226 12.Magnetic Properties of Materials we will see later.Further,the susceptibility for ferromagnetic ma- terials depends on the field strength,H. The magnetic field parameters at a given point in space are, as explained above,the magnetic field strength H and the mag- netic induction B.In free (empty)space,B and uoHl are identi- cal,as seen in Eq.(12.3).Inside a magnetic material the induc- tion B consists of the free-space component (uoH)plus a contribution to the magnetic field (uoM)which is due to the pres- ence of matter [Figure 12.2(a)],that is, B=uoH uoM, (12.5) where M is called the magnetization of the material.Combining Egs.(12.3)through (12.5)yields: M=XH. (12.6) H,B,and M are actually vectors.Specifically,outside a mater- ial,H(and B)point from the north to the south pole.Inside of a ferro-or paramagnetic material,B and M point from the south N N N HoH H (a) (b) (c) (d) FiGURE 12.2.Schematic representation of magnetic field lines in and around different types of ma- terials.(a)Para-or ferromagnetics.The magnetic induction (B)inside the material consists of the free-space component(uoH)plus a contribution by the material (uoM);see Eq.(12.5).(b)The magnetic field lines outside a material point from the north to the south poles,whereas inside of para-or ferromagnetics,B and poM point from south to north in order to maintain continuity. (c)In diamagnetics,the response of the material counteracts (weakens)the external magnetic field. (d)In a thin surface layer of a superconductor,a supercurrent is created (below its transition tem- perature)which causes a magnetic field that opposes the external field.As a consequence,the magnetic flux lines are expelled from the interior of the material.Compare to Figure 11.27.we will see later. Further, the susceptibility for ferromagnetic ma￾terials depends on the field strength, H. The magnetic field parameters at a given point in space are, as explained above, the magnetic field strength H and the mag￾netic induction B. In free (empty) space, B and 0H are identi￾cal, as seen in Eq. (12.3). Inside a magnetic material the induc￾tion B consists of the free-space component (0H) plus a contribution to the magnetic field (0M) which is due to the pres￾ence of matter [Figure 12.2(a)], that is, B
0H 0M, (12.5) where M is called the magnetization of the material. Combining Eqs. (12.3) through (12.5) yields: M
$ H. (12.6) H, B, and M are actually vectors. Specifically, outside a mater￾ial, H (and B) point from the north to the south pole. Inside of a ferro- or paramagnetic material, B and M point from the south 226 12 • Magnetic Properties of Materials N S N S N S N S 0H 0H B S N 0M 0M 0M 0M (a) (b) (c) (d) FIGURE 12.2. Schematic representation of magnetic field lines in and around different types of ma￾terials. (a) Para- or ferromagnetics. The magnetic induction (B) inside the material consists of the free-space component (0H) plus a contribution by the material (0M); see Eq. (12.5). (b) The magnetic field lines outside a material point from the north to the south poles, whereas inside of para- or ferromagnetics, B and 0M point from south to north in order to maintain continuity. (c) In diamagnetics, the response of the material counteracts (weakens) the external magnetic field. (d) In a thin surface layer of a superconductor, a supercurrent is created (below its transition tem￾perature) which causes a magnetic field that opposes the external field. As a consequence, the magnetic flux lines are expelled from the interior of the material. Compare to Figure 11.27