物理二 - 120.118.228.134120.118.228.134 › uipweb › wsite › public › attachment ›...
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![Page 1: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/1.jpg)
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物理物理 二二
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教科書教科書
普通物理學普通物理學((下冊下冊))原著:原著:HARRIS BENSONHARRIS BENSON
譯者:朱達勇、谷天心、徐植蔚、鄭宜男譯者:朱達勇、谷天心、徐植蔚、鄭宜男學銘圖書、歐亞書局學銘圖書、歐亞書局
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Chapter 1Chapter 1
靜電靜電
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§§ 11--11
電荷電荷
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•物質由原子構成•=>原子核•=>質子(帶正電),中子(電中性),電子(帶負電)
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•中性原子有等量電子及質子 =>失去或獲得電子,成為帶電離子
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•*接觸或摩擦•=>使電荷轉移•=>物體留有淨正電荷或淨負電荷•=>物體相吸或相斥•*電荷單位=>庫侖(C)
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§§ 11--22
導體及絕緣體導體及絕緣體
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**物質依導電性區分物質依導電性區分
•導體=>電荷可在其中自由流動,如金屬
•絕緣體=>電荷無法通過,如木頭•半導體=>可添加雜質改變導電性,如矽
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§§ 11--33
靜電感應靜電感應
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•Fig.•A及B金屬球與地絕緣,但彼此接觸
•Fig.
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§§ 11--44
金箔驗電器金箔驗電器
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•Fig.•感應,測物體是否帶電•若驗電器本身已有電荷(如正電荷)•=>可測物體帶電之極性
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§§ 11--55
庫侖定律庫侖定律
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•庫侖定律•=>兩電荷Q及q間的電力大小正比於Q和 q的乘積
•=>與兩電荷距離 r的平方成反比
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1616
229
2
/100.9 cmNk
kr
kQqF
為庫侖常數,其中
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1717
rr
kqQF
2
向量形式
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)(
)(*
吸引力
斥力
所受力
rFF
rFF
Fq
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1919
遵循疊加原理遵循疊加原理
N
N
FFFF
qN
qqq
113121
1
21
...
,...,,*
受到之電力則
個電荷
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2020
Chapter 2Chapter 2
電場電場
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2121
§§ 22--11
電場電場
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•電荷會在環繞它的空間中建立電場
•電場強度:一單位電荷放置於該點上所受的力
tqF
E
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•Fig.•Q=>建立電場•Qt=>測試電荷
rrkQ
E
rr
QkqF t
ˆ
ˆ
2
2
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•若電場強度已知,則任一電荷q所受之力
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•線性疊加原理亦適用於電場•N個電荷在某點造成之總電場強度
NEEEE
...21
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§§ 22--22
電力線電力線
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•用連續的場線或電力線來表示電場•線條由正電荷出發,終止於負電荷•Fig.
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•電場較強之處,電力線密集在一起•電場微弱處,電力線稀疏•Fig.
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•電場強度正比於線的密度=>通過垂直於電場方向單位面積上的電力線數目
•Fig.
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☆電力線特性總結☆電力線特性總結
•1.靜電場線由正電荷出發且宗終止於負電荷
•2.起始或終結的線數正比於電荷的大小
•3.電場方向為沿電力線切線方向
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•4.電場強度正比於線的密度=>通過垂直於電場方向單位面積上的電力線數目
•5.電力線不會相交
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§§ 22--33
電場及導體電場及導體
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•Fig.•外加電場Eext作用於導體•自由電子往Eext相反方向移動•一側留下正電荷
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•建立內部電場Eint
•淨電場(Eext-Eint)尚未為零,電子持續移動
•淨電場為零•達靜電平衡
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•Fig.•達靜電平衡條件=>導體表面上各點之電場均垂直於表面
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3636
§§ 22--44
均勻靜電場中電荷的運動均勻靜電場中電荷的運動
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•電場中,一質量m,帶電量q之粒子受一電力
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3838
由牛頓第二定律得由牛頓第二定律得
mEq
a
amEqamF
加速度
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3939
§§ 22--55
連續電荷分佈連續電荷分佈
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•場源為點電荷•電場強度•電荷為連續分佈
rrkq
E 2
![Page 41: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/41.jpg)
4141
•Fig.•分割為若干極小電荷元dq
•視dq為一點電荷
•dq所貢獻之電場
rr
kdqEd 2
![Page 42: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/42.jpg)
4242
•由疊加原理,總電場強度為各貢獻之和
rr
kdqE ˆ
2
![Page 43: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/43.jpg)
4343
§§ 22--66
電偶極電偶極
![Page 44: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/44.jpg)
4444
•電偶極=>兩個電量相等而極性相反之電荷,維持一固定距離稱之
•原子受外來電場作用,電荷會反向移動=>建立一感應電偶極
•Fig.
![Page 45: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/45.jpg)
4545
•Fig.•求電偶極產生之電場 2/322 )(
2araQk
Ey
![Page 46: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/46.jpg)
4646
•Fig.
QQd
dQp
指向方向由
電偶極矩
![Page 47: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/47.jpg)
4747
Chapter 3Chapter 3
高斯定律高斯定律
![Page 48: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/48.jpg)
4848
§§ 33--11
電通量電通量
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4949
•通過一平面之電通量被定義為•Fig.
CmN
EAE
/2
單位為
![Page 50: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/50.jpg)
5050
•若表面對電場有某些角度之傾斜
•Fig.
AE
EA
E
E
cos
![Page 51: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/51.jpg)
5151
•電場不均勻或表面A不是平面時•Fig.
AdEA
AE
AE
E
ii
E
,在 0
...11
![Page 52: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/52.jpg)
5252
§§ 33--22
高斯定律高斯定律
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5353
•Fig.•通過此封閉之高斯球面的總電通量為
)4( 2rE
dAEEdAE
![Page 54: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/54.jpg)
5454
☆高斯定律☆高斯定律
•通過封閉面的淨通量,等於被該封閉面包圍之淨電荷的1/o倍 o
EQ
![Page 55: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/55.jpg)
5555
§§ 33--33
導體導體
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5656
•Fig.•想像一恰在任意導體內部的高斯面,這個面上的各點均有E=0
![Page 57: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/57.jpg)
5757
•導體上的任何淨電荷必須留在表面•導體內部的電場為零
![Page 58: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/58.jpg)
5858
Chapter 4Chapter 4
電位電位
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5959
•電場強度=>每單位電荷所受之作用力
•電位=>每單位電荷的位能
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6060
§§ 44--11
位勢位勢
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6161
•Fig.•逆著電場方向移動一荷電粒子,外力必須作功
•外力與電力大小相等且方向相反時,粒子動能不改變
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6262
•系統將外力所做之功以位能形式儲存
為最終及起始位能及 if
ifEXT
UU
UUUW
![Page 63: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/63.jpg)
6363
•一電荷q在靜電場中移動時,電位變化量定義為:每單位電荷靜電位能的改變量 q
UV
![Page 64: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/64.jpg)
6464
•兩點間的電位已知,等速移動一電荷q所需的外力作功
)( ifEXT VVqVqW
![Page 65: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/65.jpg)
6565
代表系統對外力做功
代表外力對系統做功
00
EXT
EXT
WW
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6666
•Fig.•點A到點B的位能變化為極小變量的總和
B
AAB sdEVV
![Page 67: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/67.jpg)
6767
§§ 44--22
均勻電場中的電位及均勻電場中的電位及電位能電位能
![Page 68: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/68.jpg)
6868
sEsdE
sdEV
E
為常數均勻電場,
![Page 69: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/69.jpg)
6969
•Fig.
EdVV
ExxEVx
iEE
AB
x
分量電場僅
,均勻電場 ˆ
![Page 70: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/70.jpg)
7070
•電力線垂直於等位面,其方向由高電位指向低電位
•沿等位面移動,則dV=0•等位面移動一粒子不需作功
![Page 71: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/71.jpg)
7171
•電荷在電場中運動=>由能量守恆U+K=0
•+q電荷由高電位移往低電位,將獲得動能K=-U=-q V
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7272
§§ 44--33
點電荷的電位及電位能點電荷的電位及電位能
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7373
•一點電荷Q附近的電場為•Fig.
rrkQ
rEE r ˆˆ2
![Page 74: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/74.jpg)
7474
•A沿著任何路徑移到B的電位變化量為
)11
(AB
AB rrkQVV
![Page 75: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/75.jpg)
7575
•令r=∞處V=0,則與Q相距r處之電位為
•Fig.
rkQ
V
![Page 76: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/76.jpg)
7676
☆多點電荷系統的電位☆多點電荷系統的電位
•許多場源存在時=>空間中某點之總電位=>各電荷在該點造成電位之代數和
i
i
rkQ
V
![Page 77: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/77.jpg)
7777
**兩電荷系統之電位能兩電荷系統之電位能
•將兩電荷由相距無窮遠處移到相距r處,外力所需作功之大小
rkqQ
U
![Page 78: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/78.jpg)
7878
•數個電荷構成之系統之總電位能
ij
jiij r
qkqU
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7979
§§ 44--44
由電位導出的電場由電位導出的電場
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8080
•Fig.
kdzjdyidxsd
kEjEiEE zyx
ˆˆˆ
ˆˆˆ
極小位移
直角座標
![Page 81: 物理二 - 120.118.228.134120.118.228.134 › UIPWeb › wSite › public › Attachment › f... · 30 ☆電力線特性總結 •1.靜電場線由正電荷出發且宗終止 於負電荷](https://reader036.vdocuments.site/reader036/viewer/2022081607/5ed76bd02a2f0d6edb31ee90/html5/thumbnails/81.jpg)
8181
kzV
jyV
ixV
E
dzEdyEdxEsdEdV zyx
ˆˆˆ
)(
電場可寫為
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8282
§§ 44--55
連續型電荷分佈連續型電荷分佈
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8383
•電荷元素dq在P點貢獻之電位•Fig.
r
dqkV
rkdq
dV
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8484
•計算電位之第二種方法=>由已知電場求之
B
AAB sdEVV
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8585
§§ 44--66
導體導體
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8686
•靜電平衡狀態下,導體表面及內部所有點有相同電位
•導體表面尖銳處有較大電場強度=>空氣中放電現象
•Fig.
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8787
Chapter 5Chapter 5
電容器與介電質電容器與介電質
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8888
§§ 55--11
電容電容
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8989
•電容器=>兩個導體組成,中間隔以絕緣物質
•電荷Q正比於板間電位差V =>Q=CV
•C為比例常數=>電容
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9090
•平行板電容器•Fig.
mFdA
C
/1085.8 120
0
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9191
§§ 55--22
串聯與並聯串聯與並聯
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9292
☆串聯☆串聯
2121
2121
111CCCC
QCQ
CQ
QQQVVV
eqeq
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9393
☆並聯☆並聯
21
2121 )(CCC
VCCQQQ
eq
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9494
§§ 55--33
電容器中所儲存的能量電容器中所儲存的能量
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9595
•儲存於電容器中的能量=>電源對該電容器充電時所做的功W => 功被電容器以電位能UE儲存
22
0
2
21
21
2
2
CVQVC
QU
CQ
dqCq
W
E
Q
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9696
§§ 55--44
電場的能量密度電場的能量密度
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9797
•平行板電容器儲存的能量為•Fig.
20
20
21
)(21
Eu
AdEU
E
E
能量密度
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9898
§§ 55--55
介電質介電質
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9999
☆不連接電池情況☆不連接電池情況
•Fig.•電位差減少倍•稱為介電常數
00 E
EV
V DD
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100100
☆連接電池情況☆連接電池情況
•Fig.•板上荷電量增加為倍
0CCD
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101101
§§ 55--66
從原子觀點看介電質從原子觀點看介電質
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102102
•原子在外加電場作用下=>獲得感應電偶極矩
•感應電場指向與外加電場相反•介電質內部電場減少
0
0E
EEE iD
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103103
§§ 55--77
有介電質時的高斯定律有介電質時的高斯定律
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104104
•Fig.
00 fbf
D
QQQAdE
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105105
Chapter 6Chapter 6
電流與電阻電流與電阻
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106106
§§ 66--11
電流電流
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107107
•在t時間內流經電荷量Q=>平均電流 => Iav= Q / t
•若為非穩定流 => 瞬時電流 => I =dQ / dt
•Fig.
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108108
•Fig.•導線中傳導電子 => 隨機性熱運動•一電位差施加於導線 => 電子獲得漂移速度
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109109
§§ 66--22
電流密度電流密度
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110110
•導線上電子之運動受電場作用之淨效應
•Fig.•電流 I = nAqvd
•電流密度dvnqJ
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111111
§§ 66--33
電阻電阻
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112112
•導體上某兩點間的電位差V,電流I => 電阻 R = V / I
•電流密度與電場之關係
EEJ
1
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113113
**電阻率與溫度關係電阻率與溫度關係
•Fig.
電阻率之溫度係數
)](1[ 00 TT
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114114
§§ 66--44
歐姆定律歐姆定律
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115115
•一裝置兩端之電位差正比於流經該裝置之電流
•V = IR•Fig.•歐姆性裝置 => I-V關係為一直線
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116116
§§ 66--55
功率功率
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117117
RV
RIIVP
Vdtdq
dtdU
P
22
)(
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118118
Chapter 7Chapter 7
直流電路直流電路
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119119
•電流流經電阻 => 電阻發熱 => 消耗電能
•電路之電流要持續 => 需有提供電能之裝置 => 電動勢源
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120120
§§ 77--11
電動勢電動勢
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121121
•電動勢源 =>可將某種形式之能量,如化學能,轉變成電位能 =>電池
•Fig.
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122122
•電動勢(emf)定義: Wne / q•驅使電荷環繞封閉迴路作運動時,對每單位電荷所作的功
•Fig.•端電壓Vba=Vb-Va
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§§ 77--22
克希荷夫法則克希荷夫法則
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•克希荷夫接點法則 => 進入或離開某個接點之電流,其代數和為零
•Fig.
I
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•克希荷夫迴路法則 => 環繞一封閉迴路之電位變化量代數和為零
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§§ 77--33
串聯與並聯串聯與並聯
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☆串聯☆串聯
•Fig.
Neq RRRRRRIVVV
21
2121 )(
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☆並聯☆並聯
•Fig.
Neq RRRR
RV
RV
III
1111
21
2121
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§§ 77--44
RCRC 電路電路
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•電路包含電容器 => 電容充放電=> 電流會隨時間變化(是時間t之函數)
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☆放電☆放電
•Fig.
RCt
RCt
eIIeQQkRCt
Q
dtRCQ
dQR
dtdQ
CQ
dtdQ
IIRCQ
00ln
10
0
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☆充電☆充電
•Fig.
RCt
RCt
eIIeQQkRCt
QCE
dtRCQCE
dQRC
dtdQ
QCE
dtdQ
ICQ
IRE
00 )1()ln(
1
0
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§§ 77--55
直流儀表直流儀表
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•安培計 => 測量電流儀表•伏特計 => 測量電位差儀表•以檢流計為基礎•Fig.
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•惠司登電橋•Fig.•I1R1=I2Rs及I1R2=I2Rx
•Rx=(R2/R1)Rs
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Chapter 8Chapter 8
磁場磁場
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§§ 88--11
磁場磁場
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•帶電粒子受磁場影響•Fig.
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§§ 88--22
載流導體上的作用力載流導體上的作用力
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•導線上有電流流動 => 電子整體有一漂移速度 => 感受磁力作用 =>作用力轉移至導線上
•Fig.•Fig.
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BIF
BIFnAevI
BevnAF
d
d
向量式
)(
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§§ 88--33
電流迴路所受的轉矩電流迴路所受的轉矩
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•均勻磁場作用一電流迴路 => 靜力為零 => 可有一轉矩 => 轉矩有令迴路旋轉趨勢
•Fig.
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sin)sin2
)((2
ˆ)̂()̂(
ˆ)̂()̂(
2
1
IABa
IcB
jIcBiBkcIF
jIcBiBkcIF
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•Fig.
列之傾向此轉矩有令磁矩方向排
轉矩
磁偶極矩
B
nNIA
ˆ
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§§ 88--44
檢流計檢流計
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•Fig.•偏轉角度正比於電流量
INAB
NIAB
B
sp
B
sin
sin
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§§ 88--55
磁場中帶電粒子的運動磁場中帶電粒子的運動
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•Fig.•軌道半徑正比於粒子之線動量而反比於磁場強度
qBmv
rr
mvqvB
maF
2
得
牛頓第二定律
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150150
mqB
f
qBm
vr
T
qBm
vr
c
2
22
迴旋頻率
軌道週期為
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151151
§§ 88--66
電場與磁場之聯合電場與磁場之聯合
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•一粒子在同一區域內同時受到電場與磁場的作用之總作用力=> 勞侖茲力
)( BvEqF