Magnetic theory

A body that attracts small pieces of iron and points towards north-south direction when suspended freely, is called a magnet. The end of a magnet pointing towards north is called the N-Pole while the other is called the S-Pole. Like poles of two magnets repel, while unlike poles attract, each other. The magnetism of the magnet is concentrated in the poles of the magnet. The two poles of a magnet cannot be separated from each other. If a magnet is broken into two pieces, two new magnets are obtained. Each new magnet has both the poles N-pole and a S-pole. This process may be repeated many times as desired but each time a magnet with both poles is obtained.

Induction and magnetic field

A magnetic field, like an electric field, can be represented by lines called lines of induction, whose direction at every point is that of the magnetic induction vector. The number of induction lines per unit area normal to the direction of the magnetic field is called the magnetic induction and is denoted by the letter B. The unit of induction in MKS system is Weber per square meter (Wb/m²) where one Weber is equal to one line of induction.

Similarly, in the CGS system, the unit of induction is Maxwell per square centimetre where one Maxwell is equal to one line of induction. Weber/m² is called a Tesla (T) and Maxwell/cm² is called a Gauss.

In a uniform magnetic field, where the magnetic induction vector has a constant magnitude, the lines are straight and equally spaced. If the pole pieces of an electromagnet are large and close together, there is a region between the poles where the magnetic field is approximately uniform. The total number of lines of induction threading through a surface is called the magnetic flux through the surface and is denoted by φ. In a special case where B is uniform and normal to a finite area A,

φ = B ● A (2.12)

where

φ = magnetic flux at surface B = flux density

A = area

Since B is in Wb/m² and A is in m², the flux is in Webers. Since the induction B at a point equals the flux per unit area, it is often referred to as the flux density.

The largest values of magnetic induction that can be produced in the laboratory are of the order 10Wb/m² or 10⁵ Gauss (1 Weber/m² = 10⁴ Gauss), while in the magnetic field of the earth the induction is only few hundredth thousandths of Weber per square meter or a few tenths of a Gauss.

Magnetic field is described as the area surrounding a magnet and can be shown by drawing imaginary lines of force to indicate the path that an isolated N pole would take if it were free to move. How close together the lines are drawn depends on the field strength. Lines of field around a bar magnet are as shown in FIG. 2.12.

FIG. 2.12. Magnetic fields of bar magnet.

Magnetic Permeability

Magnetic permeability is an intrinsic property of a material. It is the ability of a material to concentrate magnetic lines. It is denoted by the Greek letter µ. Any material that is easily magnetized, such as soft iron, concentrate the magnetic flux. This is the main feature separating magnetic materials from nonmagnetic materials. The magnetic permeability is equal to the induced magnetic flux density B divided by external magnetic field intensity (magnetizing force) H. i.e.

H

= B

µ ^{, (2.13)}

where

µ = magnetic permeability

For air, vacuum, and non-magnetic materials the µ is constant. For air and vacuum the value

The µr is a dimensionless quantity because it is a ratio comparing two flux densities. Since air, vacuum and any other non-magnetic material cannot affect a magnetic field by induction, they all have the µr equal to 1. For magnetic materials µr can be very large. Typical values for iron with the applied field are thus easily disturbed on the removal of the external field leaving the material, partially magnetized. Flux can exist in the materials even in the absence of external magnetization force such as in permanent magnets. Magnetic specimen in the form of ring with a toroidal winding can be magnetized from its original un-magnetized state. The plot of respective values of flux density B and intensity of magnetization H is known as magnetization curve. Examples of these curves are given in Figs 2.13. (a) and (b). The horizontal base line, or X axis is marked off in units of magnetization force H, in Oersteds.

The vertical, or Y axis indicates flux density B in Gauss. Its shape varies from one type of material to another due to their magnetic permeability.

As the magnetizing force H is applied to iron, the domain walls move so as to favour the growth of domains that happen to have their direction of magnetization more or less along the external field direction. As the field is further increased, forces are great enough to cause the gradual rotation of magnetization direction into exact alignment with the field. Finally, when all dipoles are aligned, B has reached a constant value, or is saturated.

FIG. 2.13. Hysteresis curve for hard (a) and soft materials (b).

If the field is removed after the specimen is magnetized, the material tends to return to its unmagnetized state. But the motion of domain walls is partially inhibited by crystal boundaries and their crystal imperfections. This produces a kind of friction which causes the walls to lag behind the position they would take if they moved easily within the specimen.

This means that the magnetic dipoles are not perfectly elastic and they do not return to their original position when the external force is removed.

From the curves shown in FIG. 2.13. for soft and hard iron it is evident that the permeability is not constant and is given by the ratio of B to H, which can be found at any point by noting the respective values.

2.2.2 Induced magnetic flux