※ 引述《wellilin (QQ12)》之銘言：
: http://www-o.ntust.edu.tw/~lib/pdf/Master/99/m990901.pdf
: 第二題 第一小題
＿＿＿＿＿＿＿＿＿＿＿＿＿＿
▕ ▕
＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿...y=d ＿＿ +
∣ ＿ Vo
εrε0 ∣ ε0 ▕ -
∣ ▕
＿＿＿＿＿＿＿∣＿＿＿＿＿＿＿...y=0 ▕
▕ ▕
▕＿＿＿＿＿＿＿＿＿＿＿＿＿▕
由Laplace'e EQ:▽^2V=0 ; BC: (1) V(y=0) = 0
(2) V(y=d) = Vo
解得 V(y) = c1y + c2 ; 帶入BC=> V(y) = (Vo/d)y (volt)
→ ^
E = -▽V(y) =-ay (Vo/d) (V/m)
for dielectric : ε= εrε0 (0 < x < X)
→ → → ^
Dd = εrε0 E (C/m^2) ; ρs(upper) = Dd‧-ay (C/m^2)
→ ^
ρs(lower) = Dd‧+ay (C/m^2)
for air : ε= ε0 (X < x < L)
→ → → ^
Da = ε0 E (C/m^2) ; ρs(upper) = Da‧-ay (C/m^2)
→ ^
ρs(lower) = Da‧+ay (C/m^2)
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