作者ed78617 (鸡爪)
看板Physics
标题[题目]电磁学研究所考古题
时间Mon Jul 26 17:17:15 2010
[领域]electrodynamics (题目相关领域)
[来源]清大电子工程研究所 电磁学 (课本习题、考古题、参考书...)
[题目]
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?
(题目虽然全打，其实我主要是想问(a)，因为我(a)小题就卡关了)
[瓶颈] (写写自己的想法，方便大家为你解答)
我觉得(a)应该是要用J=σE来解，J的变化便是free charge的变化。
dielectric 上的 free charge 会在electrodes上感应出电荷，令free charge流向两边
的electrodes。问题是E要怎麽求？
烦请高手指导
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1F：推 youmehim:J=σE ▽．E=ρ/ε ▽．J+dρ/dt=0 07/26 17:27
2F：→ ed78617:问一下，这里的free charge是均匀分布在材料里的，那高斯 07/26 17:29
3F：→ ed78617:定律要怎麽用？ 07/26 17:29
4F：→ ed78617:对不起，上面问错了。我是要问，ρ和位置的关系为何 07/26 17:42
5F：→ ed78617:我觉得ρ的分布应该还是均匀，若平行板间的电场为常数 07/26 17:44
6F：推 youmehim:均匀就是ρ(0)与位置无关 处处皆为ρ(0) 你是问这个吗? 07/26 17:45
7F：→ ed78617:呃...我是想问算出来的ρ(t)是不是还是均匀的 07/26 17:46
8F：推 youmehim:ρ(t)是均匀的 但到了electrodes(边界)处 应该会有问题 07/26 17:50
9F：→ ed78617:嗯，那我知道了，谢啦，突然觉得这题出得有点鸟XD 07/26 17:55