224 12.Magnetic Properties of Materials FIGURE 12.1.Measure- ment of the magnetic susceptibility in an in- homogeneous mag- netic field.The mag- netic field lines (dashed)follow the iron core. where V is the volume of the sample,uo is a universal constant called the permeability of free space (1.257 X 10-6 H/m or Vs/Am), and X is the susceptibility,which expresses how responsive a ma- terial is to an applied magnetic field.Characteristic values for X are given in Table 12.1.The term dH/dx in Eq.(12.1)is the change of the magnetic field strength H in the x-direction.The field strength H of an electromagnet (consisting of helical windings of a long,in- sulated wire as seen in the lower portion of Figure 12.1)is pro- portional to the current,I,which flows through this coil,and on the number,n,of the windings (called turns)that have been used to make the coil.Further,the magnetic field strength is inversely proportional to the length,L,of the solenoid.Thus,the magnetic field strength is expressed by: H=I L (12.2) The field strength is measured(in SI units)in "Amp-turns per meter"or shortly,in A/m. The magnetic field can be enhanced by inserting,say,iron,into a solenoid,as shown in Figure 12.1.The parameter which ex- presses the amount of enhancement of the magnetic field is called the permeability u.The magnetic field strength within a mate- rial is known by the names magnetic induction!(or magnetic Calling B "magnetic induction"is common practice but should be dis- couraged because it may be confused with electromagnetic induction, as shown in Figure 10.3.where V is the volume of the sample, 0 is a universal constant called the permeability of free space (1.257 106 H/m or Vs/Am), and $ is the susceptibility, which expresses how responsive a ma￾terial is to an applied magnetic field. Characteristic values for $ are given in Table 12.1. The term dH/dx in Eq. (12.1) is the change of the magnetic field strength H in the x-direction. The field strength H of an electromagnet (consisting of helical windings of a long, in￾sulated wire as seen in the lower portion of Figure 12.1) is pro￾portional to the current, I, which flows through this coil, and on the number, n, of the windings (called turns) that have been used to make the coil. Further, the magnetic field strength is inversely proportional to the length, L, of the solenoid. Thus, the magnetic field strength is expressed by: H
I L n . (12.2) The field strength is measured (in SI units) in “Amp-turns per meter” or shortly, in A/m. The magnetic field can be enhanced by inserting, say, iron, into a solenoid, as shown in Figure 12.1. The parameter which ex￾presses the amount of enhancement of the magnetic field is called the permeability . The magnetic field strength within a mate￾rial is known by the names magnetic induction1 (or magnetic 224 12 • Magnetic Properties of Materials X L N S FX I FIGURE 12.1. Measure￾ment of the magnetic susceptibility in an in￾homogeneous mag￾netic field. The mag￾netic field lines (dashed) follow the iron core. 1Calling B “magnetic induction” is common practice but should be dis￾couraged because it may be confused with electromagnetic induction, as shown in Figure 10.3.