Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

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Revised Pages

18.2 Basic Concepts • 725

I

I

N turns

H

B 0 =  0 H

(a)

I

I

B = H

(b)

l H

Figure 18.3 (a) The magnetic fieldHas

generated by a cylindrical coil is dependent on

the currentI, the number of turnsN, and the

coil lengthl, according to Equation 18.1. The

magnetic flux densityB 0 in the presence of a

vacuum is equal toμ 0 H, whereμ 0 is the

permeability of a vacuum, 4π× 10 −^7 H/m.

(b) The magnetic flux densityBwithin a solid

material is equal toμH, whereμis the

permeability of the solid material. (Adapted

from A. G. Guy,Essentials of Materials Science,

McGraw-Hill Book Company, New York, 1976.)

The magnetic field strength and flux density are related according to

B=μH (18.2)

Magnetic flux density

in a material—

dependence on

permeability and

magnetic field

strength The parameterμis called thepermeability,which is a property of the specific medium

permeability

through which theHfield passes and in whichBis measured, as illustrated in Figure

18.3b. The permeability has dimensions of webers per ampere-meter (Wb/A-m) or

henries per meter (H/m).

In a vacuum,

Magnetic flux density B 0 =μ 0 H (18.3)

in a vacuum

whereμ 0 is thepermeability of a vacuum,a universal constant that has a value of

4 π× 10 −^7 (1.257× 10 −^6 ) H/m. The parameterB 0 represents the flux density within

a vacuum as demonstrated in Figure 18.3a.

Several parameters may be used to describe the magnetic properties of solids.

One of these is the ratio of the permeability in a material to the permeability in a

vacuum, or

μr=

μ

μ 0

Definition of relative (18.4)

permeability

whereμris called therelative permeability,which is unitless. The permeability or

relative permeability of a material is a measure of the degree to which the material

can be magnetized, or the ease with which aBfield can be induced in the presence

of an externalHfield.

magnetization Another field quantity,M, called themagnetizationof the solid, is defined by the

expression

B=μ 0 H+μ 0 M (18.5)

Magnetic flux

density—as a

function of magnetic

field strength and

magnetization of a

material

In the presence of anHfield, the magnetic moments within a material tend to become

aligned with the field and to reinforce it by virtue of their magnetic fields; the term

μ 0 Min Equation 18.5 is a measure of this contribution.

The magnitude ofMis proportional to the applied field as follows:

M=χmH (18.6)

Magnetization of a

material—

dependence on

susceptibility and

magnetic field

strength