Figure 11.811.26 Calculation of Fie

Figure 11.8
11.26 Calculation of Fields Across Interfaces. A region, denoted as region (1), occupies the space x < 0 and has relative
permeability μr1 ¼ 6. The magnetic field intensity in region (1) is H1 ¼ ^x4 þ ^y  ^z2 [A/m]. Region (2) is defined as
x > 0 with μr2 ¼ 5.0. No current exists at the interface. Find B in region (2).
11.27 Interface Conditions for Permeable Materials. An interface between free space and a perfectly permeable material
exists. In free space (1), μ ¼ μ0 [H/m], ε ¼ ε0 [F/m], and σ ¼0. In the permeable material (2), μ ¼ 1, σ ¼ 0, and
ε ¼ ε0. Define the interface conditions at the interface between the two materials.
11.28 Surface Current Density at Interfaces. Two magnetic materials meet at an interface as shown in Figure 11.9.
Material (1) has relative permeability of 4 and material (2) has relative permeability of 2. The interface is at z ¼ 0.
The magnetic flux density in material (1) is given as B ¼ ^x0:1 þ ^y0:2 þ ^z0:1 T ½ . In material (2), it is known that
all tangential components of H are zero.
(a) Calculate the surface current density that must exist on the interface for this condition to be satisfied.
(b) Calculate the magnetic flux density in material (2).