Question

Figure 32-25 represents three rectangular samples of a ferromagnetic material in which the magnetic dipoles of the domains have been directed out of the page (encircled dot) by a very strong applied field B₀ . In each sample, an island domain still has its magnetic field directed into the page (encircled X ). Sample 1 is one (pure) crystal. The other samples contain impurities collected along lines; domains cannot easily spread across such lines.

The applied field is now to be reversed and its magnitude kept moderate. The change causes the island domain to grow. (a) Rank the three samples according to the success of that growth, greatest growth first. Ferromagnetic materials in which the magnetic dipoles are easily changed are said to be magnetically soft; when the changes are difficult, requiring strong applied fields, the materials are said to be magnetically hard. (b) Of the three samples, which is the most magnetically hard?

Short answer

1. The rank of the samples of a ferromagnetic material according to the growth of the domains is sample 1, sample 3, and sample 2.
2. Sample 2 is magnetically hard.

Step-by-step solution

Given

The samples have domains with different directions of the dipoles and with some impurities collected along the lines.

Determining the concept

A ferromagnetic material has a net dipole moment. When it is placed in an external field, the dipoles tend to align in the direction of the external field. So when the direction of the external field is changed, they tend to realign themselves and thus exhibit the domain structure.

(a) Determining the rank of the samples of a ferromagnetic material according to the growth of the domain

A ferromagnetic substance has regions in which the directions of the dipole moments are different. The regions are called domains. The domains are such that there is a net magnetic dipole moment of the sample. When the sample is placed in an external magnetic field, the domains align themselves along the direction of the external magnetic field.

This realignment of the domains is easier and faster if the domains with different orientations are less and smaller in size and also if the impurity of the sample is less. For sample 1, this realignment is the fastest as it has no impurity.

For sample 3, the growth ofthedomain is slightly slower as the sample has some amount of impurity.

For sample 2, the amount of impurity isthelargest among the three. Hence its domain growth istheslowest.

Therefore, the rank of the samples of a ferromagnetic material according to the growth of the domains is sample 1, sample 3, and sample 2.

(b) Determining the sample that is magnetically hard

When the direction of the external magnetic field is changed, sample 2 will betheslowest inthegrowth of the domains. Hence it is the most magnetically hard sample.

Therefore, sample 2 is magnetically hard.

A ferromagnetic sample has net dipole moment, but it may have regions of different dipole orientations. These all domains tend to align themselves along the direction of the external field. The ease of realignment decides the rate of domain growth and whether the sample is magnetically hard or soft.