A magnetic material has a hysteresis loop area of 0.4 J for each cycle. If the material is subjected to a frequency of 40 Hz, what is the total hysteresis loss per second?
16 W
Hysteresis loss arises when a ferromagnetic material is repeatedly magnetised and demagnetised by an alternating field. The magnetic domains lag behind the applied field, and the energy spent re-aligning them each cycle is dissipated as heat. Graphically, this wasted energy per cycle equals the area enclosed by the B–H hysteresis loop.
To convert energy-per-cycle into power (energy per second), multiply by how many cycles occur each second — that is, the frequency:
Ph = Wh × f
- Wh = loop area = energy loss per cycle = 0.4 J/cycle
- f = frequency = 40 Hz = 40 cycles per second
Therefore:
Ph = 0.4 × 40 = 16 W
Note that hysteresis loss is directly proportional to frequency (for a fixed loop area), so doubling the frequency would double the loss. The other values (20 W, 12 W, 10 W) do not result from the straightforward product of loop area and frequency and would require either a different loop area or a different frequency; with the given data, 16 W is the only consistent answer.
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