Chapter 22 Electric Fields PDF - Physics Lecture Slides
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NCKU
J.C.A. Huang
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These lecture slides, authored by J.C.A. Huang from NCKU, cover the fundamental concepts of electric fields, including electric charges, conductors, and related principles such as Gauss's law and Coulomb's law. The slides appear to act as an introduction in Chapter 22 and the lecture explores the movement of charged particles in electric fields.
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普物第二學期 評分標準 : 1. 平時 + 作業 : 20% 2. 期中考 : 40% 3. 期末考 : 40% 加分題報告 J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) 電荷的性質 ( Properties of electric...
普物第二學期 評分標準 : 1. 平時 + 作業 : 20% 2. 期中考 : 40% 3. 期末考 : 40% 加分題報告 J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) 電荷的性質 ( Properties of electric charge ) Benjamin Franklin (1706-1790) found that there are two kinds of electric charges : positive , negative. Like charges repel one another and unlike charges attract one another. Conservation of Charge The net charge of a closed system never changes. J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) 電荷的性質 ( Properties of electric charge ) Robert Millikan (1868-1953) discovered that electric charge always occurs as some integral multiple of a fundamental amount of charge e. electric charge q is quantized. q = Ne J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) 電磁力將電子束縛於原子核而形成原子和分子 Net charge is always a multiple of e : Qnet = Ne J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) 絕緣體與導體 ( Insulators and Conductors ) 1. Electric conductors : materials in which electric charges move freely. Metals : Gold, Copper, Silver. 2. Electric insulators : materials in which electric charges cannot move freely. Glass, Plastic, Wood 3. Semiconductors :materials in which the electrical properties are somewhere between those of insulators and those of conductors. Silicon, Germanium J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) 水通常被視為導體。這樣地假設是聰明的,注意不要用溼的 手去碰觸電子元件。事實上,純水是一個絕緣體。純水幾乎 由完整的水分子 (H2O) 所組成,當它們移動時並不帶任何淨 電荷;只有少量的離子濃度 (H+ 及 OH-) 。但是自來水就不 再是純的—它含有溶解的礦物質。這些礦物質可大大地增加離 子的濃度,使自來水成為一個導體。人體含有許多的離子, 因此是一導體。 空氣是一個可靠的絕緣體,因為空氣中大多數的分子是電中 性的,當它們在移動時不會帶有電荷。然而,空氣中確實含 有些許離子;放射性衰變或宇宙射線都可使空氣分子離子化。 J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) 動物毛皮 摩擦電 硬橡膠棒 J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) 古希臘人使用琥珀 - 由松樹樹液形成的堅硬化石 - 用以製造珠寶。當我們用 一小片布織料摩擦一小塊琥珀時,將發現琥珀會吸引些許纖維或頭髮。就當 今的知識來看,琥珀是由摩擦而帶電:在琥珀和布料之間一些電荷被轉移。 “ 電”一字乃源自於希臘字的琥珀 (elektron) 。 在一個乾燥的日子裡,當你穿著膠底鞋走過舖了地毯的房間時,一個熟悉的 現象便會發生。電荷會在地毯與你的鞋子之間以及你的鞋子與身體之間轉移。 你身上所累積的一些電荷,可能會在無意間藉由電擊作用從你的指尖轉移到 門把或朋友。 J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) 感應生電 ( Charging by induction ) J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) 接地 如何使一個導體放電?一種方法是使它接地。由於存在著金屬離子及水 分,地球是一個導體。地球是足夠大的,對許多目的而言可以將它視為 一個無限制的電荷庫。故意地使用”庫”這個字是要憶起熱庫。一個熱庫 有非常大的熱容量,使得與它交換熱而不會改變它的溫度是可能的。將 一個導體接地指的是在導體與地面 ( 或另一電荷庫 ) 之間提供一條傳導 路徑。一個帶電的導體接地後會放電,這是因為電荷由導體移出後散佈 在地球上。 在一個運送汽油的卡車上,即使非常少量的電荷的堆積都是很危險的— 一個火花就可能會引發爆炸。為了防止這種電荷堆積,卡車在開始送汽 油到加油站前會先將油箱接地。 現代的電源插座的第三個孔是稱為接地。透過插入地面的金屬棒或是透 過地下金屬水管,它可以正確地將一導線連接到地面上。 接地的導體上可以避免靜電荷的堆積。 J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) 影印機 影印機 ( 和雷射印表機 ) 的操作是建立在電荷的分離及不同電荷 之間的吸引的基礎上。 (1) 充電 : 鍍硒的鋁製滾筒藉由在電極下的轉動而 帶正電荷。 (2) 曝光 : 將欲影印文件的投射影像照射到滾筒上 ( 或利用雷 射 ) 。硒是一種光導體—一個光敏半導體。當沒有光照在硒上時,它是一 個十足的絕緣體;但是當光照到它時,它變成一個良導體。鍍在滾筒上 的硒起先是在暗處,它如同絕緣體可以被帶電。當硒被光照時,光照到 的區域變成導體。電子從鋁—一個良導體—進入到硒被光照的部分,中和 了正電荷。沒有被光照到的鍍硒區域是不允許電子從鋁流進去,所以這 些區域依舊是帶正電。 (3) 顯影 : 接下來,滾筒會和一種稱為調色劑的黑 色粉末接觸。調色劑粒子已帶有負電,因此它們會被吸引到滾筒上帶正 電的區域。調色劑黏在滾筒上有正電的地方,沒有帶電的地方調色劑是 不會黏附。 (4) 轉印 : 此時將一張紙轉動於滾筒上,正電荷被加到紙張的 背面。在紙上的電量大於滾筒上的電量,紙張會從滾筒上吸走那些帶負 電的調色劑粒子,在紙上形成原稿的影像。 (5) 定影 : 最後一步就是將 紙通過墨輥,使得調色劑熔入紙中。隨著墨水滲入紙張纖維中,複製就 完成了。 J.C.A. Huang, Professor, Department of Physics, NCKU Y.M. Hu, Associate Professor, Department of Applied Physics, National University of Kaohsiung Chapter 22 電場 (Electric Fields) J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) A piece of plastic is uniformly charged with surface charge density 1. The plastic is then broken into a large piece with surface charge density 2 and a small piece with surface charge density 3. Rank in order, from largest to smallest, the surface charge densities 1 to 3. 1. η1 > η2 > η3 2. η1 > η2 = η3 3. η1 = η2 = η3 4. η2 = η3 > η1 5. η3 > η2Department J.C.A. Huang, Professor, > η1 of Physics, NCKU Chapter 22 電場 (Electric Fields) 庫倫定律 ( Coulomb’s Law ) Charles Coulomb (1736-1806) measured the magnitudes of the electric forces between charged objects using the torsion balance, which he invented. q1 q2 Fe ke 2 r Fe : Coulomb force ke : Coulomb constant = 8.9875 109 N·m2/C2 1 ke 4 0 0 : permittivity of free space = 8.8542 10-12 C2/ N·m2 * 1C of charge is approximately equal to the charge of 6.24 1018 electrons or protons. J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) 庫倫定律 ( Coulomb’s Law ) The Coulomb’s law expressed in vector form for the electric force exerted by a charge q1 on a second charge q2 , written F12 , is q1q2 F12 ke 2 rˆ r Where r̂ is a unit vector directed from q1 to q2. J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) 電場 ( Electric Field ) The electric field E at a point in space is defined as the electric force Fe acting on a positive test charge q0 placed at that point divided by the magnitude of the test charge : Fe E q0 J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) 電位置 (Electrolocation) 早在科學家學習如何偵測以及測量電場之前,某些動物和魚類進化出產 生以及偵測電場的器官。尼羅河魔鬼在沿著牠身體長度的地方有電的器 官運作;這些器官在魚的周圍建立了一個電場。當一個附近的物體扭曲 了場線時,尼羅河魔鬼利用靠近頭部的感覺器官偵測到此變化而反應。 這些額外的感覺,使得此魚可以在眼晴看不太到的混濁河流中,偵測到 獵物或敵人。 自從尼羅河魔鬼主要依靠電位置 ( 電場中微小的變化被理解為附近物體 的存在 ) 後,牠要能夠一再地產生相同的電場是很重要的。為此,尼羅 河魔鬼靠著起伏牠背部的長鰭游泳,而保持牠的身體不易彎曲。骨幹筆 直的保持,使得負電荷和正電荷中心排成一直線且分開在一固定距離。 游動的尾巴會造成電場中的變動,使得電位置較不準確。 J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) 電場線 ( Electric Field Lines ) 1. The electric field vector E is tangent to the electric field line at each point. 2. The number of lines per unit area through a surface perpendicular to the lines is proportional to the magnitude of the electric field in that region. J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) 電場線 ( Electric Field Lines ) 1. The lines must begin on a positive charge and terminate on a negative charge. 2. The number of lines drawn leaving a positive charge or approaching a negative charge is proportional to the magnitude of the charge. 3. No two field lines can cross. J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) 電場 ( Electric Field ) qq Fe ke 20 rˆ Where r̂ is a unit vector directed from q to q0 r q q Ee ke 2 rˆ Ee ke 2i rˆi r i ri At any point, the total electric field due to a group of charges equals the vector sum of the electric fields of the individual charges. J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) 電偶極之電場 ( Electric Field of a Dipole ) E E1 E2 q q E1 E2 ke 2 ke 2 r y a2 q a 2qa E 2 E1 cos 2ke 2 2 2 2 1/ 2 ke 2 (y a ) (y a ) ( y a 2 )3 / 2 Because y >> a, we neglect a2 and write 2qa E ke 3 y J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) Why is this important? Principle of microwave oven, amongst other applications Recall: =r x F If F=qE, then =qE r sin ( where is the angle between E and r) Let d=distance between two charges Electric Dipole Moment Necessary because the charge and distance between charges are easy to characterize p=qd Note: p is a vector in the direction pointing from 1 charge to the other =pE sinor =p x E Recall that W=-U, W=F·r=Fr cos=qEd cosU=-qd E cos U = - p·E which is the potential energy of a dipole in an electric field J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 23 電場 (Electric Fields) 避雷針通常出現在高的建築物 以及老舊農舍的屋頂上。避雷 針的上方都是做成一個尖銳點。 當一個短暫的大雷雨吸引電荷 到針的頂端時,尖銳點處的強 電場會將附近的空氣分子離子 化。中性空氣分子在運動時不 會轉移淨電荷,但是離子化的 分子會,所以離子化使得電荷 能藉由空氣平緩地漏出建築物, 而不會增加到一個危險的高電 荷值。如果避雷針沒有做出一 個尖銳點,電場就不可能大到 足以將空氣離子化。 J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) 通常我們將電路與電纜放在 金屬包套中,以保護它們不 受其它元件所產生零星電場 的影響。當外來電場變化時 在,金屬包套中的自由電子 會自我重新排列。只要金屬 包套中的電荷能跟上外來電 場的變化,此外來電場在包 套內部中會被抵消掉。 J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) 一連續電荷分佈的電場 ( Electric Field of a Continuous Charge Distribution ) q q E ke 2 i rˆi E ke 2 rˆ r i ri qi dq E ke lim qi 0 i r 2 i e r 2 rˆ ˆ r k i If a charge Q is distributed uniformly not uniformly Q dQ Volume charge density V dV Surface charge density Q dQ A dA Linear charge density Q dQ d J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Field) 一帶電長棒的電場 ( Electric Field Due to a Charged Rod ) Uniform positive charge per unit length dq dx dq dx dE ke k e x2 x2 a dx a dx 1 a k ( 1 1 ) keQ E ke 2 ke 2 ke [ ]a e a x a x x a a a ( a ) keQ If a >> E a2 J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) 一均勻帶電環的電場 ( Electric Field of a Uniform Ring of Charge ) dq dE ke r2 dq x ke x dE x dE cos ( ke 2 ) 2 2 3/ 2 dq r r (x a ) kx kx kx E x 2 e 2 3 / 2 dq 2 e 2 3 / 2 dq 2 e 2 3 / 2 Q (x a ) (x a ) (x a ) keQ If x >> a Ex 2 x J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) 一均勻帶電盤的電場 ( Electric Field of a Uniformly Charged Disk ) dq 2rdr ke x ke x dE x 2 2 3/ 2 dq 2 2 3/ 2 ( 2rdr ) (x r ) (x r ) R 2 rdr R E ke x 2 2 2 3/ 2 2 3 / 2 k e x ( x r ) d (r 2 ) 0 (x r ) 0 ( x 2 r 2 ) 1/ 2 R x x ke x [ ]0 2ke ( 2 2 1/ 2 ) 1/ 2 x (x R ) If R >> x E 2ke 2 0 J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) Uniform Electric Field) J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) 在一均勻電場中帶電粒子的運動 (Motion of Charged Particles in a Uniform Electric Field) Fe qE ma eE ˆ a j m At time = 0 v xi vi v yi 0 eE At time = t v xi vi v yi a y t t m 1 2 eE 2 x vi t y a y t t 2 2m eE 2 y x The trajectory is a parabola 2mvi J.C.A. Huang, Professor, Department of Physics, NCKU Chapter 22 電場 (Electric Fields) J.C.A. Huang, Professor, Department of Physics, NCKU