第2章电磁场的基本规律第4讲.

工程电磁场复习基本知识点

第一章矢量分析与场论 1 源点是指。 2 场点是指。 3 距离矢量是，表示其方向的单位矢量用表示。 4 标量场的等值面方程表示为，矢量线方程可表示成坐标形式，也可表示成矢量形式。 5 梯度是研究标量场的工具，梯度的模表示，梯度的方向表示。 6 方向导数与梯度的关系为。 7 梯度在直角坐标系中的表示为u ?= 。 8 矢量A 在曲面S 上的通量表示为Φ= 。 9 散度的物理含义是。 10 散度在直角坐标系中的表示为??=A 。 11 高斯散度定理。 12 矢量A 沿一闭合路径l 的环量表示为。 13 旋度的物理含义是。 14 旋度在直角坐标系中的表示为??=A 。 15 矢量场A 在一点沿l e 方向的环量面密度与该点处的旋度之间的关系为。 16 斯托克斯定理。 17 柱坐标系中沿三坐标方向,,r z αe e e 的线元分别为，，。 18 柱坐标系中沿三坐标方向,,r θαe e e 的线元分别为，，。 19 221111''R R R R R R ?=-?=-=e e

20 0(0)11''4() (0)R R R R R πδ≠???????=??=? ? ?-=????? 第二章静电场 1 点电荷q 在空间产生的电场强度计算公式为。 2 点电荷q 在空间产生的电位计算公式为。 3 已知空间电位分布?，则空间电场强度E = 。 4 已知空间电场强度分布E ，电位参考点取在无穷远处，则空间一点P 处的电位P ?= 。 5 一球面半径为R ，球心在坐标原点处，电量Q 均匀分布在球面上，则点,,222R R R ?? ??? 处的电位等于。 6 处于静电平衡状态的导体，导体表面电场强度的方向沿。 7 处于静电平衡状态的导体，导体部电场强度等于。 8处于静电平衡状态的导体，其部电位和外部电位关系为。 9 处于静电平衡状态的导体，其部电荷体密度为。 10处于静电平衡状态的导体，电荷分布在导体的。 11 无限长直导线，电荷线密度为τ，则空间电场E = 。 12 无限大导电平面，电荷面密度为σ，则空间电场E = 。 13 静电场中电场强度线与等位面。 14 两等量异号电荷q ，相距一小距离d ，形成一电偶极子，电偶极子的电偶极矩 p = 。 15 极化强度矢量P 的物理含义是。 16 电位移矢量D ，电场强度矢量E ，极化强度矢量P 三者之间的关系为。 17 介质中极化电荷的体密度P ρ= 。 18介质表面极化电荷的面密度P σ= 。

外贸函电翻译参考答案修订稿

外贸函电翻译参考答案 WEIHUA system office room 【WEIHUA 16H-WEIHUA WEIHUA8Q8-

Lesson 2 1. We avail ourselves of this opportunity to introduce to you as a foreign-invested corporation specializing in arts and crafts. 2. We want to acquaint ourselves with the supply position of steel products。 3 We are enclosing a cope of pricelist. have 28 distributors across the world. 5. We are one of the leading exporters of Chinese industrial products and are desirous of entering into business relations you. Lesson 3 are a dealer in Egypt.。 2. I have?2 years of?follow-up purchase orders and shipping experience 3. We have pictures of sports shoes selling well in UK. 4. We are sending some samples and brochures under separate cover for your reference. 5. We are interested in the electric appliance in your sample. Please kindly send your quotations to us. 6. We’d like to inform that you’ll find our new products are at Stand 16. Lesson 4 1. We are looking for a reliable supplier who can provide us the laptop. 2. I would like to buy computers and computer parts. Please send me a detailed pricelist with min. Order and shipping costs.

电磁场与电磁波课后习题及答案--第四章习题解答

习题解答 4.1 如题4.1图所示为一长方形截面的导体槽，槽可视为无限长，其上有一块与槽相绝缘的盖板，槽的电位为零，上边盖板的电位为 U ，求槽内的电位函数。解根据题意，电位(,)x y ?满足的边界条件为 ① (0,)(,)0y a y ??== ② (,0)0x ?= ③ 0(,)x b U ?= 根据条件①和②，电位(,)x y ?的通解应取为 1 (,)sinh( )sin()n n n y n x x y A a a ππ?∞ ==∑ 由条件③，有 01 sinh( )sin()n n n b n x U A a a ππ∞ ==∑ 两边同乘以 sin( ) n x a π，并从0到a 对x 积分，得到 00 2sin()d sinh()a n U n x A x a n b a a ππ== ? 02(1cos )sinh()U n n n b a πππ-=04,1,3,5,sinh()02,4,6,U n n n b a n ππ? =? ? ? = ?，故得到槽内的电位分布 1,3,5, 41(,)sinh()sin() sinh()n U n y n x x y n n b a a a ππ?π π== ∑ 4.2 两平行无限大导体平面，距离为b ，其间有一极薄的导体片由d y =到b y =)(∞<<-∞x 。 a 题4.1图

上板和薄片保持电位 U ，下板保持零电位，求板间电位的解。设在薄片平面上，从0=y 到 d y =，电位线性变化，0(0,)y U y d ?=。解应用叠加原理，设板间的电位为 (,)x y ?=12(,)(,)x y x y ??+ 其中， 1(,)x y ?为不存在薄片的平行无限大导体平面间（电压为 U ）的电位，即 10(,)x y U y b ?=；2(,)x y ?是两个电位为零的平行导体板间有导体薄片时的电位，其边界条件为： ① 22(,0)(,)0x x b ??== ② 2(,)0() x y x ?=→∞ ③ 002100(0)(0,)(0,)(0,)() U U y y d b y y y U U y y d y b d b ????-≤≤??=-=? ?-≤≤?? 根据条件①和②，可设2(,)x y ?的通解为 21(,)sin()e n x b n n n y x y A b π π?∞ -==∑ 由条件③有 00100(0)sin()() n n U U y y d n y b A U U b y y d y b d b π∞ =? -≤≤??=??-≤≤??∑ 两边同乘以 sin( ) n y b π，并从0到b 对y 积分，得到 0002211(1)sin()d ()sin()d d b n d U U y n y n y A y y y b b b b d b b ππ=-+-=??022sin() ()U b n d n d b ππ 故得到 (,)x y ?=00 22121sin()sin()e n x b n U bU n d n y y b d n b b π πππ∞ -=+∑ 题 4.2图

外贸函电课后练习答案

Unit 2 Establishing Business Relations & Inquiring Credit Reference I. Translate the following sentences into English. 1. We are one of the leading importers dealing in electronic products in the area, and take this opportunity to approach you, in the hoping of establishing business relations. 2. We have been engaged in handling importing and exporting of machinery and equipment for many years, and our products have enjoyed great popularity in many countries. 3. We owe your name and address to the Commercial Counselor’s office of our Embassy in Beijing. 4. We are given to understand that you are a manufacturer of daily chemicals. One of our clients intends to buy cosmetics from your country. We will appreciate it highly if you airmail the catalogue and price list of the goods available at present. 5. For our credit standing, please refer to the Bank of China, Shanghai Branch. II. Write a letter Dear Sirs, We have obtained your name and address from the Commercial Counsel of your Embassy in Beijing and are pleased to write to establish business relations with you. We are informed that you are in the market for Chinese Cotton Piece Goods, and this item falls with the scope of our business activities. To acquaint you with our goods available for export, we are enclosing a catalogue and price list. We are looking forward to your early reply. Faithfully yours, Unit 3 Enquiries and Replies II. Translate the following sentences into English. 1. Please quote us your best price CIF Shanghai, including our 3% commission. 2. Should your price be found competitive, we intend to place an order with you for 300,000 yards of Cotton Cloth. 3. One of our customers is now interested in the Qingdao Haier Refrigerator made in your country. Please offer CIF London for 400 sets to be delivered in April.

工程电磁场基本知识点

12 矢量A 沿一闭合路径l 的环量表示为。 13 旋度的物理含义是。 14 旋度在直角坐标系中的表示为??=A 。 15 矢量场A 在一点沿l e 方向的环量面密度与该点处的旋度之间的关系为。 16 斯托克斯定理。 17 柱坐标系中沿三坐标方向,,r z αe e e 的线元分别为，，。 18 柱坐标系中沿三坐标方向,,r θαe e e 的线元分别为，，。 19 221111''R R R R R R ?=-?=-=e e 20 0(0)11''4()(0)R R R R R πδ≠???????=??=? ? ?-=?????

第二章静电场 1 点电荷q 在空间产生的电场强度计算公式为。 2 点电荷q 在空间产生的电位计算公式为。 3 已知空间电位分布?，则空间电场强度E= 。 4 已知空间电场强度分布E ，电位参考点取在无穷远处，则空间一点P 处的电位P ?= 。 5 一球面半径为R ，球心在坐标原点处，电量Q 均匀分布在球面上，则点,,222R R R ?? ???处的电位等于。 6 处于静电平衡状态的导体，导体表面电场强度的方向沿。 7 处于静电平衡状态的导体，导体内部电场强度等于。 8处于静电平衡状态的导体，其内部电位和外部电位关系为。 9 处于静电平衡状态的导体，其内部电荷体密度为。 10处于静电平衡状态的导体，电荷分布在导体的。 11 无限长直导线，电荷线密度为τ，则空间电场E=

工程电磁场教案-国家精品课华北电力学院崔翔-第4章(倪光正主编教材)

第四章准静态电磁场 4．1 准静态电磁场 1．电准静态场由麦克斯韦方程组知，时变电场由时变电荷和时变磁场产生的感应电压产生。时变电荷产生库仑电场，时变磁场产生感应电场。在低频情况下，一般时变磁场产生的感应电场远小于时变电荷产生的库仑电场，可以忽略。此时，时变电场满足 ρ =??≈??D 0E 称为电准静态场。可见，电准静态场与静电场类似，可以定义时变电位函数? ，即 ?-?=E 且满足泊松方程 ε ρ?-=?2 与电准静态场对应的时变磁场满足 0 t =????+ =??B D E H γ 2．磁准静态场由麦克斯韦方程组知，时变磁场由时变传导电流和时变电场产生的位移电流产生。在低频情况下，一般位移电流密度远小于时变传导电流密度，可以忽略。此时，时变磁场满足 0=??≈??B J H c 称为磁准静态场。可见，磁准静态场与恒定磁场类似，可以定义时变矢量位函数A ，即 A B ??= 且满足矢量泊松方程 c J A μ-=?2 与磁准静态场对应的时变电场满足 ρ =????- =??D B E t

例1：图示圆形平板电容器，极板间距d = 0.5 cm ，电容器填充εr =5.4的云母介质。忽略边缘效应，极板间外施电压 t t u 314cos 2110)(=V ，求极板间的电场与磁场。 [解]：极板间的电场由极板上的电荷和时变磁场产生。在工频情况下，忽略时变磁场的影响，即极板间的电场为电准静态场。在如示坐标系下，得 ()()()V/m t 31410113t 31410 501102d u z 4z 2z e e e E -?=-??=-=-cos .cos . 由全电流定律得出，即由 ()z z 20r 4S l t 31431410113d t H 2d e e S D l H ?-π??-=???=π=???ρεερφsin . 极板间磁场为 φφφρe e H t 314103352H 4sin .-?== A/m 也可以由麦克斯韦方程直接求解磁场强度，如下 t t 0r ??=??=??E D H εε 展开，得 t 314106694H 14sin .)(-?=??φρρ ρ 解得 φφφρe e H t 314103352H 4sin .-?== A/m 讨论：若考虑时变磁场产生的感应电场，则有 t t ??-=??-=??H B E 0μ 展开，得 t E z 314cos 103.231440ρμρ -??-=??- 解得 t E z 314cos 10537.428ρ-?= V/m 可见，在工频情况下，由时变磁场产生的感应电场远小于库仑电场。图平板电容器

外贸函电翻译参考答案

separate cover for your reference. 5. We are interested in the electric appliance in your sample. Please kindly send your quotations to us. 6. We'd like to inform that you'll find our new products are at Stand 16. Lesson 4 1. We are looking for a reliable supplier who can provide us the laptop. 2. I would like to buy computers and computer parts. Please send me a detailed pricelist with min. Order and shipping costs. 3 Regarding the model we attached here, our target price is for our market. 4. We allow you a discount of 3% for quantity over 1000 pieces of the offered item. 5. As regards our financial standing, please refer to the Bank of China, Shanghai Branch. Lesson 5

外贸函电课后练习答案大全

选择题第二单元：询价与回复一：1.You name D. has been recommended to us by the Chamber of Commerce in New York.. 2. Our market survey informs us that you are A. in the market for Audio and Electronic Equipment. 3. We should be pleased to receive you’re A. illustrated catalogue and price list. 4. We are B. well-established exporters of all kinds of Chinese good. 5. If your price are competitive, we are confident D. in selling the goods in great quantities in this market. 6. We shall appreciate B. your quoting us FOB Sydney. 7. As we are one of the leading importers in this line, we are B. in a position to handle large quantities. 第三单元：资信调查一：1.For information D. concerning our credit standing we refer you to Bank of China, Shanghai Branch. 2. We should be grateful if you would say C. whether they are likely to be reliable for a credit up to USS20.000. 3. Any information you kindly give us will be treated in strict confidence and A. without any responsibility on your part. 4. Will you please inform us, B. in confidence, of the extent of their resources and also as to their reputation? 5. D. While appreciating your decision to place regular orders with us, we respectfully request that you furnish us two references for the initial purchase. 第四单元：促销 1.（C、Having made）a special purchase of toys on very favorable terms, we are able to offer to you at the following attractive prices 2 we can only（A、hold open）this very advantageous offer for a few weeks.. 3 the recent advance in the cost of raw materials （B、has compelled）us to make a slight increase in the Prices 4 although costs have been （C、rising）steadily since last October , we have not yet （raised）our prices 5 （B、with a view to ）supporting your sales, we are sending some samples of our new makes. 第五单元：报盘与还盘 1A comparison of your offer （A、with that of ）our regular suppliers shows that their figures are more favorable. 2 If your prices are competitive, we are confident（D、in selling）the goods in great quantities in this market. 3 we confirm our fax just sent （A、offering you firm）these goods. 4 we offer you the following items（D、subject to）your reply reaching here by 4p.m today our time. 5 although we appreciate good quality of your goods, we are sorry to say that your prices appears to be（C、on the high side）. 6 we trust that we may be （C、favored）with a continuance of your valued orders. 7 we hope that you will see your way to （B、grant）us your order, and assure you in advance of its most careful execution 8 not having heard from you since, we should be glad to know whether there is any disadvantage in our terms which we could （B、remove）. 9 you are （C、assured）that we will quote our best prices as soon as we are told what products of ours you need. 10 in all probability this offer will not be （A、repeated）for some time, and we according look forward to receiving an early reply from you. 第六单元: 订单一、Fill in the blanks with your choices 1.This order the sample you sent us on March 24.（A、is placed on） 2.We hope you will give your usual best attention this order.（B、to the execution of） 3.We have decided to place a trial order for the following stated in your letter.（B、on the terms） 4.we would like to supply you with the product, we are unable to fill your order owing to the heavy backlog of commitments. (B、Much as) 5.We must apologize you being unable to fill your present order.（D、To… for ） 6.We have accepted your Order No.234. Please open the relevant L/C,here two weeks prior to the date of shipment.（A、which must reach） 7.We are enclosing our latest catalogue some of the items may be of interest to you.（C、in the hope that） 8.The order is given strictly on the condition that shipment must be made not later than the first day of May.（B、enclosed）第七单元：支付一、单选 1.As requested, we have immediately arranged (A、with) our bankers to extend the expiry date of our L/C for two weeks (up to) 10th March. 2.As arranged, we would ask you to open an irrevocable credit in (C、our) favor and shall hand over shipping documents (against) acceptance of our draft. 3.We inform you that we have opened an irrevocable credit (D、with) the London Bank in your favor. 4.We advised the bank to amend the clause (D、to read)“partial shipment are permitted”. 5.We enclose our cheque for US$ 200 (A、in payment of) your invoice No.D-124. 第九单元：保险一：选择题 1: please insure the goods (A、against) F.P.A. for US 100,000. 注：against加险别for加保额 2: please effect insurance (D、on) the cargo for US50,000 by S.S.Bright from Tianjin to seattle. 3: we have opened insurance you ordered for US9,000 (D、on) the shipment by S.S.East sun. 4: we wish to renew the above policy (C、for) the same amount and (on)the same terms as before to cover our consignment to be shipped b s.s.bright next month. 5: as requester, we have covered insurance (on) 20,000 DVD players (at) 10% above the invoice value (against) all risks. 6: unless we hear from you (A、to) the contrary before the end of this month, we shall arrange to cover the goods against t p a for the value of the goods plus freight. 7: any additional coverage（险别）other (B、than) ISS shall be for the account of the buyer. 8: we confirm that we hold the consignment covered as (from) today. 9: we have arranged (A、for) surveyor to investigate the extent of the damage and shall forward his report together with our claim. 10: we understand that these terms will apply (C、to)all our shipments of bottled sherry by regular liners to west European ports. 完形填空第二单元：Fill in each blank in the letter below with a word that fits naturally.

电磁场第四章习题

O 0=φ 4.1 两块无限大接地平行板导体相距为d,其间有一与导体板平行的无限大电荷片，其电荷面密度为S ρ，如图所示。试通过拉普拉斯方程求两导体之间导体分布。 4.2 设很长的同轴圆柱结构的内、外导体之间填充以电子云，其电荷体密度 r A =ρ )(b r a <<,其中a 和b 分别为内、外导体的半径，A 为常数。设内导体维持在电位0V ，而外导体接地用解泊松方程的方法求区域b r a <<内的电位分布。 4.3 通过解电位的泊松方程和拉普拉斯方程，确定球形电子云内部和外部的电位和电场。已知电子云内部区域b r ≤≤0，有均匀的体电荷密度0ρρ-=；在电子云外部区域b r >中，0=ρ。 4.4 一电荷量为q 质量为m 的小带电体，放置在无限大导体平面下方，与平面距离h 。求q 的值以使带电体上受到的静电力恰与重力相平衡。(设m h kg m 02.0,1023=?=-)。 4.5 一个点电荷q 与无限大导体平面距离为d ，如果把它移到无穷远处，需要做多少功？ 4.6 两点电荷Q 和Q -位于一个半径为a 的导体球直径的延长线上，分别距球心D 和D -。 (1) 证明：镜像电荷构成一偶极子，位于球心，偶极矩为232D Q a (2) 令D 和Q 分别趋于无穷，同时保持 2 D Q 不变，计算球外的电场

题 4.6 图 4.7 半径为a 的长导线架在空中，导线和墙和地面都相互平行，且距墙和地面分别1d 和2d ，设墙和地面都视为理想导体，且a d >>1，a d >>2。试求此导线对地的单位长电容。 4.8 半径为a 的接地导体球，离球心1r (a r >1)处放置一个点电荷q ，如图所示,用分离变量法求电位分布。 4.9 在一个半径为a 的圆柱面上，给定其电位分布： ? ??=00U φ 00<<-<

《电磁场与电磁波》(第四版)习题集：第2章电磁场的基本规律

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