Model srace currenKs volume current of small thickness I Jy=D8 xH=j→股=-小，=→片=5x-(传+训 I f.H dx dy dz -器}k-e+ax ÷号-6时+ ++号+的 12 comes from integrating uniform volume current over small thickness 8 General formula:f=[KxBav ds 0 For our case:B= B2+B业= 2 2 6.641,Electromagnetic Fields,Forces,and Motion Lecture 13 Prof.Markus Zahn Page 6 of 146.641, Electromagnetic Fields, Forces, and Motion Lecture 13 Prof. Markus Zahn Page 6 of 14 Model surface current y I K = D as volume current of small thickness δ y I J = Dδ ( ) ( ) z y z H I I H=J = J = H = x xD D ∂ ∇× ⇒ − − ⇒ − − ξ + δ ∂ δδ 0 I I = D D −µ δ ( ) ( ) + x= x lD ξ δ ξ ⎛ ⎞ ⎜ ⎟ − ξ+δ ⎝ ⎠ δ ∫ dx ( ) 2 2 0 2 x I l x = x D 2 ξ+δ =ξ −µ ⎡ ⎤ ⎢ ⎥ − ξ+δ δ ⎣ ⎦ ( ) ()() 2 2 2 2 0 2 I l = D 2 2 −µ ⎡ ⎤ ξ+δ ξ ⎢ ⎥ − − ξ+δ +ξ ξ+δ δ ⎣ ⎦ ( ) 2 2 2 0 2 I l 1 = D 2 2 −µ ⎡ ⎤ ξ ⎢ ⎥ − ξ + δ + + ξδ δ ⎣ ⎦ 2 0 2 2 I l 1 = D 2 −µ ⎡ ⎤ − δ ⎢ ⎥ δ ⎣ ⎦ 2 0 S 1 1 I l = f = K B dS 2D 2 µ +⇒ × ∫ ½ comes from integrating uniform volume current over small thickness δ General formula: av S f = K B dS × ∫ 0 For our case: metal air av air B B 1 B= =B 2 2 + µ x y0z ∫ V f = J H dx dy dz