Question

Identify the statement that is not true for ferromagnetic material

• A. They have large magnetic susceptibility
• B. They have a fixed value of relative permeability
• C. Energy loss is proportional to the area of the hysteresis loop
• D. Above curie temperature, they lose their non-linearity property

Hint:

Always remember that the relative permeability $\mu_r$ of a ferromagnetic substance is a differential quantity $\mu_r = \frac{1}{\mu_0}\frac{dB}{dH}$ rather than a single static scalar number. It reaches its peak value at the steepest part of the magnetization curve and drops significantly near saturation.

Answer 1

The Correct Option is B

Concept: Ferromagnetic materials are substances that exhibit strong magnetic properties due to the alignment of their constituent atomic magnetic dipoles into regions called domains. The relation between the magnetic flux density $B$ and the magnetic field intensity $H$ in these materials is profoundly non-linear, as described by a hysteresis loop. Let us analyze the foundational physical laws governing these properties:
• Magnetic Susceptibility ($\chi_m$): This parameter quantifies how easily a material becomes magnetized when exposed to an external field. For ferromagnetic materials, $\chi_m$ is exceptionally large and positive, often ranging from $10^2$ to $10^5$.
• Relative Permeability ($\mu_r$): It is defined via the relationship $B = \mu_0 \mu_r H$. Because the $B$-$H$ curve is non-linear and exhibits saturation and hysteresis, the ratio $\frac{B}{\mu_0 H}$ changes continuously depending on the history and strength of the applied magnetic field intensity $H$. Hence, $\mu_r$ is a function of $H$ and is not constant.
• Hysteresis Energy Loss: During a complete cycle of magnetization and demagnetization, the energy dissipated per unit volume per cycle is precisely equal to the enclosed area of the $B$-$H$ hysteresis loop: \[ W = \oint H \cdot dB \]
• Curie Temperature ($T_C$): Below $T_C$, the material is ferromagnetic and highly non-linear. Above $T_C$, thermal agitation completely disrupts the domain alignment, causing the material to transition into a paramagnetic state. In this paramagnetic phase, it obeys the linear Curie-Weiss law: \[ \chi_m = \frac{C}{T - T_C} \] As a result, it loses its non-linear ferromagnetic behavior. Step-by-step Evaluation of Options:
• Statement 1: "They have large magnetic susceptibility" is entirely true. Ferromagnetic domains align strongly with external fields, generating enormous internal magnetization.
• Statement 2: "They have a fixed value of relative permeability" is false. Because of the non-linear nature of the $B$-$H$ curve, $\mu_r$ depends dynamically on the current state of magnetization and varies widely throughout the loop.
• Statement 3: "Energy loss is proportional to the area of the hysteresis loop" is completely true, aligning with Steinmetz's principles of magnetic core losses.
• Statement 4: "Above curie temperature, they lose their non-linearity property" is completely true since they behave as linear paramagnetic substances for temperatures $T > T_C$. Thus, the statement that is not true is Option (2).