# Weekly report 1.4
[toc]
## Medium
### Free Space
> no charge, no current

### Material Medium ( 和 Free Space 作區別 )
Materials 分作 have strong interaction with electric field or magnetic field 兩種來討論
#### (1) strong interaction with electric field
##### a. Conductors
> free charges ( electrons, holes )
##### b. Nonconductors ( insulators or dielectric )
> bound charges, no free charges
:::success
**<補充說明>**
Nonconductors 會被稱作 dielectric 是因為 bound charges 受到電場影響，被極化產生電偶，具有介電質的性質
:::

#### (2) strong interaction with magnetic field
##### Magnetic Materials
> Fe, Co, Ni

## <插播> 導體、半導體、絕緣體
> :::spoiler 透過 Conductivity 來做區分
> 
> :::
> 

## Polarization and Dielectrics
### 前言
介電質會使電容器所量到的跨壓變小
這裡要介紹介電質對於電場的影響，而這個影響要透過極化現象來解釋
### <插播> Ideal Dielectrics
> 1. no free or conductance charges
> 2. atoms' electrons are bound in atoms
### Electronic Polarization in Dielectrics
:::spoiler 原先 a neutral atom in E_a=0
:::
:::spoiler 後來受到電場 E_a 影響 induced dipole moment in a field
:::
名詞解釋：
> Induced dipole moment 
>Induced electic field E_s
>Total lectric field in space E=E_a+E_s
elecronic polarization = 電子雲、電荷中心受到電場影響導致位移所產生的 polarization

### polarization in dielectrics
Polarization
~ the net electric field is the summation of fields due to all dipoles

polarization vector
~ a macroscopic quantity, average of massive polarized atoms in a unit volume

For most dielectrics 滿足
也就是 P 和 E 成正比 
我們令式子長這樣 
其中  稱作 electric susceptibility of the material 電極化率
當然也有不遵守線性的，比如說鐵磁性材料的 P 和 E 就不成正比

### Polarization 種類
> :::spoiler 1. Electronic Polarization of a nonpolar molecule 不具極性的分子
> 
> :::success
> Applying E field -> displacement of positively charged nucleus and negatively charged electron cloud -> Equivalent dipole moment
> :::
> :::spoiler 2. Ionic Polarization 離子化合物
> 
> :::success
> 
> :::
> :::spoiler 3. Orientational Polarization of a polar medium with polar molecules
> 
> :::success
> 
> :::warning
> polar molecules 不需要電場，天生具有極化反應
> 不過因為沒有電場，是隨機方向，平均下來 = 0
> 如果有電場，平均下來 != 0，稱做Orientational polarization 方向性極化 of a polar medium with polar molecules
> :::

### Polarization vs. frequency

如果電場不是 DC，那麼 polarization 機制會因為頻率的高低而有所不同，如圖

頻率低的結果是高頻的疊加再加上當時多出來的極化

## Surface bound charge
Assume P is **uniform** in the polarized dielectric
:::spoiler
Net volume bound charge density = 0
Surface bound charge 
Net dipole moment in volume of Sd
By the definition of polarization vector
所以
兩邊 dot 可得
Surface bound (polarization) charge density
:::

## volume bound charge
Assume P is **non-uniform** in the polarized dielectric
:::spoiler
volume bound charge density != 0
Volume bound charge in delta v
Volume bound(polarization) charge density:
In general, 
:::
:::spoiler Method 1: Potential due to polarization charge density
Total bound charge:
:::
:::spoiler Method 2: Potential due to dipole moment ( consistent with Method 1)
Manipulation of V -> in the form of charges
Bound surface charge density
Bound volume charge density
:::

:::danger
Q：這裡的前提不是不一樣嗎(uniform and non-uniform)，怎麼可以拿出來加一起？
:::

## Revisit Gauss’ Law and Displacement Field Vector
:::spoiler 外部
:::
:::spoiler 內部
:::

Gauss’ law and displacement vector field
**E** is the net electric field in the dielectric.
:::spoiler 背景知識
:::

Permittivity of the dielectric
Dielectric constant or relative permittivity

總整理
---
## Linear, isotropic, and homogeneous dielectrics
:::danger
注意 B,C 容易搞錯順序
:::

回憶一下表示法
1. Linear <-> Nonlinear
2. Homgeneous <-> Inhomgeneous
3. Isotropic <-> Anisotropic

In a general linear, isotropic and homogeneous medium,
1. Electric force：
2. Work：

Same ideas for conducting materials in which 

:::spoiler 其他

對 source 做 gradient 計算

divergence theorem

Permittivity of the dielectric
Dielectric constant or relative permittivity

Isotropic：等向性
Anisotropic：非等向性

In general, linear, isotropic and homogeneous medium
:::
:::spoiler Capacitors
Dielectric, permittivity and capacitance
發現介電性質的是 Faradays
capacitance with air
capacitance with dielectric
Relative permittivity of the dielectric 相對電容率
permittivity of the dielectric 電容率

Parallel-Plate Capacitor
fringing effect 雜散效應

Energy stored
dielectric constant
effect of dielectric constant

Coaxial Capacitor 同軸電容

Spherical Cpacitor
Isolated Sphere 是一種特例

There may be two types of given boundary condition
a. Volatge across the capacitor is specified such ass V_0
b. Charge Q is given

Dielectric breakdown and dielectric strength
:::spoiler

voltage rating 額定電壓

Boundary Condition
待整理
:::

Dielectric Breakdown
~ as the electric field in the dielectric is sufficiently large, dielectric -> conducting (當 Dielectric Breakdown 發生，變成導體，這時候就會有很大的漏電流產生)
>　Electrical breakdown can occur within solids, liquids, gases or vacuum

Dielectric strength (breakdown electric field)
~ The maximum electric field for a dielectric to tolerate without electric breakdown


## 心得
自從開始進入第三章以後，就已經從可掌控變成無法掌控了，大量的資訊灌入我的腦中，卻無法停留，讓我感到相當的無力。而且明知道自己過去有學過，但是仍然沒有辦法不額外去複習就繼續課程，真的很想把我的腦袋砸爛，一點用都沒有，記憶容量跟一顆米粒差不多小．．．雖然複習有點成效，但是每當我複習到一個進度的時候，老師又不知道上到哪裡去了，速度遠遠不及老師上課的速度。而且考試和教完課程的時間又有點太近了，所以還沒有辦法融會貫通就必須得上戰場，而且考題分配和上課的內容及時間比重有很大的不同，讓我摸不著頭緒，準備起來相當的挫折。希望我可以慢慢抓到老師出題的感覺，能夠漸入佳境，加油 fighting！