Relation between Area under $I$-$H$ hysteresis Loop and $B$-$H$ hysteresis Loop [closed]

Question

If the area under the I-H hysteresis loop and B-H hysteresis loop are denoted by $A_1$and $A_2$ (The symbols have usual meaning as set in electromagnetics), then

1. $A_2=\mu_oA_1$

2. $A_2=A_1$

3. $A_1=\mu_oA_2$

4. $A_2=\mu_o^2A_1$

The correct answer for this problem is option 1) $\boxed{A_2=\mu_oA_1}$.

My doubt lies in the official solution provided to us.

I don't understand why is$\oint HdH=0$?

Answer 1

Since $\int H dH = \frac{1}{2}H^2$, we get $$ \oint HdH=\left[\frac{1}{2}H^2\right]_{H_1}^{H_2}+\left[\frac{1}{2}H^2\right]_{H_2}^{H_1}=0 $$ Am I right? I welcome anyone's criticism.