大学物理练习题答案

大学物理练习题答案 5.3 电场强度 一(选择和填空 ,、, ,、, ,、 0 ,、,3, / (2,) 0 ,, / (2,) 0 3, / (2,) 0 qdqd,、 ,223，，4,,R2,R,d8,,R00 从O点指向缺口中心点( 二(计算题 ,、解:设杆的左端为坐标原点O，x轴沿直杆方 向(带电直杆的电荷线密度为,=q / L，在x处取一x dq ,x) (L+ddE 电荷元dq = ,dx = qdx / L，它在P点的场强: O , x L d dqqdxdE,, 22，，，，4,,L，d,x4,,LL，d,x00 2分 Lqqdx,E,总场强为 3分 2,，，4,,dL，d,4,L(L，d,x)000 方向沿x轴，即杆的延长线方向( ,、解:先计算细绳上的电荷在O点产生的场强(选细绳顶端作坐标原点O，x轴向下为正(在x处取一电荷元 dq = ,dx = Qdx/(3R) OdqxdE,它在环心处的场强为 12，，4,,4R,xdx03R Qdx, 2分 2R，，12,,R4R,x0E1整个细绳上的电荷在环心处的场强 3xRQdxQ E,, 2分 122,012,,R16,,R，，4R,x00 圆环上的电荷分布对环心对称，它在环心处的场强 E=0 2分 2 ,,,Q,,EEii由此，合场强 2分 1216,,R0to make the following points: the room temperature between relative humidity maintained at 30%-55%, and 7 days a week, 24 hours a day is required. Keep free of dust and well ventilated, brightness of at least 50 candle light. Provide the right door, the door should open outward. To have a sufficient number of dedicated power outlet, provides volt 15 amp AC power to the device. This power supply for power and air conditioning or lighting circuits apart. the whole system's color management according to the design of the comprehensive wiring system, the whole system to the implementation of an integrated color management, that is, different regions using different colors to the mark, specific color meanings are as follows: Blue: represents the regional level subsystems, terminating in the blue area of the cables between the junction between levels to information outlets. White: represents the vertical cable subsystem, terminating in the white areas of the main cable wiring and wiring between floors. Green: input from the Central Office trunks Purple: from the data of common devices such as switches to lead. 2.6.7 design results in accordance with the ideas for the design of comprehensive wiring system, in line with the new plant office building, workshop technology requirements, 155Mbps ATM, and video transmission and other requirements, in line with the 15-20 development of data communication within the development trend of the future. Based on the above design, design the system diagram in Appendix; other engineering equipment offer is attached. Part III, section I of the computer network system, System 方向竖直向下( 三(理论推导与证明题 y 证:选环心作原点，x轴沿圆环轴线方向，y、z 轴如图所示(在环上任取一电荷元dq=(Qd,) / ,r(2,)，设P点位于x处，从电荷元dq到P点的 dq ,, P 矢径为，它在P点产生的场强为 r R d ,,,x dqQd,, ˆˆ ,,dErr222dE ,,,,4r8r00,z ,ˆr为矢径方向上的单位矢量(d沿x轴的分量Er 为 , dE=dEcos, ，,为矢径与x轴正向夹角) rx 由对称性容易证明 E=0 E=0 yz 2,,,QcosQcosQx,,d,因而有 E=E , x 2223/2,0228,,r4,,r4,，，R，x,0002Q / (4,x) 当x>>R时，可得 E?,0 这相当于一个位于原点O的带电量为Q的点电荷在P点产生的场强( 5.4 电场强度通量 高斯定理 一、选择和填空 2,Rq,1-4、 D D C B 5、 q / (6,) 6、 0 7、 0 r0234,,r,r00二. 计算题 1、解:在球内取半径为r、厚为dr的薄球壳，该壳内所包含的电荷为 2 dq,,dV,Ar,4,rdr在半径为r的球面内包含的总电荷为 r34q,,dV,4,Ardr,,Ar (r?R) ,,0V24以该球面为高斯面，按高斯定理有 E,4,r,,Ar/, 10 2，，得到 E,Ar/4,， (r?R) 10 方向沿径向，A>0时向外, A<0时向里( 在球体外作一半径为r的同心高斯球面，按高斯定理有 24 E,4,r,,AR/, 20 42E,AR/，，4,r得到 ， (r >R) 20to make the following points: the room temperature between relative humidity maintained at 30%-55%, and 7 days a week, 24 hours a day is required. Keep free of dust and well ventilated, brightness of at least 50 candle light. Provide the right door, the door should open outward. To have a sufficient number of dedicated power outlet, provides volt 15 amp AC power to the device. This power supply for power and air conditioning or lighting circuits apart. the whole system's color management according to the design of the comprehensive wiring system, the whole system to the implementation of an integrated color management, that is, different regions using different colors to the mark, specific color meanings are as follows: Blue: represents the regional level subsystems, terminating in the blue area of the cables between the junction between levels to information outlets. White: represents the vertical cable subsystem, terminating in the white areas of the main cable wiring and wiring between floors. Green: input from the Central Office trunks Purple: from the data of common devices such as switches to lead. 2.6.7 design results in accordance with the ideas for the design of comprehensive wiring system, in line with the new plant office building, workshop technology requirements, 155Mbps ATM, and video transmission and other requirements, in line with the 15-20 development of data communication within the development trend of the future. Based on the above design, design the system diagram in Appendix; other engineering equipment offer is attached. Part III, section I of the computer network system, System 方向沿径向，A>0时向外，A<0时向里( ,ab4,2、解:球形电容器的电容 C, b,a 当内外导体间电势差为U时，电容器内外球壳上带电荷 ,abU4,q,CU, b,a ,qbU电容器内球 表 关于同志近三年现实表现材料材料类招标技术评分表图表与交易pdf视力表打印pdf用图表说话 pdf 面处场强大小为 E,,, 2，，,4,,aab,a 欲求内球表面的最小场强，令dE/da=0，则 ,,dE11,, ,bU,,022,,da，，ab,a，，ab,a,, 2dEb得到 并有 a,,0 22daa,b/2 ,3解:挖去电荷体密度为, 的小球，以形成球腔时的求电场问题，可在不挖时求出电场，E1而另在挖去处放上电荷体密度为,,的同, , O, ，并令任意点样大小的球体，求出电场E2 O r P O, 的场强为此二者的叠加，即可得 P E=0 ,,,2O’E -, 2P O E 1O’E 2分 E,E，E1P012 在图(a)中，以O点为球心，d为半径 作球面为高斯面S，则可求出O,与P处场图(b) 强的大小. 图(a) 14,,,23EdSE4dd , ,,,,,,,, , 11S3,P 0E O, 1P, O 有 E,E= E,d1O’1PE=E E E 1O’1 O’P2P d 3,0 方向分别如图所示. 3分 在图(b)中，以O,点为小球体的球心，图(d) 可知在O,点E=0. 又以O, 为心，2d为半图(c) 2 径作球面为高斯面S, 可求得P点场强E 2P,,23,，，E,dS,E,4,(2d),4,r(,,)/3, 220,,S 3,r,E 3分 ,2P212,d0, E(1) 求O,点的场强 . 由图(a)、(b)可得 O' ,d E = E=， 方向如图(c)所示. 2分 O’1O’ 3,0,(2)求P点的场强.由图(a)、(b)可得 EP to make the following points: the room temperature between relative humidity maintained at 30%-55%, and 7 days a week, 24 hours a day is required. Keep free of dust and well ventilated, brightness of at least 50 candle light. Provide the right door, the door should open outward. To have a sufficient number of dedicated power outlet, provides volt 15 amp AC power to the device. This power supply for power and air conditioning or lighting circuits apart. the whole system's color management according to the design of the comprehensive wiring system, the whole system to the implementation of an integrated color management, that is, different regions using different colors to the mark, specific color meanings are as follows: Blue: represents the regional level subsystems, terminating in the blue area of the cables between the junction between levels to information outlets. White: represents the vertical cable subsystem, terminating in the white areas of the main cable wiring and wiring between floors. Green: input from the Central Office trunks Purple: from the data of common devices such as switches to lead. 2.6.7 design results in accordance with the ideas for the design of comprehensive wiring system, in line with the new plant office building, workshop technology requirements, 155Mbps ATM, and video transmission and other requirements, in line with the 15-20 development of data communication within the development trend of the future. Based on the above design, design the system diagram in Appendix; other engineering equipment offer is attached. Part III, section I of the computer network system, System 3,,,r 方向如(d)图所示. ,,E,E，E,d,PPP122,,3,4d0,, 5.6 静电场的环路定理 电势能 一. 填空题 ,,1、 E,dl,0,L 单位正电荷在静电场中沿任意闭合路径绕行一周，电场力作功等于零 有势(或保守力) 2、功的值与路径的起点和终点的位置有关，与电荷移动的路径无关 保守 ?5.7 电势 一.选择题和填空题 1-5、,,,,, ,、0 , / (2,) 0 ,、q / (6,,R) 0 QS,,,1,,、 ,,2,4R,4R,,,0 二.计算题 ,、解:设坐标原点位于杆中心O点，x轴沿杆的方向，如图所示(细杆的电荷线密度,,q / (2l)，在x处取电荷元dq = ,dx,qdx / (2l)，它在P点产生的电势为 dqqdxdU,, P，，，，4,,l，a,x8,,ll，a,x00 整个杆上电荷在P点产生的电势 lqdxq2l,ql,,U,,ln1，，， ,lnl，a,x ,,P,,l,l，，8,,ll，a,x,,8,la8,l,,000,、解:设内筒所带电荷线密度为,，则两筒间的场强分布为 ,,,r, E, 22,,r,0R1E r r两筒间的电势差为 ,RRU,,RRrd221,22,,ln U,U,U, ,Edr120,,RR1U,,r,,R1222001 ,U0,由此得 ，，2,,lnR/R021to make the following points: the room temperature between relative humidity maintained at 30%-55%, and 7 days a week, 24 hours a day is required. Keep free of dust and well ventilated, brightness of at least 50 candle light. Provide the right door, the door should open outward. To have a sufficient number of dedicated power outlet, provides volt 15 amp AC power to the device. This power supply for power and air conditioning or lighting circuits apart. the whole system's color management according to the design of the comprehensive wiring system, the whole system to the implementation of an integrated color management, that is, different regions using different colors to the mark, specific color meanings are as follows: Blue: represents the regional level subsystems, terminating in the blue area of the cables between the junction between levels to information outlets. White: represents the vertical cable subsystem, terminating in the white areas of the main cable wiring and wiring between floors. Green: input from the Central Office trunks Purple: from the data of common devices such as switches to lead. 2.6.7 design results in accordance with the ideas for the design of comprehensive wiring system, in line with the new plant office building, workshop technology requirements, 155Mbps ATM, and video transmission and other requirements, in line with the 15-20 development of data communication within the development trend of the future. Based on the above design, design the system diagram in Appendix; other engineering equipment offer is attached. Part III, section I of the computer network system, System 设两筒间任一点(距轴线距离为r)的电势为U，则 ,,rr,rdr,ln,有 U,U,E,dr, 1,,RR112,,R2,,r010 ,Urr0 (1) ,,,2U,lnUUln10,,，，2RlnR/RR01211 ,RR,,Rdr22,2或 U,U,E,dr,,ln 2,,rr2,,r,r,200 ,URR202 U (2) U,ln，U,，ln20，，RRr,2,rln/021 可以证明，(1)、(2) 两式是相等的 ,,U，，lnr/Rr01,, 2U,ln,U，U1,000,,，，，，lnR/RlnR/RR21121,, lnR/R,lnr/RUR，，，，21102,U，UU ,，ln000，，，，lnR/RRRrln/2121 所以两金属圆筒间的电势分布可以用(1)、(2)式表示都可，只要答一个. ,,、解:设x轴沿细线方向，原点在球心处，在x处取线元dx，其上电荷为，该dq,,dx 线元在带电球面的电场中所受电场力为: 2 dF = q,dx / (4,,x) 0 dx 整个细线所受电场力为: x r，l,,qdxql0 O R rx 0+l r0F,, ,2r0，，4,,x4,,rr，l 0000 方向沿x正方向( 电荷元在球面电荷电场中具有电势能: dW = (q,dx) / (4,,x) 0 整个线电荷在电场中具有电势能: r，l,,,,r，lqdxq00,,lnW,, ,,,r0,x,r4,4,000,, 5.8 电场强度与电势梯度 一.选择题和填空题 ,、, ,,,, ,、 E,,2a(xi，yj),2bzk to make the following points: the room temperature between relative humidity maintained at 30%-55%, and 7 days a week, 24 hours a day is required. Keep free of dust and well ventilated, brightness of at least 50 candle light. Provide the right door, the door should open outward. To have a sufficient number of dedicated power outlet, provides volt 15 amp AC power to the device. This power supply for power and air conditioning or lighting circuits apart. the whole system's color management according to the design of the comprehensive wiring system, the whole system to the implementation of an integrated color management, that is, different regions using different colors to the mark, specific color meanings are as follows: Blue: represents the regional level subsystems, terminating in the blue area of the cables between the junction between levels to information outlets. White: represents the vertical cable subsystem, terminating in the white areas of the main cable wiring and wiring between floors. Green: input from the Central Office trunks Purple: from the data of common devices such as switches to lead. 2.6.7 design results in accordance with the ideas for the design of comprehensive wiring system, in line with the new plant office building, workshop technology requirements, 155Mbps ATM, and video transmission and other requirements, in line with the 15-20 development of data communication within the development trend of the future. Based on the above design, design the system diagram in Appendix; other engineering equipment offer is attached. Part III, section I of the computer network system, System 5.9 静电场中的电偶极子 一.选择题和填空题 ,、, ,、 ，，，，,,/2,,a120 ,、0 pE sin, 二.计算题 解:选杆的左端为坐标原点，x轴沿杆的方向 (在x处取一电荷元,dx，它在点电荷所在处产生场强为: ,dx d l dE, dx ,2q ，，4,,d，x00O x x 整个杆上电荷在该点的场强为: d+ x l,,dxl E,, 2,04,,4,,dd，，，l，，d，x00 点电荷q所受的电场力为: 0 ,ql0F,,0.90 N 沿x轴负向 ，，4,,dd，l0 6.1 静电场中的导体 一.选择题和填空题 ,,, CDA ,—,CDD Qd/(2,S)7、 0 Qd/(,S) 0 8、 不变 减小 二.计算题 to make the following points: the room temperature between relative humidity maintained at 30%-55%, and 7 days a week, 24 hours a day is required. Keep free of dust and well ventilated, brightness of at least 50 candle light. Provide the right door, the door should open outward. To have a sufficient number of dedicated power outlet, provides volt 15 amp AC power to the device. This power supply for power and air conditioning or lighting circuits apart. the whole system's color management according to the design of the comprehensive wiring system, the whole system to the implementation of an integrated color management, that is, different regions using different colors to the mark, specific color meanings are as follows: Blue: represents the regional level subsystems, terminating in the blue area of the cables between the junction between levels to information outlets. White: represents the vertical cable subsystem, terminating in the white areas of the main cable wiring and wiring between floors. Green: input from the Central Office trunks Purple: from the data of common devices such as switches to lead. 2.6.7 design results in accordance with the ideas for the design of comprehensive wiring system, in line with the new plant office building, workshop technology requirements, 155Mbps ATM, and video transmission and other requirements, in line with the 15-20 development of data communication within the development trend of the future. Based on the above design, design the system diagram in Appendix; other engineering equipment offer is attached. Part III, section I of the computer network system, System 1解:(1) 由静电感应，金属球壳的内表面上有感生电荷-q，外表面上带电荷q+Q( (2) 不论球壳内表面上的感生电荷是如何分布的，因为任一电荷元离O点的 距离都是a，所以由这些电荷在O点产生的电势为 dq,q, U,,,q4,,a4,,a00 (3) 球心O点处的总电势为分布在球壳内外表面上的电荷和点电荷q在O点 产生的电势的代数和 U,U，U，UOq,qQ，q qqQ，qQ111q ,,，,，，,()4,,r4,,a4,,b,,rab4,,b4000002、 解 ,,, E,E，E,0o，q感 ,,,q+ .。. EEr,,,,，q0感d 4,,d0,为水平向右的单位矢量。 r0 由于导体球接地，圆心O点的电势为零，则 U,U，U,0 O，q感 qU ,,感4,,d0 ,,, E,E，E,0O，q感 ,qr0,,,,2？E,,E4,,d，q感0 6.2 静电场中的电介质 一.选择题和填空题 1—2 、B A to make the following points: the room temperature between relative humidity maintained at 30%-55%, and 7 days a week, 24 hours a day is required. Keep free of dust and well ventilated, brightness of at least 50 candle light. Provide the right door, the door should open outward. To have a sufficient number of dedicated power outlet, provides volt 15 amp AC power to the device. This power supply for power and air conditioning or lighting circuits apart. the whole system's color management according to the design of the comprehensive wiring system, the whole system to the implementation of an integrated color management, that is, different regions using different colors to the mark, specific color meanings are as follows: Blue: represents the regional level subsystems, terminating in the blue area of the cables between the junction between levels to information outlets. White: represents the vertical cable subsystem, terminating in the white areas of the main cable wiring and wiring between floors. Green: input from the Central Office trunks Purple: from the data of common devices such as switches to lead. 2.6.7 design results in accordance with the ideas for the design of comprehensive wiring system, in line with the new plant office building, workshop technology requirements, 155Mbps ATM, and video transmission and other requirements, in line with the 15-20 development of data communication within the development trend of the future. Based on the above design, design the system diagram in Appendix; other engineering equipment offer is attached. Part III, section I of the computer network system, System 3、无极分子 电偶极子 4、, r 1 ,r 6.3 电位移 有电介质时的高斯定理 一.选择题和填空题 1—2、D A 3、 ,/(2,r) ,/(2, , , r) 0r 4、 , , , ， ,, ) 0 r 5、 q/(4,,,R)0r q / (4,,R) 0 二.计算题 ,解:在圆柱导体内、外分别作半径为r、长为L的同轴圆柱形高斯面，并应用 D 的高斯定理( 圆柱内: 2,rLD,0 得 D = 0 ，，r,a E = 0 ，，r,a 圆柱外: 2,rLD = ,L ,,,r得 ， (r,a) 为径向单位矢量 ，，D,,,,/2πrr00,,,,,，，,,/2π,,rr (a,r,b) ，，E,D/,,0r010r,,, ，， (r,b) E,D/,,,,,/2π,r r2000 6.4 电容 电容器 一.选择题和填空题 1—3、,,, to make the following points: the room temperature between relative humidity maintained at 30%-55%, and 7 days a week, 24 hours a day is required. Keep free of dust and well ventilated, brightness of at least 50 candle light. Provide the right door, the door should open outward. To have a sufficient number of dedicated power outlet, provides volt 15 amp AC power to the device. This power supply for power and air conditioning or lighting circuits apart. the whole system's color management according to the design of the comprehensive wiring system, the whole system to the implementation of an integrated color management, that is, different regions using different colors to the mark, specific color meanings are as follows: Blue: represents the regional level subsystems, terminating in the blue area of the cables between the junction between levels to information outlets. White: represents the vertical cable subsystem, terminating in the white areas of the main cable wiring and wiring between floors. Green: input from the Central Office trunks Purple: from the data of common devices such as switches to lead. 2.6.7 design results in accordance with the ideas for the design of comprehensive wiring system, in line with the new plant office building, workshop technology requirements, 155Mbps ATM, and video transmission and other requirements, in line with the 15-20 development of data communication within the development trend of the future. Based on the above design, design the system diagram in Appendix; other engineering equipment offer is attached. Part III, section I of the computer network system, System ,、增大 增大 二.计算题 解:以左边的导线轴线上一点作原点，x轴通过两导线并垂直于导,+,-,,线(两导线间x处的场强为 ，E,2,,x2,,(d,x)00 d,Rd-RRx,11两导线间的电势差为 ,，U()dxO,x,,,2xdx0R ,,d,RRd,Rd,, ,ln(lnln) ,,Rd,R,,R200 设导线长为L的一段上所带电量为Q，则有，故单位长度的电容 ,,Q/L ,,0, C,Q/(LU),,/Ud,RlnR 6.5 静电场的能量 能量密度 一.选择题和填空题 ,,, D A 3、 减小 减小 二.计算题 ,D解:因为所带电荷保持不变，故电场中各点的电位移矢量保持不变， w1111220,,,,又 wDEDD 022,,,2,,rrr00 W,W/,因为介质均匀，?电场总能量 0r 三. 判断改错题 答: (1) 正确( (2) 介质内场强与原来一样( (3) 电场能量增大为原来的,倍( r to make the following points: the room temperature between relative humidity maintained at 30%-55%, and 7 days a week, 24 hours a day is required. Keep free of dust and well ventilated, brightness of at least 50 candle light. Provide the right door, the door should open outward. To have a sufficient number of dedicated power outlet, provides volt 15 amp AC power to the device. This power supply for power and air conditioning or lighting circuits apart. the whole system's color management according to the design of the comprehensive wiring system, the whole system to the implementation of an integrated color management, that is, different regions using different colors to the mark, specific color meanings are as follows: Blue: represents the regional level subsystems, terminating in the blue area of the cables between the junction between levels to information outlets. White: represents the vertical cable subsystem, terminating in the white areas of the main cable wiring and wiring between floors. Green: input from the Central Office trunks Purple: from the data of common devices such as switches to lead. 2.6.7 design results in accordance with the ideas for the design of comprehensive wiring system, in line with the new plant office building, workshop technology requirements, 155Mbps ATM, and video transmission and other requirements, in line with the 15-20 development of data communication within the development trend of the future. Based on the above design, design the system diagram in Appendix; other engineering equipment offer is attached. Part III, section I of the computer network system, System