電磁場與電磁波第8講邊界條件電容能量(編輯修改稿)
2025-05-27 01:32 本頁面
【文章內(nèi)容簡介】 常數(shù) ,與電荷 Q 和導(dǎo)體之間的電位差 V12都無關(guān) .電容器即使沒有電壓提供或?qū)w上沒有自由電荷它也是存在的 . 16 Capacitance C can be determined from above equation by either (1) assuming a V12 and determining Q in terms of V12, or (2) assuming a Q and determining V12 in terms of Q. At this stage, since we have not yet studied the methods for solving boundaryvalue problems (which will be taken up in Chapter 4), we find C by the second method. The procedure is as follows: 1. 對已知的幾何形狀 ,選擇合適的坐標(biāo)系 . 2. 假設(shè)導(dǎo)體上攜帶了電荷 +Q and Q. 3. 通過高斯定理或其它關(guān)系根據(jù)假設(shè)的電荷量 Q來確定 E. 4. 求出導(dǎo)體兩端的電位差 V12. 5. Find C by taking the ratio Q/V12. 112 2V E d l???＝snE???17 Example 318 P124 18 Example 319 P125 19 (1) Series＆ Parallel Connections of Capacitors Parallel Connections of Capacitors 電容器的電壓相等 nCCCC ???? ?21//Series connections of capacitors(電容器的電量相等 ) nnsr CCCC11111???? ?(2) Capacitances In Multiconductor Systems 20 QqP靜電能來源： 外力克服電場力做功轉(zhuǎn)化而來 ， 靜電場能僅與帶電體的最終帶電狀態(tài)有關(guān)而與到達這一狀態(tài)的中間過程無關(guān) 。 靜電能：當(dāng)電荷放入電場中 ， 就會受到 電場力 的作用 ， 電場力做功使電荷位移 ， 這說明電場具有能量 。 靜電場內(nèi)儲存著能量 ， 這種能量通常被稱為靜電能 。 電場越強 ， 對電荷的力就越大 ， 做功的能力就越強 ， 說明電場具有的能量就越大 。 212 1 2 1= ( ) PPW W Q E dl Q V V? ? ? ? ??3. Electrostatic Energy 能量的零點 ： 最初 電荷 都分散在彼此相距很遠(yuǎn) (無限遠(yuǎn) )的位置上 。 通常規(guī)定 ， 處于這種狀態(tài)下的靜電能為零 。 靜電場能量 We等于于把各部分電荷從無限分散的狀態(tài)聚集成現(xiàn)有帶電體系時抵抗靜電力所作的全部功 。 21 Bring a charge Q2 from infinity against the field of a charge Q1 in free space to a distance R12 12012222 4 RVQW????11120212 4 VQRW ????)( 22112 21 VQVQW ??(1) Two charges 1Q 2Q12R1P 2Pwhere V2 is the potential at P2 established by charge Q1, chose the reference point for the potential at infinity。 This work is stored in the assembly of the two charges as potential energy. Another form where V1 is the potential at P1 established by charge Q2 . 22 Bring another charge Q3 from infinity to a point that is R13 to charge Q1 and R23 from charge Q2 in free space ,an additional work is required that equals where V3 is the potential at P3 established by charges Q1 and Q2 , W3 , which is stored in the assembly of the three charges Q1 , Q2 , and Q3 , is ???????? ????23021301333 44 RQRVQW???????????? ??????233213311221023 41RRRWWW??(2) Three charges 1Q 2Q12R1P 2P3Q3P13R 23R23 We can rewrite W3 in t
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