--- title: "Hysteresis loop energy, hard and soft magnetic materials" subject: "Electrical Machines I" chapter: 1 key: "semester_4/electrical_machines_i:hysteresis-area-energy-hard-soft" source: https://www.bctengineer.com/q/semester_4/electrical_machines_i/hysteresis-area-energy-hard-soft site: BCT Engineering --- # Hysteresis loop energy, hard and soft magnetic materials Electrical Machines I · Chapter 1: Magnetic Circuits and Induction - Asked in: 2073 Magh, 8 marks - Video: [What is Hysteresis Loop? | Hysteresis Loss Explained in Hindi | B-H Curve, Retentivity, Coercivity](https://www.youtube.com/watch?v=VCoDHTIWUaA) — Electrical Engineering MCQ's - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/electrical_machines_i/hysteresis-area-energy-hard-soft - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines_i/chapter-1 ## Question What do you understand by magnetic hysteresis? Prove that the area of hysteresis loop is proportional to the energy loss per unit volume. Differentiate between hard and soft magnetic materials. ## Short answer Magnetic hysteresis is the lag of B behind H during a magnetization cycle, forming a loop whose area equals energy lost per unit volume per cycle, given by ∮H dB. Soft magnetic materials have narrow loops with low coercivity and high permeability, used in transformer cores; hard materials have wide loops with high retentivity and coercivity, used for permanent magnets. ## Answer **Magnetic hysteresis** is the lagging of flux density B behind the magnetising force H when a ferromagnetic material is taken through a cycle of magnetisation. As a result the B–H curve forms a closed loop, and energy equal to its area is lost per cycle. #### Hysteresis loop ```text B | __ a b _|.-' / / | / c / | / --*-----/---+--/---*--- H / | / f / ___.|' d -' |e ``` ob = residual flux density (retentivity), oc = coercive force, a and d = positive and negative saturation. #### Proof: area ∝ energy loss per unit volume Ring: mean length $l$, area $A$, $N$ turns, current $i$. By Ampere's law $Hl = Ni$, so $i = Hl/N$. When B changes by $dB$ the induced emf is $e = NA\,dB/dt$. Energy supplied by the source in time $dt$: $$ \begin{aligned} dW &= e\,i\,dt = NA\frac{dB}{dt}\cdot\frac{Hl}{N}\,dt = (Al)\,H\,dB \end{aligned} $$ Per unit volume, $dw = H\,dB$. For one complete cycle $$ w = \oint H\,dB = \text{area of B–H loop} \quad (\text{J/m}^3) $$ The energy stored while B rises is only partly returned while B falls; the net amount, equal to the loop area, is converted into heat. Total hysteresis loss: $$ P_h = (\text{loop area}) \times V \times f \ \text{W} \approx \eta B_m^{1.6} f V $$ #### Hard and soft magnetic materials | Point | Soft magnetic material | Hard magnetic material | |---|---|---| | Loop shape | Narrow, tall | Wide, nearly square | | Hysteresis loss | Small | Large | | Coercivity | Low | High | | Retentivity | Low to moderate | High | | Permeability | High | Low | | Magnetise / demagnetise | Easily | With difficulty | | Uses | Transformer and machine cores, relays | Permanent magnets, meters, loudspeakers | | Examples | Silicon steel, CRGO, soft iron, ferrite | Alnico, ferrite magnets, NdFeB, carbon steel | Soft materials are chosen for ac machines because their small loop area gives low core loss; hard materials are chosen where the magnetism must be kept. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Magnetic hysteresis is: A. The lagging of B behind H in a ferromagnetic material B. The lagging of H behind B only in air C. The leakage of flux D. The heating of windings Answer: A. B lags H so the B-H curve forms a closed loop and its area is energy lost per cycle. (Key point: Hysteresis) 2. In the proof, energy per cycle per unit volume is: A. Integral of H dB over a cycle = loop area B. Integral of B dH over a cycle C. Maximum B only D. H x B at one point Answer: A. dw = H dB, and the cyclic integral is the loop area. (Key point: Proof step) 3. Soft magnetic materials have: A. Wide loop, high coercivity B. Narrow tall loop, low coercivity, high permeability C. Wide loop, high retentivity D. No hysteresis loss at all Answer: B. They magnetise and demagnetise easily with small loop area, so they suit machine cores. (Key point: Soft materials) 4. Which assignment of use is correct? A. Soft: permanent magnets; hard: transformer cores B. Soft: transformer cores; hard: permanent magnets (e.g. Alnico, NdFeB) C. Both: transformer cores D. Hard: relays Answer: B. Hard materials keep magnetism, soft materials give low core loss in ac machines. 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