Question

The mass of a specimen of a ferromagnetic material is $0.5\text{kg}$ and its density is $8000{\text{kg/m}}^3$. What is the energy equivalent area of hysteresis loop of alternating magnetizing field of frequency $100\text{Hz}$, if the hysteresis loss per second is $240\times {10}^{-3}\text{J/s}$?

• A. $3.84{\text{J/m}}^3$
• B. $1.92{\text{J/m}}^3$
• C. $38.4{\text{J/m}}^3$
• D. $19.2{\text{J/m}}^3$

Answer 1

The correct option is C $38.4{\text{J/m}}^3$

Given,
$m=0.5\text{kg};\rho =8000{\text{kg/m}}^3;n=100\text{Hz}$

Hysteresis loss per second, $E=240\times {10}^{-3}\text{J/s}$

Area of hysteresis loop gives the loss of energy per unit volume of material in one cycle of magnetization and demagnetization.

So, total loss per unit time is,

$E=\text{Area}\times \text{volume}\times \text{Frequency}$

Substituting the values, we get,

$240\times {10}^{-3}=\text{Area}\times \frac{0.5}{8000}\times 100$

$\therefore \text{Area}=38.4{\text{J/m}}^3$

Hence, option $\left(C\right)$ is the correct answer.