Ferromagnetism — Question 2

Question 2

A model hysteresis loop distinguishes remanence from coercive field

A model major loop has increasing-field branch $M_\uparrow=M_s\tanh[(H-H_c)/H_0]$ and decreasing-field branch $M_\downarrow=M_s\tanh[(H+H_c)/H_0]$, with positive constants. These branches are phenomenological.

1. Find remanent M on each branch and the H values where M is zero.

2. At those zero-M points find B. Explain why the field that makes B zero generally differs from the field that makes M zero.

Question 2 - Solution

A model hysteresis loop distinguishes remanence from coercive field

(a) Method and calculation

$$\boxed{M_\downarrow(0)=M_s\tanh(H_c/H_0),\quad M_\uparrow(0)=-M_s\tanh(H_c/H_0)}.$$$$\boxed{M_\uparrow=0\text{ at }H=H_c;\quad M_\downarrow=0\text{ at }H=-H_c}.$$

(b) Interpretation and further calculation

$$B=\mu_0(H+M)\Rightarrow\boxed{B\big|_{M=0}=\pm\mu_0H_c\ne0}.$$$$\boxed{B=0\iff M(H)=-H},\quad\text{which is a different intersection.}$$

Physical check

Always specify whether a quoted coercivity refers to zero induction B or zero magnetization M.