# Magnetic hysteresis loop area meaning

Tags:
1. Sep 11, 2015

### EmilyRuck

Let's consider the Magnetic hysteresis loop of a certain material: this is an example. In many sites and books it is written that its area is proportional to the energy wasted as heat, so $A = kE_d$.
In particular, that area "is related to the amount of energy dissipation upon reversal of the field" (this is the source). I would like to ask some clarifications:

1) When exactly is that energy dissipated? When the impressed magnetic field $\mathbf{H}$ decreases from the saturation point or when $\mathbf{H}$ increases till the saturation point?
2) How can be circuitally represented that energy dissipation in the circuit of a transformer like this?
3) Maybe $E_d$ can be obtained as an integral. If $A = kE_d$, what are the steps needed to mathematically show this result and which is the meaning of $k$? (If a link is more convenient than directly typing the steps, it would be excellent as well)
I can't see how dimensionally can be obtained an energy quantity (Joule) from A/m ($\mathbf{H}$) and from Tesla ($\mathbf{B}$).

2. Sep 11, 2015

### Hesch

Magnetic energy density ( Ed ) = ½*B*H [ J/m3 ]. So Ed = 0 in b, c, e, f in the attached figure and has a max value i a, d.

If the area of the hysterisis curve = 0, no energy will be dissipated as per cycle.

Units: B*H = [N/(Am)] * [ A/m ] = [ N/m2 ] = Nm/m3 = [ J/m3 ]

3. Oct 7, 2015

Thank you!