IV.Artificial Dielectric E V E-/G:-6ES d EA q=oA= d C=9=8A d 上● ●●●●●● Figure 6.6.1 (a)Plane parallel ●●●●●●● capacitor with region between ●●●●●● ● electrodes occupied by a dielectric. (b)Artificial dielectric composed of cubic array of perfectly conducting spheres having radius R and spacing (a) (b) Courtesy of Hermann A.Haus and James R.Melcher.Used with permission. For spherical array of non-interacting spheres(s >R) p=4元8。R3E。i2→P2=Np2=4πE。R3E。N N=⅓ p=0 4π R s =y。8。E e(electric susceptibility) D=8E+P=8o[1+Ve]E=8E 8(relative dielectric constant) 8=8,6=6,1+v]=1+4(餐） 6.641,Electromagnetic Fields,Forces,and Motion Lecture 7 Prof.Markus Zahn Page 6 of 276.641, Electromagnetic Fields, Forces, and Motion Lecture 7 Prof. Markus Zahn Page 6 of 27 IV. Artificial Dielectric s v v E, E d d = σ= = ε ε s A qA v d =σ = ε = = q Aε C v d Courtesy of Hermann A. Haus and James R. Melcher. Used with permission. For spherical array of non-interacting spheres (s >> R) π⇒ π ε ε _ 3 3 z P = 4 R E i P = N p = 4 R E N oo z z oo N = 1 3 s ⎡⎤ ⎛ ⎞ ⎛⎞ ⎛⎞ ⎢ ⎥ π ψ ψπ ⎜ ⎟ ⎜⎟ ⎜⎟ ⎢ ⎥ ⎝⎠ ⎝⎠ ⎣⎦ ⎝ ⎠ ε ε 3 3 o eo e R R P= 4 E= E =4 s s ψe (electric susceptibility) + +ψ ⎡ ⎤ ⎣ ⎦ εε ε D= E P= 1 E= E o oe r ε (relative dielectric constant) ⎛ ⎞ ⎛ ⎞ ⎡ ⎤ +ψ + π ⎜ ⎟ ⎣ ⎦ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ε εε ε ε 3 ro o e o R = = 1 = 14 s _ d + ε E υ