模拟法测静电场[1英译对照]

模拟法测绘静电场模拟法测绘静电场The simulation for measuring the electrostatic field 实验目的 实验目的 experiment goal 1 学习用模拟法测绘静电场的原理和方法 Study the principle and the method for measuring the electrostatic field 2 加深对电场强度和电位概念的理解 Understanding the concept of electric field intensity and electric potential 实验原理 实验原理 experiment principle 在一些科学研究和生产实践中 往往需要了解带电体周围静电场的分布情况 一般来 说带电体的形状比较复杂 很难用理论方法进行计算 用实验手段直接研究或测绘静电场 通常也很困难 因为仪表 或其探测头 放入静电场 总要使被测场原有分布状态发生畸变 而且除静电式仪表之外的一般磁电式仪表不能用于静电场的直接测量 因为静电场中不会 有电流流过 对这些仪表不起作用 所以 人们常用 模拟法 间接测绘静电场的分布 For some scientific research and the production practice we need to understand the electrostatic field distribution for around the charged body Generally speaking the charged body shape is quite complex there are some difficulty to gain the electrostatic field distribution for the theory method and experiment method Because the measuring appliance or its detecting head puts in the electrostatic field will result to distortion for the field original distribution Moreover general moving coil instrument cannot use in the electrostatic field except electrostatic instrument because no current to wind in the electrostatic field and have not any effect to these measuring appliances Therefore The simulation for measuring the electrostatic field is expected 一 模拟的理论依据一 模拟的理论依据 simulation theory 模拟法在科学实验中有着极其广泛的应用 其本质是用一种易于实现 便于测量的物理状 态或过程的研究去代替另一种不易实现 不便测量的状态或过程的研究 The analogue method has the extremely widespread application in the scientific experiment its essence is using the easy physical state to replace a state which is not easy to realize 为了克服直接测量静电场的困难 我们可以仿造一个与待测静电场分布完全一样的电流场 用容易直接测量的电流场去模拟静电场 In order to overcome the difficulty for the direct measurement electrostatic field we may copy with the testing static electricity field distribution direct which is can be measure completely which is the same as electricity flow field 静电场与稳恒电流场本是两种不同的场 但是它们两者之间在一定条件下具有相似的空间 分布 即两种场遵守的规律在形式上相似 它们都可以引入电位 而且电场强度U 它们都遵守高斯定理 对静电场 电场强度在无源区域内满足以下积分关系EU The electrostatic field and the steady continuous current field originally are two kind of different fields but has the similar spatial distribution under the controlled condition namely two kind of fields observe rule in formally similar They may introduce the electric potential moreover electric field intensity They observe the gauss EU theorem For the electrostatic field the electric field intensity satisfies the following integral relations in the source region 0 s dsE0 l dlE 而对于稳恒电流场 电流密度矢量 J 在无源区域内也满足类似的积分关系 But for the steady continuous current field current density vector J also satisfies the similar integral relations in the source region 0 s dsJ0 l dlJ 由此可见 和在各自区域中满足同样的数学规律 若稳恒电流场空间内均匀地充满了EJ 电导率为的不良导体 不良导体内的电场强度 与电流密度矢量之间遵循欧姆定律 EJ Thus it can be seen andcan satisfies the similar mathematics rule in the respective EJ region If in the steady continuous current field space there is filled with the good conductor conductivity for poor conductor the electric field intensity and the E current density vector can follow the ohm s law J J E 因而 和 在各自的区域中也满足同样的数学规律 在相同边界条件下 由电动力学EE 的理论可以严格证明 象这样具有相同边界条件的相同方程 其解也相同 因此 我们可 以用稳恒电流场来模拟静电场 也就是说静电场的电力线和等势线与稳恒电流场的电流密 度矢量和等位线具有相似线的分布 所以测定出稳恒电流场的电位分布也就求得了与它相 似的静电场的电场分布 Therefore and also satisfies the similar mathematics rule EE in the respective region Under the same boundary condition it can be proved strictly by electrodynamics s theory For same equation like this its solution is also same under the same boundary condition Therefore we may use the steady continuous current field to simulate the electrostatic field The power line and the equipotential line for the electrostatic field haves the similar line distribution with current density vector and equipotential line for the steady continuous current field s Therefore the electrostatic field distribution can be obtained from the steady continuous current field 二 横拟长同轴圆柱形电缆的静电场二 横拟长同轴圆柱形电缆的静电场 simulating electrostatic field for the electric cable with long coaxial cylindrical 利用稳恒电流场与相应的静电场在空间形式上的一致性 则只要保证电极形状一定 电极电位不变 空间介质均匀 在任何一个考察点 Uses the steady current field with the corresponding electrostatic field have the same the spatial uniformity so long as in any inspection spot electrode geometry is certain the electrode potential is invariable the spatial medium is even 均应有 或 should have U稳恒U静电E稳恒 静电 EU稳恒 或 下面以同轴圆柱形电缆的电场和相应的模拟场 稳恒电流场U静电E稳恒 静电 E 来讨论这种等效性 Below discusses this kind of equivalence by the coaxial cylindrical electric cable s electric field and the corresponding simulation field steady continuous current field 如图 1 a 所示 在真空中有一半径为的长圆柱形导体 A 和一个内径为的长圆筒形导体 a r b r B 它们同轴放置 分别带等量异号电荷 由高斯定理可知 在垂直于轴线的任一个截面 S 内 都有均匀分布的辐射状电力线 这是一个与坐标无关的二维场 在二维场中电场Z 强度平行于平面 其等位面为一簇同轴圆柱面 因此 只需研究任一垂直横截面上EXY 的电场分布即可 As shown in Figure 1 a in the vacuum for oval cylindrical conductor A radius is and an inside tubular conductor B radius is their coaxial laying aside a r b r has the isometric opposite electric charge separately By the gauss theorem in any section S which is vertical coaxial has the uniform distribution radiating power line this is one two dimensional field which is not relate with the coordinate The electric field intensity is parallel in the two dimensional field to the plane its equipotential surface is a bunch of coaxial circles cylinder Therefore only need to study the electric field distribution in any vertical lateral section the electric 距轴心 O 半径为处 见图 1 b 的各点电场强度为 place apart from the axle center O with r radius sees Figure 1 b each electric field intensity isr r E 0 2 图 1 同轴电缆及其静电场分布 Figure 1 coaxial cable and distribution of static electricity field 式中为 A 或 B 的电荷线密度 is electric charge linear density for A or B 其电位 为 Its electric potential is 1 a a r r ar r r UdrEUU a ln 2 0 若时 则有 If then has b rr 0 b U b rr 0 b U a b a r r U ln 2 0 代入式 1 得 Substitution Formula 1 2 a b b ar r r r r UU ln ln 距中心处场强为 apart from the center the field intensity isrr 3 r r r U dr dU E a b ar r 1 ln 若上述圆柱形导体 A 与圆筒形导体 B 之间不是真空 而是均匀地充满了一种电导率为的 不良导体 且 A 和 B 分别与直流电源的正负极相连 见图 2 则在 A B 间将形成径向电 流 建立起一个稳恒电流场 可以证明不良导体中的电场强度与原真空中的静电场 r E r E 是相同的 If between cylindrical conductor A and tubular conductor B is not the r E vacuum but filled one kind of poor conductivity with evenly for poor conductor even A and B connected separately with direct current power positive and negative side see in Figure 2 in A B electric current will form with the radial direction establishes a steady continuous current field It can be proved that electric field intensity in the good r E conductor is same as the original vacuum electrostatic field 取厚度为的圆柱形同轴不良导体片来研究 设材料的电阻率为 则从半径t 1 为的圆周到半径为的圆周之间的不良导体薄块的电阻为 Takes thickness rrdr withfor the cylindrical coaxial good conductor piece Supposes the electronic t resistivityis from radius to radius for the circumference between the good rrdr conductor the thin block s resistance is 4 r dr t dR 2 图 2 同轴电缆的模拟模型 Figure 2 coaxial cable s modeling model 半径到 rb之间的圆柱片电阻为 The radius to the rb between column piece resistance rr is 5 r r tr dr t rR b r r br b ln 22 由此可知 半径到之间圆柱片的电阻为 Thus it may be known the radius to a r b r a r b r between column piece s resistance is 6 a b rr r r t R ba ln 2 若设 则径向电流为 If if then the radial direction electric current 0 b U 0 b U 0 b U is 7 a b a rr a r r tU R U I ba ln 2 距中心处的电位为 apart from the center the electric potential isrr 8 a b b arrr r r r r UIRU ba ln ln 则稳恒电流场为 Then the steady continuous current field is r E 9 r r r U dr dU E a b ar r 1 ln 可见式 8 与式 2 具有相同形式 说明稳恒电流场与静电场的电位分布函数完全相同 即柱 面之间的电位与均为直线关系 并且 即相对电位仅是坐标的函数 与电场 r Ulnr r U a U 电位的绝对值无关 显而易见 稳恒电流的电场 与静电场的分布也是相同的 因为EE Obviously formular 8 has the same form with formular 2 shown that the distribution function of the steady continuous current field and the electrostatic field potential distribution function is completely same namely between the cylinder electric potential is the linear with namely the relative electric potential is function only of the r Ulnr coordinate has no relate with the electric field electric potential s absolute value Obviously the distribution for the steady continuous current s electric field is also same as the electrostatic field because E dr dU dr dU E rr 实际上 并不是每种带电体的静电场及模拟场的电位分布函数都能计算出来 只有在 分 布均匀而且几形状对称规则的特殊带电体的场分布才能用理论严格计算 上面只是通过一 个特例 证明了用稳恒电流场模拟静电场的可行性 In fact not all the electrostatic field for charged body and the simulation field potential distribution function can calculate only for shape symmetrical rule special charged body field distribution in Sigma the distribution to be able to use the theory to calculate strictly As an exceptional case simulates the electrostatic field is proved the feasibility for simulating the electrostatic field with the steady continuous current field the feasibility 为什么这两种场的分布相同呢 我们可以从电荷产生场的观点加以分析 在导电质中没有电 流通过时 其中任一体积元 宏观小 微观大 即其内仍包含大量原子 内正负电荷数量相 等 没有净电荷 呈电中性 当有电流通过时 单位时间内流入和流出该体积元内的正或 负电荷数量相等 净电荷为零 仍然呈电中性 因而 整个导电质内有电流通过时也不存 在净电荷 这就是说 真空中的静电场和稳恒电流通过时导电质中的场都是由电极上的电 荷产生的 事实上 真空中电极上的电荷是不动的 在有电流通过的导电质中 电极上的 电荷一边流失 一边由电源补充 在动态平衡下保持电荷的数量不变 所以这两种情况下 电场分布是相同的 Why two kind of field s distribution is same We can analyze from the field viewpoint from the electric charge If no electric current in conductor any space element macroscopic small microscopic big namely still contained massive atoms the positive and negative electric charge quantity is to be equal no the electric charge is exist the telegram is neutrality When there is electric current internal flow enters and flows out in the unit time in this space element just positive or negative charge quantity is equal the electric charge is zero only still neutrality Therefore the electric charge is zero even for the electric current That is electrostatic field in the vacuum and the steady continuous current are produce by electric charge on electrodes In fact in the vacuum the electrode s electric charge is motionless when the electric current flow electric conduction electrode s electric charge drains on one side at the same time but supplemented by the power source the electric charge quantity is invariable under the dynamical equilibrium Therefore the electric field distribution of two kind is the same 三 模拟条件三 模拟条件 simulated conditon 模拟方法的使用有一定的条件和范围 不能随意推广 否则将会得到茺谬的结论 用 稳恒电流场模拟静电场的条件可以归纳为下列三点 Analogy procedure has certain condition and the scope and cannot promote at will otherwise obtain the erroneous conclusion For the steady continuous current field simulation to electrostatic field s condition three points as follows 1 稳恒电流场中的电极形状应与被模拟的静电场中的带电体几何形状相同 1 the geometry for steady continuous current field s electrode should have the same as the electrostatic field charged body 图 3 同轴电缆模拟模型的互易装置 Figure 3 coaxial cable analog modeling reciprocal installment 2 稳恒电流场中的导电介质应是不良导体且电导率分布均匀 并满足 电极 导电 质才能保证电流场中的电极 良导体 的表面也近似是一个等位面 In the steady continuous current field conductive media should be poor conductor and the conductivity distribution is even and only satisfies 电极 导电质 then guarantee that the electrode good conductor the surface in the electricity flow field is an equipotential surface 3 模拟所用电极系统与被模拟电极系统的边界条件相同 3 boundary condition should be the same for simulation electrode system and the simulated the electrode system 四 静电场的测绘方法四 静电场的测绘方法 Fourth electrostatic field mesured method 由 3 式可知 场强在数值上等于电位梯度 方向指向电位降落的方向 考虑到 E 是矢量 E 而电位是标量 从实验测量来讲 测定电位比测定场强容易实现 所以可先测绘等位线 U 然后根据电力线与等位线正交的原理 画出电力线 这样就可由等位线的间距确定电力线 的疏密和指向 将抽象的电场形象地反映出来 By fomular 3 the value of field intensity is of electric potential gradient potential drop direction Considered E is a vector but the electric potential is a scalar from the experiment measure the electric potential is U easier to compared to the field intensity therefore the equipotential line may survey first then acts according to orthogonal principle for the power line and the equipotential line orthogonal principle draws the power line line s density and the direction can be obtained by the equipotential line spacing then the abstract electric field can be reflected vividly 五 利用互易关系五 利用互易关系 直接直接 测绘电力线测绘电力线 Fifth direct surveys the power line using the reciprocal relations 用电流场模拟静电场 在相同的边界条件下 两种场的电位分布完全相同 通过测定 电流场的电位分布 我们就得到了静电场的电位分布 然后根据等位线和电力线正交的关 系 即可画出电力线 是否可以直接测绘出电力线呢 我们注意到 在电流场中 由于电荷 沿电力线的方向流动 即电流线在电力线的方向 而电流线不能穿过导电玻璃的边缘或切 口 因而电流线必平行于导电玻璃的边缘或切口 又垂直于电极表面 故电力线平行于导 电玻璃的边缘或切口 垂直于电极表面 而等位线与电力线垂直 由于导电玻璃可以根据 需要加工成任意形态 因而我们可以人为地制造边缘或切口 使其在电力线方向 Useing the current flow field to simulate the electrostatic field under the same boundary condition two kinds of field s potential distributions is completely same we obtained the electrostatic field potential distribution from the flow field s potential distribution then basing on the orthogonal s relations between equipotential line and the power line then draw the power line Whether can survey the electric power cotton suiting directly We note in electricity flow field as a result of electric charge s flowing along power line direction flowing namely electricity streamline is the power line s direction but the electricity streamline cannot pass through the edge or the margin of the conductive glass for the electricity streamline must be parallel to edge or the margin of the conductive glass and is also vertical to the electrode surface Therefore the power line is parallel to edge or the margin of the conductive glass edge or the margin and is vertical to the electrode surface But the equipotential line is vertical to the power line Because shape of the conductive glass process can be the random according to needs thus we may make artificially the edge or the margin along power line direction 如果在导电玻璃边缘 或电力线 的地方用一个电极表面去代替它 而在电极表面 或等位线 的地方用一个边缘去代替它 那么所得到的新的等位线的形状将是原电极时电力线的形状 而新的电力线即为原等位线 这个关系称为互易关系 实际上是通过电极的变换 使电力 线和等位线这两个相互正交的曲线族得到互换 使原来不能直接测定的电力线改变成可以 直接测定的等位线 从理论上也可以证明此关系 If the conductive glass edge or power line can be replaced with an electrode surface but in electrode surface or equipotential line with an edge then the new equipotential line s shape will be obtain from the original electrode power line s shape for the new power line is the original equipotential line This relations are called the reciprocal relations In fact through electrode s transformation these two mutual orthogonal set of curves can be exchange for the power line and the equipotential line the immediate determinant power line can be obtained from the immediate determinant equipotential line This relations may also be proved theoretically 应用互易关系我们可以直接测绘电力线 在导电玻璃上切割出半径为和的两个同心圆 1 r 2 r 切口 再沿同心圆的任意半径方向制作出两个扇形电极 加上电压 如图 3 所示 就得 1 V 到了同轴电缆模拟模型的互易装置 利用此互易装置描绘出的等位线即为原模拟模型的辐 射状电力线 It is possible to survey the power line directly using the reciprocal Cuts two concentric circle margins with the radiusand manufactures two fan shaped 1 r 2 r electrodes along the concentric circle random radius direction apply the voltage as shown in Figure 3 obtained the coaxial cable modeling reciprocal installment Equipotential line which describes using this reciprocal installment namely for original analog modeling radiating power line 实验装置 实验装置 test installation EQL 2 型电场描绘仪 包括导电玻璃 双层固定支架 同步探针等 如图 4 所示 支架采 用双层式结构 上层放记录纸 下层放导电玻璃 电极已直接制作在导电玻璃上 并将电 极引线接出到外接线柱上 电极间制作有 电导率远小于电极且各向均匀的导电介质 接通直流电源 10V 就可进行实验 在导 电玻璃和记录纸上方各有一探针 通过金 属探针臂把两探针固定在同一手柄座上 两探针始终保持在同一铅垂线上 移动手 柄座时 可保证两探针的运动轨迹是一样 的 由导电玻璃上方的探针找到待测点后 按一下记录纸上方的探针 在记录纸上留 下一个对应的标记 移动同步探针在导电 玻璃上打出若干电位相同的点 由此即可 描绘出等位线 图 4 EQL 2 型电场描绘仪 Figure 4 EQL 2 electric field description meter The EQL 2 electric field description meter including conductive glass double decked steady rest synchronized probe and so on as shown in Figure 4 two layer structure the record paper is putted on the upper formation the conductive glass is putted on the lower level The electrode has manufactured directly on the conductive glass and leads the contact conductor outside on the wiring column the even conductive media is putted between the electrodes with the conductivity is much smaller than an electrode The connection direct current power supply 10V may carry on the experiment Two probes is set respectively above the conductive glass and the record paper and are fixed on the identical handle foundation through the metal probe arm so two probes can keep the identical lead perpendicular line When moving handle two probes have the same paths When find the testing spot lying on the probe above conductive glass then push the probe above the paper the corresponding mark is left on the record paper The motion of synchronization probe can find some spot with the same electric potential on the conductive glass then the equipotential line can be described according to 实验仪器 实验仪器 instrument EQL 2 型双层式静电场测绘仪一套 直流稳压电源 10V 1A 一台 导线等 A EQL 2 two layer electrostatic field graphometric set DC Power Supply 10V 1A wires 实验内容与要求 实验内容与要求 experiment content and require 1 描绘同轴电缆的静电场分布 1 description the distribution of static electricity field for coaxial cable 1 利用图 2 b 所示模拟模型 将导电玻璃上内外两电极分别与直流稳压电源的正负 极相连接 电压表正负极分别与同步探针及电源负极相连接 移动同步探针测绘同轴电缆 的等位线簇 要求相邻两等位线间的电位差为 1 伏 共测六条等位线 每条等位线测定出 八个均匀分布的点 以每条等位线上各点到原点的平均距离为半径画出等位线的同心圆r 簇 然后根据电力线与等位线正交原理 再画出电力线 并指出电场强度方向 得到一张 完整的电场分布图 在坐标纸上作出相对电位 和的关系曲线 并与理论结果比 r U a Urln 较 再根据曲线的性质说明等位线是以内电极中心为圆心的同心圆 1 according to model shown in Figure 2 b the inside outside electrodes of the conductive glass is connected with the positive negative side separately of power positive negative side of the voltmeter is connected with the synchronized probe negative side of the power then move equipotential line bunch for synchronization probe of survey coaxial cable The potential difference between two neghbour equipotential line is 1 volt eight uniform distributions the spot is mesured on each equipotential line altogether 6 equipotential lines Draw the concentric circle bunch as the radius is mean distance from spot to the zero point Then draw the power line according to orthogonal principle between the power line and the equipotential line and pointed out the electric field intensity direction so a complete electric field distribution map can be obtained Makes the curve between and on the coordinate paper then compare wit