模拟法测绘静电场实验示范报告
【实验目的】
1．理解模拟实验法的适用条件。
2．对于给定的电极，能用模拟法求出其电场分布。
3．加深对电场强度和电势概念的理解
【实验仪器】
JDY型双层静电场测试仪、JDY型静电场描绘电源、模拟装置（同轴电缆和电子枪聚焦电极）。
【实验原理】
1、静电场的描述
电场强度E是一个矢量。因此，在电场的计算或测试中往往是先研究电位的分布情况，因为电位是标量。我们可以先测得等位面，再根据电力线与等位面处处正交的特点，作出电力线，整个电场的分布就可以用几何图形清楚地表示出来了。有了电位U值的分布，由
便可求出E的大小和方向，整个电场就算确定了。
2、模拟法
实验上想利用磁电式电压表直接测定静电场的电位，是不可能的，因为任何磁电式电表都需要有电流通过才能偏转，而静电场是无电流的。再则任何磁电式电表的内阻都远小于空气或真空的电阻，若在静电场中引入电表，势必使电场发生严重畸变；同时，电表或其它探测器置于电场中，要引起静电感应，使原场源电荷的分布发生变化。人们在实践中发现，有些测量在实际情况下难于进行时，可以通过一定的方法，模拟实际情况而进行测量，这种方法称为“模拟法”。
由于静电场和稳恒电流场服从的规律的数学形式相同,如又满足相同的边界条件,则电场、电位分布完全相类似，所以可用电流场模拟静电场。这种模拟属于数学模拟。
静电场(无电荷区) 稳恒电流场(无电流区)
3、讨论同轴圆柱面的电场、电势分布
（1）静电场
根据理论计算，A、B两电极间半径为r处的电场强度大小为
A、B两电极间任一半径为r的柱面的电势为
（2）稳恒电流场
在电极A、B间用均匀的不良导体（如导电纸、稀硫酸铜溶液或自来水等）连接或填充时，接上电源（设输出电压为VA）后，不良导体中就产生了从电极A均匀辐射状地流向电极B的电流。电流密度为
式中E′为不良导体内的电场强度，ρ为不良导体的电阻率。
半径为r的圆柱面的电势为
结论：
稳恒电流场与静电场的电势分布是相同的。由于稳恒电流场和静电场具有这种等效性，因此要测绘静电场的分布，只要测绘相应的稳恒电流场的分布就行了。
[实验内容与步骤]
1、 测量无限长同轴圆柱间的电势分布。
（1）在测试仪上层板上放定一张坐标记录纸，下层板上放置水槽式无限长同轴圆柱面电场模拟电极。加自来水填充在电极间。
（2）接好电路。调节探针，使下探针浸入自来水中，触及水槽底部，上探针与坐标纸有1-2mm的距离。
（3）接通电源，K2扳向“电压输出”位置。调节交流输出电压，使AB两电极间的电压大约为12.00V左右，确定后保持不变。
（4）移动探针，在A电极附近找出电势为10.00V的点，用上探针在坐标纸上扎孔为记。同理再在A周围找出电势为10.00V的等势点8个，扎孔为记。
（5）移动探针，在A电极周围找出电势分别为8.00V，6.00V，4.00V，2.00V的各8个等势点（操作中也可以是1.20V,3.02V等且圆越大，应多找几点），方法如步骤（4）。
（6）分别用8个等势点连成等势线（应是圆），确定圆心的位置。量出各条等势线的坐标r（不一定都相等），并分别求其平均值。
（7）用游标卡尺分别测出电极A和B的直径2a和2b 。
（8）计算各相应坐标r处的电势的理论值V理，并与实验值比较，计算百分差。
（9）根据等势线与电力线相互正交的特点，在等势线图上添置电力线，成为一张完整的两无限长带等量异号电荷同轴圆柱面的静电场分布图。
（10）以lnr为横坐标，V实为纵坐标，做V实-lnr曲线，并与V理-lnr曲线比较
2、测量聚焦电极的电势分布（选做）
分别测10.00V、9.00V、8.00V、7.00V、6.00V、5.00V、4.00V、3.00V、2 .00V、1.00V、0.00V等(可以对称地选择其中5个)，一般先测5 .00V的等位点，因为这是电极的对称轴。
步骤同上
[数据记录]
模拟电场分布测试数据
实验室给定电压表示值误差:0.05V
VA= 12.00±0.05V 2a=（1.624±0.002）×10-2m 2b=（8.580±0.002）×10-2m
处理：
1、用圆规和曲线板绘出园柱形同轴电缆电场等位线(注意电极的位置).
2、根据电力线垂直等位面,绘出电力线.
贴图2：聚焦电极(本次)
3、在圆柱形电缆电场分布图上量出各等位线的半径,计算V并与理论值比较,求出其相对误差.
（1）
；则
；
（2）要具体计算
（3）要具体计算
（4）要具体计算
（5）要具体计算
结果分析：
（1）由图中可以看出实际测量值都在理论值的下方，说明实验的误差主要来自系统误差。本次测量中误差最小为0.2%，最大为9.6%，认为系统误差在操作中某实验条件未符合时引入的，并且半径越小的地方误差越大。这充分说明实验中要保证水槽的水介质要均匀分布，并且描绘的等势点不能太少，否则半径的确定也会引入较大的误差。
（2）等势面由人工拟合，因此半径的计算较粗糙，估计至少
，分析对第1组的影响，
由
知，
说明在确定数据点时，一定要保证装置以及操作的稳定性，另外数据尽量多，以减少实验值的波动性。
第二篇：模拟法测静电场[1英译对照]
模拟法测绘静电场The simulation for measuring the electrostatic field
［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］[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
；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' theorem. For the electrostatic field, the electric-field intensity satisfies the following integral relations in the source region
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
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Thus it can be seen, andcan satisfies the similar mathematics rule in the respective 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 current density vector can follow the ohm's law
=′
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 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“=”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, 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 radius (sees Figure 1(b)) each electric-field intensity is
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)
若
时
，则有If ,， then has
代入式(1)得Substitution Formula (1)
(2)
距中心处场强为apart from the center, the field intensity is
(3)
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
是相同的。If between cylindrical conductor A and tubular conductor B is not the 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 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 withfor the cylindrical coaxial good conductor piece,. Supposes the electronic resistivityis , from radius 
to radius for the circumference between the good conductor, the thin block's resistance is
(4)
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 is
(5)
由此可知，半径
到之间圆柱片的电阻为Thus it may be known, the radius to between column piece's resistance is
(6)
若设
，则径向电流为If,if , then the radial direction electric current is
(7)
距中心处的电位为apart from the center, the electric potential is
(8)
则稳恒电流场为Then the steady continuous current field is
(9)
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 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
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σ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σ电极>>σ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 σ电极>>σ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，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，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 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“直接”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 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］[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］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］[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 with the theory result. equipotential line is concentric circle according to nature of the curve, the center of circle and the electrode is the same.
(2)利用图3所示模拟模型，应用互易关系直接测绘同轴电缆的电力线分布。(2) according to model shown in Figure 3, describe directly the power line distribution for coaxial cable according to reciprocal relations.
2.描绘聚集电极的电场分布
利用图5所示模拟模型，测绘阴极射线示波管内聚集电极间的电场分布。要求测出7～9条等位线，相邻等位线间的电位差为1伏。该场为非均匀电场，等位线是一簇互不相交的曲线，每条等位线的测量点应取得密一些。画出电力线，可了解静电透镜聚焦场的分布特点和作用，加深对阴极射线示波管电聚焦原理的理解。
2. description of electric field distribution for Accumulated electrode
according to model shown in Figure 5, surveys the electric field distribution between the cathode ray oscillographic tube and cohesion collecting electrode. 7~9 equipotential lines is need, space's potential difference is 1 volt for the neighboring equipotential line. This electric field is inhomogeneous, the equipotential line is the curve which a bunch does not intersect mutually, the measuring point should be dense for each equipotential line. After drawing the power line, the distributed characteristic and the function will be understood for focusing field of the electrostatic lens, deepen the understanding of electric focusing principle for the anticathode beam oscillographic tube.
［注意事项］
由于导电玻璃边缘处电流只能沿边缘流动，因此等位线必然与边缘垂直，使该处的等位线和电力线严重畸变，这就是用有限大的模拟模型去模拟无限大的空间电场时必然会受到的“边缘效应”的影响。如要减小这种影响，则要使用“无限大”的导电玻璃进行实验，或者人为地将导电玻璃的边缘切割成电力线的形状。
图5静电透镜聚焦场的模拟模型
［预习思考题］
1.用电流场模拟静电场的理论依据是什么?
2.用电流场模拟静电场的条件是什么?
3.等位线与电力线之间有何关系?
4.如果电源电压Ua增加一倍，等位线和电力线的形状是否发生变化?电场强度和电位分布是否发生变化?为什么?
5.试举出一对带等量异号线电荷的长平行导线的静电场的“模拟模型”。这种模型是否是唯一的?
［思考题］
1.根据测绘所得等位线和电力线的分布，分析哪些地方场强较强，哪些地方场强较弱?
2.从实验结果能否说明电极的电导率远大于导电介质的电导率?如不满足这条件会出现什么现象?
3.在描绘同轴电缆的等位线族时，如何正确确定圆形等位线族的圆心，如何正确描绘圆形等位线?
4.由(2)式中可导出圆形等位线半径的表达式为：
试讨论及
与的关系，说明电力线的疏或密随值的不同如何变化。
5.由上题给出的的表达式计算各等位线圆半径的理论值
，与实验测定的等位线圆半径e比较求百分误差，分析误差原因。
6.由导电玻璃与记录纸的同步测量记录，能否模拟出点电荷激发的电场或同心圆球壳形带电体激发的电场?为什么 ?
附: 试做记录
模拟法测绘静电场(同轴电缆电场的模拟) The simulation for measuring the electrostatic field (coaxial cable electric field simulation)
1. 完成时间:20##年3月10曰
2. 在C306教室19号桌试做
3. ra=0.50cm,rb=7.50cm