Question

Draw a neat diagram of cycle of magnetisation and explain coercivity and residual magnetisation and explain why area enclosed for soft iron is less than for steel.

Accepted Answer

Hysteresis Curve : When a ferromagnetic substance is placed in a magnetic field, it is magnetised by induction. If we vary the magnetic intensity $H$ of the magnetising field, the intensity of magnetisation $M$ and the magnetic flux density $B$ in the (ferromagnetic) substance do not vary linearly with $H .$ In other words, the susceptibility $X_{m} (= M / H)$ and the permeability $μ (= B / H)$ of the substance are not constants, but vary with $H$ and also depend upon the past history of the substance.

The variation in $M$ with variation in $H$ is shown in Fig. 13. The point $O$ represents the initial demagnetised state of the substance $(M = 0)$ and a zero magnetic intensity $(H = 0)$ . As $H$ is increased, $M$ increases non-uniformly along OA. At the substance acquires a state of magnetic saturation. Any further increase in $H$ does not produce any increase in $M$

If now the magnetising field $H$ is decreased, the magnetisation $M$ of the substance also decreases following a new path $AB$ (not the original path $AO$ ). Thus, $M$ lags behind $H .$ When $H$ becomes zero, $M$ still has a value equal to $OB .$ The magnetisation remaining in the substance when the magnetising field is reduced to zero is called the “residual magnetism”. The power of retaining this magnetism is called the “retentivity” or the “remanence” of the substance. Thus, the retentivity of a substance is a measure of the magnetisation remaining in the substance when the magnetising field is removed. In Fig. 13, OB represents the retentivity of the substance.

If now the magnetising field $H$ is increased in the reverse direction, the magnetisation $M$ decreases along $BC,$ still lagging behind $H$ , until it becomes zero at $C$ where $H$ equals $OC .$ . The value $OC$ of the magnetising field is called the “coercive force” or “coercivity” of the substance. Thus, the coercivity of a substance is a measure of the reverse magnetising field required to destroy the residual magnetism of the substance.

.As $H$ is increased beyond $OC$ , the substance is increasingly magnetised in the opposite direction along $CD .$ At $D$ the substance is again magnetically saturated.

By taking $H$ back from its maximum negative value (through zero) to its original maximum positive value, a symmetrical curve $DEFA$ DEFA is obtained. At points $B$ and $E$ where the substance is magnetised in the absence of any external magnetising field, it is said to be a “permanent magnet”.

It is thus found that the magnetisation $M$ (and also the magnetic flux density $B$ ) always lags behind the magnetising field $H$ . The lagging of $M$ (or of $B$ ) behind $H$ is called “hysteresis. The closed curve $ABCDEFA$ which represents a cycle of magnetisation of the substance is known as the “hysteresis curve (or loop)” of the substance. On repeating the process, the same closed curve is traced again but the portion $OA$ is never obtained.

Hysteresis Loss : a ferromagnetic substance consists of local regions called ‘domains’, each of which is spontaneously magnetised. In an demagnetised substance the directions of magnetisation in different domains are different so that, on an average, the resultant magnetisation is zero.

When we magnetise the substance by placing it in an external magnetising field, then those domains which are favourably oriented with respect to the external field grow in size and also each domain rotates so that its direction of magnetisation becomes aligned with the field direction. During this process energy is taken by the substance. When the external field is removed, the domain boundaries do not move completely back to their original positions, that is, the substance retains some magnetisation (hysteresis effect). Therefore, the energy supplied to the substance during magnetisation is not fully recovered. The balance of energy left in the substance is lost as heat. This is called ‘hysteresis loss’.

It can be proved that the energy lost per unit volume of a substance in a complete cycle of magnetisation is equal to the area of the hysteresis loop (M-H curve).

This knowledge has a practical application. On seeing the $M - H$ loops of various ferromagnetic materials we can select the one which gives minimum hysteresis loss when put to a cycle of magnetisation. This material will be most suitable for constructing the cores of the transformers and of the armatures of dynamos and motors. Besides this, an idea of the other magnetic properties of the material such as retentivity and coercivity can be obtained from the hysteresis curve. This helps us in selecting the proper magnetic material for a particular purpose.

A comparison of the magnetic properties of ferromagnetic substances can be made by the comparison of the shapes and sizes of their hysteresis loops. In Fig. 14, are shown hysteresis loops of soft iron and steel for the same values of $M$ $H$ . We can draw following conclusions regarding the magnetic properties of these substances from these loops

(i) The retentivity of soft iron $(OB')$ is greater than the retentivity of steel $(OB) .$
(ii) The coercivity of soft iron $(OC)$ is less than the coercivity of steel $(OC) .$
(iii) The hysteresis loss in soft iron is smaller than that in steel (because the area of the soft-iron loop is smaller than the area of steel loop).
(iv) Curves between magnetic flux density $B$ and magnetising field $H$ would reveal that the permeability of soft-iron is greater than that of steel.

Kumar Mittal Solutions for Exercise 1: QUESTIONS

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