Question 7.5: Planes z = 0 and z = 4 carry current K = -10 ax A/m and K = ...

The parallel current sheets are shown in Figure 7.14. Let

H=H_{o}+H_{4}

where H_{o} and H_{4} are the contributions due to the current sheets z = 0 and z=4, respectively. We make use of eq. (7.23).

H=\frac{1}{2}K\times a_{n}

(a) At (1,1,1), which is between the plates (0\lt z=1\lt 4)

H_{o}=1/2 K\times a_{n}=1/2(-10a_{x})\times a_{z}=5a_{y}A/m

H_{4}=1/2 K\times a_{n}=1/2(10a_{x})\times (-a_{z})=5a_{y}A/m

Hence

H=10a_{y}A/m

(b) At (0,-3,10), which is above the two sheets (z=10\gt 4\gt 0)

H_{o}=1/2(-10a_{x})\times a_{z}=5a_{y}A/m

H_{4}=1/2(10a_{x})\times a_{z}=-5a_{y}A/m

Hence

H=0A/m