vg/(µ₀|BH|), where |BH| is the magnitude of the product of B and H at the magnet's operating point. So using the magnet at a point of large |BH| keeps it small, and the maximum of this product is (BH)max. Besides kJ/m³, the CGS unit MGOe is also used, with 1 MGOe being about 7.96 kJ/m³. It is the value most often compared in discussions of making magnets smaller or raising motor output.
The operating point of a magnet is the intersection of the demagnetization curve with a straight line (the permeance line) set by the shapes of the magnet and gap. The permeance coefficient Pc = −B/(µ₀H), which expresses the slope of this line, becomes small when the demagnetizing field is large, as when a thin plate magnet is magnetized through its thickness. For an ideal magnet with a straight demagnetization curve, |BH| is largest at the point where B = Br/2 (Pc = 1), giving (BH)max = Br²/(4µ₀). Estimating the upper limit with this formula, Br = 1.6 T gives about 510 kJ/m³ (about 64 MGOe), close to the theoretical limit for Nd₂Fe₁₄B, the main phase of neodymium magnets.
(BH)max is usually given at room temperature, and performance at high temperature and resistance to demagnetization must be judged by other indicators. As temperature rises, remanence and coercivity fall, and magnets with a small intrinsic coercivity HcJ are partly demagnetized irreversibly by reverse fields or heat. So even with a large (BH)max, grades with a large HcJ are chosen for motors used at high temperature. Sm-Co magnets fall short of neodymium magnets in (BH)max, but their properties change little with temperature, so they are used in high-temperature applications. Price, susceptibility to rust and the supply of resources also influence the actual choice.
(BH)max grew throughout the 20th century each time a new magnet material appeared. In Japan, Kotaro Honda's KS steel (1917) and Tokushichi Mishima's MK steel (1931) are well known, and alnico, ferrite and Sm-Co magnets followed. In 1982 Masato Sagawa and colleagues developed sintered Nd-Fe-B magnets, and some commercial products today exceed about 400 kJ/m³. As a guide to typical values, ferrite magnets give about 10 to 40 kJ/m³, Sm-Co magnets about 130 to 250 kJ/m³ and sintered neodymium magnets about 250 to 440 kJ/m³, and each is chosen according to the demands of the application.
Answer: A. About 390 kJ/m³
On the straight line in the second quadrant, the magnitude of the product of B and H, |BH| = (Br + µ₀H)(−H), is greatest at H = −Br/(2µ₀), B = Br/2, giving (BH)max = Br²/(4µ₀). Substituting values, 1.40²/(4 × 4π×10⁻⁷) = 1.96/(5.03×10⁻⁶) ≈ 3.9×10⁵ J/m³, about 390 kJ/m³ (about 49 MGOe). About 1560 kJ/m³ multiplies the two ends of the line, Br and Br/µ₀, and about 780 kJ/m³ divides by 2 only once. The theoretical upper limit estimated by the same formula from the saturation magnetization of Nd₂Fe₁₄B (about 1.6 T) is about 510 kJ/m³, and high-performance commercial neodymium magnets reach about 80% of it (about 400 to 440 kJ/m³).
1 MGOe is about 7.96 kJ/m³. For example, 50 MGOe is about 398 kJ/m³, and dividing a value in kJ/m³ by about 8 gives the approximate MGOe. MGOe is the megagauss-oersted of the CGS system and is still widely used in magnet catalogs.
For the same shape and size, a magnet with a larger (BH)max can generally create a stronger field. But holding force varies greatly with the magnet's shape, the direction of magnetization, the thickness of the iron it attracts and the gap between them, and is not set by (BH)max alone. Making a magnet thin can lower the operating point through the demagnetizing field, so its performance is not fully used.
Yes. As temperature rises the remanence falls, so (BH)max also becomes smaller. Neodymium magnets show a relatively large drop with temperature, while Sm-Co magnets show a small one. In addition, insufficient coercivity causes irreversible demagnetization at high temperature, so the demagnetization curve at the service temperature should be checked.
However, the magnetic moments of Dy and Tb couple antiparallel to those of Fe, so the more is added, the lower the saturation magnetization, and the remanent flux density and maximum energy product actually decrease.
What is the main purpose of adding Dy or Tb to neodymium ma…Saturation magnetization Curie temperature Magnetocrystalline anisotropy Coercivity Domain wall Eddy-current loss Ferrimagnetism Magnetic domain Superparamagnetism