Magnetic materials

On the demagnetization curve of a permanent magnet, let the magnitude of the reverse field that brings the flux density B to zero be the coercivity HcB, and the magnitude of the reverse field that brings the magnetization M to zero be the intrinsic coercivity HcJ. From the relation B = µ₀(H + M), which relationship between them is correct?

  1. AHcJ ≥ HcB
  2. BHcJ ≤ HcB
  3. CAlways HcJ = HcB, regardless of the material
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Answer: A. HcJ ≥ HcB

When B reaches zero at a reverse field H = −HcB, B = µ₀(H + M) gives M = HcB > 0, so the magnetization is still positive. Bringing M to zero requires an even stronger reverse field, so HcJ ≥ HcB. The options HcJ ≤ HcB and always equal are therefore wrong. Also, in a reverse field M does not exceed the remanent magnetization, so HcB cannot exceed Br/µ₀. In materials with a very large HcJ, such as neodymium magnets, HcB levels off near this upper limit of Br/µ₀. Whether a magnet resists demagnetization at high temperature or in a strong reverse field is judged by HcJ, which shows whether the magnetization itself reverses. In soft magnetic materials with small coercivities, the difference between the two is negligibly small.

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  1. For an ideal permanent magnet whose demagnetization curve is the straight line B = Br + µ₀H (with a sufficiently large HcJ) and whose remanent flux density is Br = 1.40 T, which value is closest to the maximum energy product (BH)max? Take µ₀ = 4π×10⁻⁷ H/m.
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