[題目]電磁學研究所考古題

[ed78617 (雞爪)]

[領域]electrodynamics                             (題目相關領域)

[來源]清大電子工程研究所 電磁學                     (課本習題、考古題、參考書...)

[題目]

Consider a shorted pair of parallel plate electrodes of area "A" sandwiched a
lossy dielectric slab of thickness "d" with dielectric permittivity "ε" and
conductivity "σ". Assume that the lossy dielectric has a uniformly
distributed free volume charge density ρ(0) at t = 0 and that the fringing
field can be neglected.

(a)What is the volume charge density between these two electrodes as a
   function of time and position?

(b)What is the electric field between these two electrodes as a function of
   time and postion?

(c)What is the surface charge density at the plates as a function of time?

(d)What is the current flow through the short circuit as a function of time?

(題目雖然全打，其實我主要是想問(a)，因為我(a)小題就卡關了)

[瓶頸]                             (寫寫自己的想法，方便大家為你解答)

我覺得(a)應該是要用J=σE來解，J的變化便是free charge的變化。
dielectric 上的 free charge 會在electrodes上感應出電荷，令free charge流向兩邊
的electrodes。問題是E要怎麼求？

煩請高手指導

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推 youmehim:J=σE  ▽．E=ρ/ε  ▽．J+dρ/dt=0
→ ed78617:問一下，這裡的free charge是均勻分佈在材料裡的，那高斯
→ ed78617:定律要怎麼用？
→ ed78617:對不起，上面問錯了。我是要問，ρ和位置的關係為何
→ ed78617:我覺得ρ的分佈應該還是均勻，若平行板間的電場為常數
推 youmehim:均勻就是ρ(0)與位置無關 處處皆為ρ(0)   你是問這個嗎?
→ ed78617:呃...我是想問算出來的ρ(t)是不是還是均勻的
推 youmehim:ρ(t)是均勻的 但到了electrodes(邊界)處 應該會有問題
→ ed78617:嗯，那我知道了，謝啦，突然覺得這題出得有點鳥XD