Question 2.41: Two homogeneous, linear, isotropic magnetic materials have a...
Two homogeneous, linear, isotropic magnetic materials have an interface at x = 0. At the interface, there is a surface current with a density JL = 20 uy A/m. The relative permeability µr1 = 2 and the magnetic field intensity in the region x < 0 is H1 = 15ux +10 uy + 25uz A/m. The relative permeability µr2 = 5 in the region x > 0. Find the magnetic field intensity in the region x > 0.
The magnetic field is separated into components and the boundary conditions are applied independently. For the normal component, (2.180) implies
\mu_{2} \mu_{0} H_{2 n}-\mu_{1} \mu_{0} H_{1 n}=0 (2.180)
\mu_{2} \mu_{0} H _{2 n }=\mu_{1} \mu_{0} H _{1 n } \Rightarrow H _{2 x }=\frac{\mu_{1}}{\mu_{2}} H _{1 x }=\frac{2}{5} 15=6 A / m
For the tangential components, we use (2.186) and write
H _{2 t }- H _{1 t }= J _{ s } \Rightarrow H _{2 z }= H _{1 z }+J_{ y }=25+20=45 A / m
There is no change in the y component of the magnetic field intensity. Therefore,
H2 = 6 ux +10 uy + 45 uz A/m .