B.Estimate of Error introduced by EQS approximation Z=d Z-0 Figure 3.3.2 Plane parallel electrodes having no resistance,driven at their outer edges by a distribution of sources of EMF. Courtesy of Hermann A.Haus and James R.Melcher.Used with permission. E=0=6 -Eo z=d Osu= +Eo z=0 K2b+b2du=0→K,=-bdcu=-bεdE dt 2 dt 2 dt .s-民阔-H2r=ms胎-4= dEo dt dt fE.ds=-「u H.da Figure 3.3.3 Parallel plates of Figure 3.3.2,showing volume containing lower plate and radial surface current density at r=0 r=b its periphery. Courtesy of Hermann A.Haus and James R.Melcher.Used with permission. Z Z=d Figure 3.3.4 Cross-section of system z=0 shown in Figure 3.3.2 showing surface and contour used in evaluating correction E field. Courtesy of Hermann A.Haus and James R.Melcher.Used with permission. 6.641,Electromagnetic Fields,Forces,and Motion Lecture 3 Prof.Markus Zahn Page 2 of 126.641, Electromagnetic Fields, Forces, and Motion Lecture 3 Prof. Markus Zahn Page 2 of 12 B. Estimate of Error introduced by EQS approximation Courtesy of Hermann A. Haus and James R. Melcher. Used with permission. _ _ z z 0 V E i Ei d = = 0 su 0 E zd E z0 ⎧⎪− = σ = ⎨ ⎪+ = ⎩ ε ε 2 su su 0 r r d dd b b E K2 b b 0 K dt 2 dt 2 dt σ σ π +π = ⇒ =− =− ε ( ) 2 0 0 C S dE r dE H ds E da H 2 r r H t dt 2 dt φ φ ∂ = ⇒π = π ⇒= ∂ ε εε ∫ ∫ i i v C S H E ds da t ∂ =− µ ∂ ∫ ∫ i i v Courtesy of Hermann A. Haus and James R. Melcher. Used with permission. Courtesy of Hermann A. Haus and James R. Melcher. Used with permission