om=-n网-）→m亿=2)=，Mg om(2=-5)=-oM。 7xH=j=0→H=-VΨ 7(可=-2平=pm=-7.( - 驰了a-2rs的2ro 4πoF-r 二+ 4元4oF-r oM。2πr'dr e o-egp -登- Ψ(z) Mo/2{R+d-[R2+d2]2} -d/2 d/2 6.641,Electromagnetic Fields,Forces,and Motion Lecture 8 Prof.Markus Zahn Page 5 of 136.641, Electromagnetic Fields, Forces, and Motion Lecture 8 Prof. Markus Zahn Page 5 of 13 ⎧ ⎫ ⎡ ⎤⎡ ⎤ ⎪ ⎪ ⎛⎞ ⎛⎞ ⎨ ⎬ ⎢ ⎥⎢ ⎥ + − −− − + + ++ ⎜⎟ ⎜⎟ ⎪ ⎪ ⎝⎠ ⎝⎠ ⎣ ⎦⎣ ⎦ ⎩ ⎭ 1 1 2 2 2 2 M0 2 2 dd dd = Rz z Rz z 2 22 22 σ − µ − ⇒σ µ i ( ) ( ) a b sm 0 sm 0 0 = n M M z= = M d 2 ( ) σ − − sm 0 0 z= = M d 2 µ ∇ ⇒ xH= J=0 H= −∇ Ψ ∇ µ −µ ∇ Ψ ρ −∇ µ ( ) i( ) 2 00 m 0 H= = = M ( ) −ρ ρ ( ) ∇ Ψ ⇒Ψ µ πµ − ∫ 2 m m 0 V' 0 r ' dV ' = r = 4 r r' ( ) σ π σ −π ( ) ( ) Ψ + πµ − πµ − ∫ ∫ R R sm sm r'=0 0 0 r'=0 z = 2 r ' dr ' z = 2 r ' dr ' d d 2 2 z = 4 r r' 4 r r' µ π µ π − ⎡⎤ ⎡ ⎛ ⎞ ⎛ ⎞ πµ + − ⎢⎥ ⎢ πµ + + ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎣⎦ ⎣ ∫ ∫ R R 0 o 0 o 1 1 2 2 2 2 r'=0 r'=0 2 2 0 0 M 2 r ' dr ' M 2 r ' dr ' = d d 4 r' z 4 r' z 2 2 ⎤ ⎥ ⎥⎦ ( ) ( ) ⎡ + + ⎤ ⎣ ⎦ ⎡ ⎤ + + ⎣ ⎦ ∫ 1 2 2 2 1 2 2 2 r ' dr ' = r' z a r' z a ( ) = = ⎧ ⎫ ⎪ ⎪ ⎡ ⎤⎡ ⎤ ⎛ ⎞ ⎛ ⎞ Ψ −− ⎨ ⎬ ⎢ ⎥⎢ ⎥ + + ⎜ ⎟ ⎜ ⎟ ⎪ ⎪ ⎢ ⎥⎢ ⎥ ⎝ ⎠ ⎝ ⎠ ⎣ ⎦⎣ ⎦ ⎩ ⎭ R R 1 1 2 2 2 2 0 2 2 r' 0 r' 0 M d d z = r' + z r' z 2 2 2