麻省理工电磁学课程lec4

合集下载

mit电磁学物理讲义

MAGNETIC MATERIALS OVERVIEWDr. James LivingstonMagnetic materials provide the "driving force" that turns our electric motors, generates electricity in power stations and sound in our speakers, and stores information on our credit cards and computer disks. Materials science has created magnetic materials far more powerful than those available only a few decades ago, resulting in a tremendous impact on modern technology.Review of magnetics basicsMagnetic fields are created by electric charges in motion (electric currents, orbital motion of electrons, SPIN of electrons)Magnetic fields exert forces on electric charges in motion (current-carrying wires, charged-particle beams, orbital motion of electrons, SPIN of electrons)Materials categoriesIf atoms have no net spin, materials are diamagnetic (weakly repelled by field)If a net spin, but uncoupled to neighbors, paramagnetic (weakly attracted)If equal net spins are coupled antiparallel, antiferromagnetic (weakly attracted)If unequal net spins are coupled antiparallel, ferrimagnetic (strongly attracted)If net spins are coupled parallel, FERROMAGNETIC (very strongly attracted)Only ferri- and ferromagnetic materials are considered magnetic materialsHard and soft magnetic materials"Soft" (temporary-magnet) materials lose their net magnetization (form domains) when a magnetic field is removed - used for AC or on-off applications"Hard" (permanent-magnet) materials retain their magnetization after field is removed - used for applications requiring a steady magnetic fieldProperties of magnetic materialsSaturation magnetization is a measure of the magnetic field a material can produce when all atomic magnets are aligned - how "magnetic" it isCoercivity is the reverse magnetic field required to reduce the net magnetization to zero - how "permanent" it is. ("soft" = low coercivity, "hard" = high coercivity)(Other properties often quoted are the permeability of soft materials, which varies inversely with coercivity, and the energy product of hard materials, related to area of "hysteresis loop" & depends on both coercivity and saturation magnetization)History of hard (permanent-magnet) materialsLodestones - natural magnets based on magnetite (Fe3O4)Carbon steel (Fe-C) 18th-c. England (horseshoe shaped or bar magnets)Alloy steel (Fe-C+W, Mo, Cr, Co, etc.) - 19th and early 20th-c. (horseshoe or bar)Alnico (Fe+Al,Ni,Co) - 1930s & 1940s - helped Allies win World War IIHard Ferrite (Ba-Fe-O or Sr-Fe-O) - 1950s & 1960s - higher coercivity, cheap!Rare Earth (Sm-Co, Nd-Fe-B) - 1970s-1990s - VERY powerful, but NOT cheap Applicationsmagneticmaterials are used in applications requiring a steady (permanent)Hardmagnetic field. Recent increases in coercivity (resistance to demagnetization) and energy product (dependent on both coercivity and saturation magnetization, and related to the area within the hysteresis loop) have greatly increased the use of permanent magnets in modern technology. The widest applications are in motors, speakers, and sensors, but large quantities of Nd-Fe-B magnets are also used in permanent-magnet MRI systems, each of which uses about 2 tons of permanent magnet.For most applications, the amount of permanent magnet required is inversely proportional to the energy product. Available energy products have increased by a factor of fifty since the 1930s, allowing a corresponding decrease in the size of the magnet, and thus the size of the device. (e.g., small motors made possible by Nd-Fe-B magnets spin the disks and move the heads in computer disk drives, and small speakers produce music in the tiny earphones of i P ods and the like.)At least as important have been increases in coercivity by even greater factors, which allow a greater flexibility of magnet shape. Low-coercivity steel magnets required long bar magnets or horseshoe shapes to minimize demagnetization from reverse fields produced by the north and south poles at the ends of the magnet. (Before the advent of alnico magnets in the 1930s, telephone receivers were long and separate from the speakers because they included a long horseshoe-shaped steel magnet.)Materials for magnetic recording have also improved dramatically in recent years. The first magnetic recorder, patented in 1898, used steel piano wire. Magnetic tapes employing particles of iron oxide coated on plastic tapes were developed in Germany in the 1930s. Such tapes were used in the first commercial computers in the 1950s, and advanced versions remain in use today for audio and video applications, but today's computers instead store information in patterns of north and south poles on disks coated with thin films of cobalt-rich alloys.There have also been dramatic improvements in the properties of soft magnetic materials. Decreases in coercivity have decreased the energy losses of soft materials in ac applications, as have increases in electrical resistivity. Many transformers today useamorphous Fe-rich alloys, cooled so rapidly from the melt that they are unable to crystallize. An area of extensive current research is materials for recording heads, and improved materials have contributed to the remarkable increases in the density of information storage (bits per square inch).。

麻省理工MIT(微观经济学)lec01_02_orderings and utility representation

14.123 Lectures 1-2, Page 3
Introduction
• Economics is about explaining and predicting choice. • It is assumed that economic agents choose their most desirable alternative among the set of feasible ones. – Interpret it “as if”, not necessarily “deliberate”. – “This morning I took the shuttle to MIT because this was the best possible way to come in.” Discuss. • Desirability is represented by preferences and/or utility. – Attitudes may be expressed over outcomes never experienced (Would you prefer to be Superman or Spiderman?).
14.123 Lectures 1-2, Page 6
Utility Representation
• DEF. Utility fcn u : X → represents if u(x) ≥ u(y) x y. • THM: If u represents , then is complete and transitive. ■ Follows from the same properties of ≥ on real numbers. ■ • THM: If X is finite and is complete and transitive, then there exists a utility function that represents . ■ u(x) = |{y∈X : xy}|: # of alternatives that x beats weakly.■ • THM: If X is countable and is complete and transitive, then there is a utility function with a bounded range that represents . ■ X ≡ {x1,x2,…}. Let u(x-1)=0, u(x0)=1. For all n=1,2,…, set u(xn) = [max{u(xk)|xnxk,n>k} + min{u(xk)|xkxn,n>k}]/2 .■

Lec4_Introduction_to_Quantum_Mechanics

Lecture 4
Semiconductor physics II
Introduction to Quantum Mechanics
1
What is Quantum Mechanics
Classical theoretical physics -- Newton's laws of motion. -- The motion of large objects, such as planets and satellites. Quantum mechanics -- the behaviors of electrons and high-frequency electromagnetic waves. Wave mechanics: The formulation of quantum mechanics to describe behavior and characteristics of these electrons. -- Schrodinger wave equation
5
Maximum kinetic energy
Tmax
Quanta －thermal radiation emitted from a heated surface in discrete packets of energy －Postulated by Planck in 1900 The energy of these quanta
13
Using the technique of separation of variables
Ψ ( x, t ) = ψ ( x )φ (t )
a function of the position
2
Principles of Quantum Mechanics

麻省理工-Feedback Control Systems-Lec01

September 9, 2010
Fall 2010
16.30/31 1–6
State-Space Approach
• Basic questions that we will address about the state-space approach: • What are state-space models? • Why should we use them? • How are they related to the transfer functions used in classical control design? • How do we develop a state-space model? • How do we design a controller using a state-space model?
• Observation: classical control the process tends to be a bit cryptic, is designer intensive (lots of simple but detailed calculations), and typically very iterative • So our focus in this class is on state space methods for several reasons: • More systematic design tools exist - can be easily codiﬁed and implemented numerically – easy integrate optimization • Easily handle larger-scale systems (many modes) and many sensors and actuators (MIMO).

麻省理工公开课：电和磁

麻省理工公开课：电和磁磁麻省理工公开课：电和磁本课程共36集翻译完欢迎学习课程介绍由麻省理工传奇人物Walter Lewin教授精心打造的物理课程——电和磁。

老教授风趣幽默，善於用直观的实验来演示复杂深刻的物理原理，使得课程具有启发性和趣味性。

本课出了基础的电磁学，还包括了许多有趣的相关主题：闪电、起博器、电击疗法、心电图、金属探测器、乐器、磁悬浮效应、高速火车、电动机、收音机、电视机等。

本课程还包括一个“自制一个电动机大赛”。

收藏课程列表课件打包下载名称视频下载[第1集] 是什么将世界连在一起[第2集] 电场和偶极子[第3集] 电通量和高斯定律[第4集] 静电势能和电势[第5集] 静电屏蔽[第6集] 高压击穿和闪电[第7集] 电容和场能[第8集] 电介质及极化[第9集] 电流、电阻率和欧姆定律[第10集] 电池和电动势[第11集] 磁场和洛伦兹力[第12集] 复习一(神秘陀螺)[第13集] B场中的运动电荷[第14集] 毕奥萨伐尔定律[第15集] 安培定律[第16集] 电磁感应[第17集] 动生电动势和发电机[第18集] 位移电流和同步电机[第19集] 心电图、极光、磁悬浮[第20集] 电感和RL电路[第21集] 材料磁性[第22集] 磁滞和麦克斯韦方程组[第23集] 复习二[第24集] 变压器、RC电路[第25集] LRC电路和谐振[第26集] 行波和驻波[第27集] 共振[第28集] 电磁波能量及坡印廷矢量[第29集] 斯涅尔定律、折射及全反射[第30集] 偏振和马吕斯定律[第31集] 彩虹[第32集] 复习三[第33集] 双缝干涉和干涉仪[第34集] 光栅和分辨率[第35集] 多普勒效应和宇宙大爆炸[第36集] 告别演出。

《麻省理工开放课程：电路与电子学》6002Lec01中文讲义

15
必须被定义。
若
仅仅在灯丝内当
时是正确的。
6.002 2000 年秋第一讲
16
6.002 2000 年秋第一讲
17
6.002 2000 年秋第一讲
18
6.002 2000 年秋第一讲
19
那么，这给我们带来什么好处呢？
使用集总电路抽象（LCA），以简单的代数代替了微分方程。
例如：
1
课前说明：
讲师：Prof. Anant Agarwal ■ 教材：Agarwal&Lang(A&L) ■ 仔细阅读所发资料第三页 ■ 课程任务：
课后作业练习实验随堂考试期末考试
6.002 2000 年秋第一讲
2
■ 作业中可有两次不做（作业 11 除外） ■ 对互相协作的要求
课后作业可以与其他人合作，但不准抄袭
6.002 2000 年秋第一讲
10
简单的方法……
这样，为了计算电流我们以一个独立电阻
来代替灯泡。
R 代表我们唯一感兴趣的特性。就像质点：用质量 m 代替物体来求得
6.002 2000 年秋第一讲
11
简单的方法……
R 代表我们唯一感兴趣的特性。 R 元件的电压和电流有以下关系：
称为元件的伏安关系特性
在集总问题规定下，电压循环一周满足什么关系呢？
6.002 2000 年秋第一讲
20
在集总问题规定下，电压循环一周满足什么关系呢？
基尔霍夫电压定律：（KVL）集总参数电路中延任一回路电压之和为零
6.002 2000 年秋第一讲
21
电流有什么特性呢？
考虑
6.002 2000 年秋第一讲

麻省理工电磁学课程lec6_7 2

Lectures 6 & 7 Page 3 of 40
D= u
D da = dV n D
u S V P
a
Db su P b sp n E Eb = o a su sp
P= P
e (electric susceptibility)
D= P= o E
1 e E= E o
(relative dielectric constant) r
R = = 1 e = 1 4 r o o o s
Lectures 6 & 7 Page 4 of 40
III. Equipotential Sphere in a Uniform Electric Field
lim r, Eo r cos
r
Eo z Eo r cos
r R, 0
dipole p cos 4 r2 o
with p 4 E R3 o o
This dipole is due to the surface charge distribution on the sphere.
r R, r R, s o Er o
Q inside V = qN d da dV p
S V
paired charge or equivalently polarization charge density
6.013, Electromagnetic Fields, Forces, and Motion Prof. Markus Zahn Lectures 6 & 7 Page 2 of 40

(麻省理工免费课程)C语言内存管理和C++面向对象编程_lec02

Recap
Pointers
Memory management
Data structures
Linked list example
Tools and tips
Goodbye
An example without pointers
What will this print?
void p r o c e s s v a r ( i n t x ) { x = 5; } void fun () { int x = 3; process var (x) ; p r i n t f ( "%d\n" , x ) ; }
Conceptually
Keep track of what memory belongs to your program, making sure
all addresses you give to other functions are valid for those
functions and
you deallocate memory you are not using while you still know
Eunsuk Kang and Jean Yang The Adventures of Malloc and New
Recap
Pointers
Memory management
Data structures
Linked list example
Tools and tips
Goodbye
Pointer syntax
Memory management
Data structures
Linked list example

2024年度电磁学全套ppt课件

VS
防止涡流的措施
为了减小涡流的影响，可以采取以下措施：增加金属导体的电阻率、减小金属导体的厚度、采用相互绝缘的薄片叠加而成的导体等。这些措施可以有效地减小涡流的大小，从而减小涡流对设备的影响。
2024/3/24
27
06
交流电产生、传输和转换过程Fra bibliotek析2024/3/24
28
正弦交流电产生原理和特点介绍
感应电动势的大小与磁通量变化的快慢成正比，即与磁通量对时间的导数成正比。
2024/3/24
法拉第电磁感应定律是电磁学的基本定律之一，揭示了电磁感应现象的本质和规律。
24
动生和感生两种类型分析比较
2024/3/24
动生电动势
由于导体在磁场中运动而产生的感应电动势。其大小与导体在磁场中的有效长度、导体在磁场中的运动速度以及磁场的磁感应强度有关。
由电荷产生的特殊物理场，描述电荷间相互作用。
2024/3/24
磁场
由运动电荷（电流）产生的特殊物理场，描述磁极间相互作用。
电场性质
对放入其中的电荷有力的作用，且力的方向与电荷的正负有关。
磁场性质
对放入其中的运动电荷（电流）有力的作用，且力的方向与电荷的运动方向及磁场方向有
关。
4
库仑定律与高斯定理
安培环路定理
磁场中沿任何闭合回路L的线积分，等于穿过这回路的所有电流强度的代数和的μ0倍。
2024/3/24
6
洛伦兹力与霍尔效应
洛伦兹力
运动于电磁场的带电粒子所受的力。根据洛伦兹力定律，洛伦兹力可以用方程，称为洛伦兹力方程。
霍尔效应
当电流垂直于外磁场通过半导体时，载流子发生偏转，垂直于电流和磁场的方向会产生一附加电场，从而在半导体的两端产生电势差，这一现象就是霍尔效应。

电磁英文4

麻省理工电磁学第四课演讲稿-Electrostatic.Potential.-.Electric.EnergyTranscript - Lecture 4We're going to talk about, again, some new concepts.And that's the concept of electrostatic potential...electrostatic potential energy.For which we will use the symbol U and independently electric potential.Which is very different, for which we will use the symbol V.Imagine that I have a charge Q one here and that's plus, plus charge, and here I have a charge plus Q two and they have a distant, they're a distance R apart.And that is point P.It's very clear that in order to bring these charges at this distance from each other I had to do work to bring them there because they repel each other.It's like pushing in a spring.If you release the spring you get the energy back.If they were -- they were connected with a little string, the string would be stretched, take scissors, cut the string they fly apart again.So I have put work in there and that's what we call the electrostatic potential energy. So let's work this out in some detail how much work I have to do.Well, we first put Q one here, if space is empty, this doesn't take any work to place Q one here.But now I come from very far away, we always think of it as infinitely far away, of course that's a little bit of exaggeration, and we bring this charge Q two from infinity to that point P.And I, Walter Lewin, have to do work.I have to push and push and push and the closer I get the harder I have to push and finally I reach that point P.Suppose I am here and this separation is little R.I've reached that point.Then the force on me, the electric force, is outwards.And so I have to overcome that force and so my force, F Walter Lewin, is in this direction.And so you can see I do positive work, the force and the direction in which I'm moving are in the same direction.I do positive work.Now, the work that I do could be calculated.The work that Walter Lewin is doing in going all the way from infinity to that location P is the integral going from in- infinity to radius R of the force of Walter Lewin dot dR.But of course that work is exactly the same, either one is fine, to take the electric force in going from R to infinity dot dR.Because the force, the electric force, and Walter Lewin's force are the same in magnitude but opposite direction, and so by flipping over, going from infinity to R, to R to infinity, this is the same.This is one and the same thing.Let's calculate this integral because that's a little easy.We know what the electric force is, Coulomb's law, it's repelling, so the force and dR are now in the same direction, so the angle theta between them is zero, so the cosine of theta is one, so we can forget about all the vectors, and so we would get then that this equals Q one, Q two, divided by four pi epsilon zero.And now I have downstairs here an R squared.And so I have the integral now dR divided by R squared, from capital R to infinity.And this integral is minus one over R.Which I have to evaluate between R and infinity.And when I do that that becomes plus one over capital R.Right, the integral of dR over R squared I'm sure you can all do that is minus one over R.I evaluate it between R and infinity and so you get plus one over R.And so U, which is the energy that -- the work that I have to do to bring this charge at that position, that U is now Q one, times Q two divided by four pi epsilon zero. Divided by that capital R.And this of course this is scalar, that is work, it's a number of joules.If Q one and Q two are both positive or both negative, I do positive work, you can see that, minus times minus is plus.Because then they repel each other.If one is positive and the other is negative, then I do negative work, and you see that that comes out as a sign sensitive, minus times plus is minus.So I can do negative work.If the two don't have the same polarity.I want you to convince yourself that if I didn't come along a straight line from all the way from infinity, but I came in a very crooked way, finally ended up at point P, at that point, that the amount of work that I had to do is exactly the same.You see the parallel with eight o one where we dealt with gravity.Gravity is a conservative force and when you deal with conservative forces, the work that has to be done in going from one point to the other is independent of the path. That is the definition of conservative force.Electric forces are also conservative.And so it doesn't make any difference whether I come along a straight line to thispoint or whether I do that in an extremely crooked way and finally end up here.That's the same amount of work.Now if we do have a collection of charges, so we have pluses and minus charges, some pluses, some minus, some pluses, minus, pluses, pluses, then you now can calculate the amount of work that I, Walter Lewin, have to do in assembling that.You bring one from infinity to here, another one, another one, and you add up all that work, some work may be positive, some work may be negative.Finally you arrive at the total amount of work that you have to do to assemble these charges.And that is the meaning of capital U.Now I turn to electric potential.And for that I start off here with a charge which I now call plus capital Q.It's located here.And at a position P at a distance R away I place a test charge plus Q.Make it positive for now, you can change it later to become a negative.And so the electrostatic potential energy we -- we know already, we just calculated it, that would be Q times Q divided by four pi epsilon zero R.That's exactly the same that we have.So the electric potential, electrostatic potential energy, is the work that I have to do to bring this charge here.Now I'm going to introduce electric potential.Electric potential.And that is the work per unit charge that I have to do to go from infinity to that position.So Q doesn't enter into it anymore.It is the work per unit charge to go from infinity to that location P.And so if it is the work per unit charge, that means little Q disappears.And so now we write down that V at that location P.The potential, electric potential at that location P, is now only Q divided four pi epsilon zero R.Little Q has disappeared.It is also a scalar.This has unit joules.The units here is joules per coulombs.I have divided out one charge.It's work per unit charge.No one would ever call this joules per coulombs.We call this volts, called after the great Volta, who did a lot of research on this.So we call this volts.But it's the same as joules per coulombs.If we have a very simple situation like we have here, that we only have one charge, then this is the potential anywhere, at any distance you want, from this charge.If R goes up, if you're further away, the potential will become lower.If this Q is positive, the potential is everywhere in space positive for a single charge. If this Q is negative, everywhere in space the potential is negative.Electro- electric static potential can be negative.The work that I do per unit charge coming from infinity would be negative, if that's a negative charge.And the potential when I'm infinitely far away, when this R becomes infinitely large, is zero.So that's the way we define our zero.So you can have positive potentials, near positive charge, negative potentials, near negative charge, and if you're very very far away, then potential is zero.Let's now turn to our Vandegraaff.It's a hollow sphere, has a radius R.About thirty centimeters.And I'm going to put on here plus ten microcoulombs.It will distribute itself uniformly.We will discuss that next time in detail.Because it's a conductor.We already discussed last lecture that the electric field inside the sphere is zero.And that the electric field outside is not zero but that we can think of all the charge being at this point here, the plus ten microcoulombs is all here, as long as we want to know what the electric field outside is.So you can forget the fact that it is a -- a sphere.And so now I want to know what the electric potential is at any point in space.I want to know what it is here and I want to know what it is here at point P, which is now a distance R from the center.And I want to know what it is here.At a distance little R from the center.So let's first do the potential here.The potential at point P is an integral going from R to infinity if I take the electric force divided by my test charge Q dot dR.But this is the electric field, see, this force times distance is work, but it is work per unit charge, so I take my test charge out.And so this is the integral in R to infinity of E dot dL -- dR, sorry.And that's a very easy integral.Because we know what E is.The electric field we have done several times.Follows immediately from Coulomb's law and so when you calculate this integral you get Q divided by four pi epsilon zero R which is no surprise because we already had that for a point charge.So this is the situation if r, little r, is larger than capital R.Precisely what we had before.We can put in some numbers.If you put in R equals R, which is ho point three meters, and you put in here the ten microcoulombs, and here the -- the thirty centimeters, then you'll find three hundred thousand volts.So you get three times ten to the fifth volts.If you take r equals sixty centimeters, you double it, if you double the distance, the potential goes down by a factor of two, it's one over R, so it would be a hundred and fifty kilovolts.And if you go to three meters, then it is ten times smaller, then it is thirty kilovolts. And if you go to infinity which for all practical purposes would be Lobby seven, if you go to Lobby seven, then the potential for all practical purposes is about zero. Because R is so large that there is no potential left.So if I, if I, Walter Lewin, march from infinity to this surface of the Vandegraaff, and I put a charge Q in my pocket, and I march to the Vandegraaff, by the time I reach that point I have done work, I multiply the charge now back to the potential, that gives you the work again, because potential was work per unit charge, and so the work that I have done then is the charge that I have in my pocket times the potential, in this case the potential of the Vandegraaff.If I go all the way to this surface, which is three hundred thousand volts.If I were a strong man then I would put one coulomb in my pocket.That's a lot of charge.Then I would have done three hundred thousand joules of work.By just carrying the one coulomb from Lobby seven to the Vandegraaff.That's about the same work I have to do to climb up the Empire State Building.The famous MGH, my mass times G times the height that I have to climb.So I know how the electric potential goes with distance.It's a one over R relationship.Now I have arrived at the Vandegraaff, I am at the surface, with my test charge, and now I go inside.And I slosh around inside, I feel no force anymore.There is no electric field inside.So as I move around inside, I experience no force.That means I do no work.So that means that the potential must remain constant.So the absence of an electric field here implies that the electric potential everywhere is exactly the same inside is the same as on the sphere.Because no further work is needed in marching around with a test charge.And so for this special case, I could make a graph of the electric potential versus R and this is then the radius of the Vandegraaff and that would be a constant all the way up to this point and then it would fall off as one over R here.And in for the numbers that we have chosen, the potential at the maximum here would be three hundred thousand volts.Just as when you look at maps, where you see contours of equal height of mountains, which we call equal altitudes, here we have surfaces of equipotential.And if you had a point charge or if you had the Vandegraaff, these surfaces would be concentric spheres.The further out you go, if the charge is positive, the lower the potential would be. They would be nicely spherical surfaces.Suppose now we had more than one charge, we had a plus Q one charge, and we had a minus Q two charge, for instance.And you're being asked now what is the potential at point P.Well, now the electric potential at point P, VP, is the potential that you would have measured if Q one had been there alone.And you have to add the potential that you would have seen if Q two had been there alone.Just adding work per unit charge for one with work per unit charge of the other.And if this is negative, then this quantity is negative, and this is positive.So when you have configurations of positive and negative charges then of course depending upon where you are in space, if you're close to the plus charge, the potential is almost certainly positive, because the one over R is huge.If you're very close to the negative charge, again the one over R of this little charge will dominate and so you get a negative potential.And so you have surfaces of positive potential and you have equipotential surfaces of negative potentials and so there are surfaces which have zero potential.And they're not always very easy to envision.But what I want to show you is some work that Maxwell himself did in figuring out these equipotentials.And so I have here a transparency of publication by Maxwell.You see a charge, let's assume it is plus four and plus one-- it could be minus four and minus one, but let's assume they're plus.And you see the green lines, which we have seen before, which are the field lines.Don't pay any attention to the green field lines now.The red lines are equipotentials.And you have to rotate them about the vertical, because they're of course surfaces, this is three-dimensional.I have not drawn all the equipotential surfaces in red because they become too cluttered here.But I've tried to put most of them in red.Since this charge is positive and that charge is positive, everywhere in space, no matter where you are, the potential has to be positive.There is not a single point where it could be negative.If you are very far away from the plus four and the plus one, then you expect that the equipotential surfaces are spheres, because it's almost as if you were looking at a plus five charge.So it doesn't surprise you that when you go far out that you ultimately get spherical shapes.When you're very close to the plus four they are perfect spheres, when you're very close to the plus one, they are perfect spheres.But then when you're sort of in between, neither close to the plus four nor to the plus one, they have this very funny shape.It reminds me the shape of this balloon a little bit.Sort of like this.You see.And there is one surface which is most unusual equipotential surface which here has a point where the electric field is zero.It's sort of like twisting the neck of a goose, you get something like this, and so you have here a surface which has a point here and it is exactly at that point where the electric field is zero.That does not mean that the potential is zero, of course not, the potential is positive here.If you come with a positive charge from the Lobby seven and you have to march up to that point, you have to do positive work.You have to overcome both the repelling force from the plus four and the repelling force from the plus one.But finally when you reach that point you can rest because there is no force on you at that point.That's what it means that the electric field is zero.It does not mean that you haven't done any work.So never confuse electric fields with potentials.I want to draw your attention to the fact that the green lines, the field lines, are everywhere perpendicular to the equipotentials.I will get back to that during my next lecture.That is not an accident.That is always the case.Now, Maxwell shows you something that is a little bit more complicated.Here, he calculated for us the equipotential surfaces, the red ones are the surfaces. Again you have to rotate them about the vertical to make it three-dimensional.And now we have a minus one charge and a plus four.And so whenever it is red, the surface, the potential is positive, and whenever I have drawn it blue, the potential is negative.First, if we were very far away from both the plus four and the minus one, you expect to be looking at a charge which is effectively plus three.And so if you go very far away for sure the potential is everywhere positive and you expect them to be spherical again.If you look here you're very far away from the plus four and the minus one, indeed this has already the shape of a sphere.So that's clear that the plus four and the minus one far away behave like a plus three.If you're very close to the plus four, you get nice spheres around the plus four, positive potential, if you're very close to the minus one, notice that the blue surfaces are almost nice spheres, but now they're all negative because you're very close to the minus one.So a negative potential.There is here one surface which now has zero potential.It has to be because if you're negative potential close to the minus one and you have positive potential very far out, you got to go through a surface where it's zero.And so there is here a surface, I still have put it in blue, which is actually everywhere on this surface the potential is zero.Is the electric field zero there?Absolutely not.Electric field should not be confused with potential.What it means is that if you take a test charge in your pocket and you come from infinity and you walk to that surface, that by the time you have reached that surface, you've done zero work.That's what it means.That the potential is zero.There is here one point which we discussed earlier in my lectures where the electric field is zero.The potential is not zero there.The potential is definitely positive here.Because here was the zero surface.Here is already positive surface, and this is a positive surface.So the potential is positive.However, if you reach that point there's no force on your charge.So that means electric field is zero.And it's not so easy of course to calculate these surfaces.Maxwell was capable of doing that a hundred ten years ago.And nowadays we can do that very easily with computers.Equipotential surfaces which have different values can never intersect.Plus five volt surface can never intersect with a plus three or a minus one.And you think about why that is.Why that is, that would be a total violation of the conservation of energy.So equipotential surfaces, different values, can never intersect.All right.So you've seen that for the various charge configurations, the equipotential surfaces have very complicated shapes and cannot always be calculated in a very easy way. Now comes the question why do we introduce electric potentials, who needs them? And who needs equipotential surfaces?Isn't it true that if we know the electric field vectors everywhere in space that, that determines uniquely how charges will move, what acceleration they will obtain, that means how their kinetic energy will change.And the answer is yeah, if you know the electric field everywhere in space sure. Then you can predict everything that happens with a charge in that field.But there are examples where the electric fields are so incredibly complicated that it is easier to work with equipotentials because the change in kinetic energy as I will discuss now really depends only on the change in the potential when you go from one point to another.So you will see very shortly that sometimes if you're only interested in change of kinetic energy and not necessarily interested in the details of the trajectory, then equipotentials come in very handy.Never confuse U which is electrostatic potential energy with V which is electric potential.This has unit joules.And this has unit joules per coulombs, which we call volts.If I have a collection of charges, pluses and minuses, U has only one value.It is the work that I have to do to put all these crazy charges exactly where they are. But the electric potential is different here from there from there to there to there to there.If you're very close to a plus charge, you can be sure that the potential is positive. If you're very close to a -- a negative charge, you can be sure that the potential is negative.But U has only one number.It's only one value.They're both scalars.Don't confuse one with the other.In a gravitational field, matter, like a piece of chalk, wants to go from high potential to low potential.If I just release it with zero speed, there it goes, high potential to low potential.In analogy, positive charges will also go from a high electric potential to a low electric potential.And of course this is unique for electricity, negative charges will go from a low potential to a high electric potential.Suppose I had a position A in space and I had another position B and I specify theSo here we have A, potential is VA, and here we have point B where the potential is VB.By definition, the potential of VA as we discussed before is the integral -- by the way if these are separated by some random distance R, whatever you want.So the potential of A is defined as the integral going from A to infinity of E dot dR.That is the definition of the potential of A.There is an E here which is force per unit charge.So it is not work.If there were force DR it would be work but it is force per unit charge that makes it E.So the potential of B, for definition, is the integral from B to infinity of E dot dR.And so therefore the potential difference between point A and B, VA minus VB, equals the integral from A to B of E dot dR, and for reasons that I still don't understand after having been in this business for a long time, books will always tell you they reverse VA and B so they give you VB, VB minus VA.And then they say well we have to put a minus sign in front of the integral.It's the same thing.So books always give it to you in this form.But it is exactly the same.Hope you realize that.This is the two equations that I have here are the same.VA minus VB is the integral from A to B of E dot dR.If I flip this over then all I have to do is put a minus sign here and the two are identical.Notice that if there is no electric field between A and B they have the same potential,Because when you march from A to B with a charge in your pocket no work is done. So the potential remains the same.I will change this dR to a different symbol, which I call dL.dR would mean that we go from A to infinity along this straight line and then we go from B to infinity along the straight line but it makes no difference how you go.If you go from A to B this potential difference and you go in this way then VA minus VB is not going to change.And so if now I introduce here a element dL, which is a small vector, and if the local E vector here is like so, at this point here, then VA minus VB is then the integral of E dot dL.In other words I can replace the R by an L and you may choose any path that you prefer.And that's the way that we will show you this equation most of the time.So it makes no difference how you march because we are dealing here with conservative fields.So let's now make the assumption that VA is hundred fifty volts.And that VB for instance is fifty volts.So it's a very specific example.What does it mean now?It means that if I put plus Q charge in my pocket and I come all the way from Lobby seven and I walk up to point B.So Walter Lewin, plus Q charge in his pocket, goes from Lobby seven to point B, I have to do work and the work I have to do is the product of my charge Q with the potential.So that is Q the work I have to do is Q times VB.So in this case it's fifty times Q, whatever that charge is that I have in my pocket.This is in joules.Now, I go from Lobby seven to point A.I have to do more work.I have to do hundred fifty Q joules of work.You can think of it I first come to A to B, I'm already exhausted, I have to put in another work to get all the way to point A.So you can imagine if I have this plus Q charge at point A, where there it's-- it's a higher potential, it wants to go back all by itself to B.It wants to go from a higher potential to a lower potential.Look, the E vector is in this direction.Positive charge will go to a lower potential.And as it moves from A to B energy is released.How much energy?Well, this is the amount of work I have done to get to A, this is the amount of work I did to get to B, and so if now the charge goes back from A to B, it's the difference that becomes available in terms of kinetic energy.It's a change in potential energy.And that change in potential energy, so the change in potential energy...when the plus Q charge goes from A to B, that change is Q times VA minus VB. QVB at point B and QVA at point A.So this is the potential energy that is in principle available if the charge moves from A to B.And you remember from eight oh one the work energy theorem.If we deal with conservative forces, then the sum of potential energy and kinetic energy of an object is the same.That's also true for gravitational forces.In other words, this difference in potential energy that becomes available like potential energy becomes available when I drop my chalk from a high potential to a low potential, that's converted to kinetic energy.So this difference now is also converted into kinetic energy of that moving charge. And so that would be the kinetic energy at point B minus the kinetic energy at point A.Which is really the work energy theorem.It's the conservation of energy.Now any piece of metal, no matter how crumby or dented it is, is an equipotential. As long as there is no charge moving inside the metal.And that's obvious that it's an equipotential.Because these charges inside the metal, these electrons, when they experience an electric field, they begin to move immediately in the electric field, and they will move until there is no force on them anymore, and that means they have effectively made the electric field zero.So charges inside the conductor always move automatically in such a way that they kill the electric field inside.If the electric field hadn't been zero yet, they would still be moving.And so each metal that you have, no matter where you bring it, as long as there are no electric currents inside, will always be an equipotential.So I can take a trash can and bring it into an external field and then very shortly after I've brought it in when things have calmed down, the trash can will be an equipotential and the electric field inside the metal will everywhere will everywhere be zero.So I could for instance attach point A to a trash can, metal trash can, so the whole trash can would be at a hundred fifty volts, and I could put point B, make it part of my -- of my soda, which is also made of metal.。

麻省理工大学电磁学应用讲义

Anode, phosphors + -V
(3)
-
H Cathode ray tube (CRT)
Figure 12-1. Magnetic deflection in a cathode ray tube
In high-voltage cathode-ray tubes (CRT's) used for television or computer displays the electrons are quickly accelerated near the cathode and then move with energy ~eV [J], where V is the tube voltage (see (3) in the notes for R13). Since: eV = mv2/2 (4)
6.013 Lecture 12: Magnetic Forces and Devices
A. Overview Magnetic forces are central to a wide array of actuators and sensors. These forces can be calculated using either energy methods or the Lorentz force law, which is: f = q(E +v × µoH) Newtons (1)
Force balance: -eEe -e v H -eV × µoH
Figure 12-5. Forces on electron moving through electromagnetic fields
If an open-circuited wire of length W moves atv perpendicular to H, all the electrons will move until a force-balance equilibrium is reached for which the net force on any electron is zero. Otherwise there would be no equilibrium. The balancing force inside a wire is electric and is equal to -e Ee, as illustrated in Figure 12-5. That is, the charges will move inside the wire and accumulate at its ends until there is sufficient electric potential across the wire to halt their movement. Specifically, this Lorentz force balance requires: -ev × µoH = eEe

《电磁学Mawell》课件

《电磁学Mawell》课件一、教学内容本节课将深入探讨《电磁学》教材中第四章“麦克斯韦方程组”的内容。

具体包括：麦克斯韦方程组的推导，电磁波的传播，以及边界条件的应用。

二、教学目标1. 理解并掌握麦克斯韦方程组的物理意义和数学表达。

2. 学会运用麦克斯韦方程组分析和解决实际问题。

3. 了解电磁波的传播特性及其在现实生活中的应用。

三、教学难点与重点难点：麦克斯韦方程组的推导和运用。

重点：电磁波的传播特性及其应用。

四、教具与学具准备教具：黑板、粉笔、电磁学教学挂图。

学具：笔记本、教材、《电磁学》学习指导书。

五、教学过程1. 实践情景引入（5分钟）通过展示电磁波的日常应用，如手机、电视等，引发学生对电磁学的兴趣。

2. 麦克斯韦方程组推导（15分钟）（1）复习电磁场基本概念。

（2）引导学生推导出麦克斯韦方程组。

（3）讲解麦克斯韦方程组的物理意义。

3. 电磁波传播特性讲解（15分钟）（1）介绍电磁波的传播速度、波长、频率等基本概念。

（2）讲解电磁波的传播方程。

（3）分析电磁波在不同介质中的传播特性。

4. 例题讲解（15分钟）讲解一道关于电磁波传播的例题，引导学生运用麦克斯韦方程组解决问题。

5. 随堂练习（10分钟）布置一道关于麦克斯韦方程组的随堂练习，巩固所学知识。

6. 课堂小结（5分钟）六、板书设计1. 麦克斯韦方程组推导过程。

2. 电磁波的传播特性。

3. 例题解答过程。

七、作业设计1. 作业题目：（1）推导麦克斯韦方程组。

（2）已知电磁波的频率和波长，计算其传播速度。

（3）分析电磁波在不同介质中的传播特性。

2. 答案：（1）见教材第四章。

（2）传播速度 = 波长× 频率。

（3）见教材第四章。

八、课后反思及拓展延伸1. 反思：本节课学生对麦克斯韦方程组的掌握程度，以及随堂练习的完成情况。

2. 拓展延伸：引导学生学习电磁学在通信、雷达等领域的应用，提高学生的实践能力。

重点和难点解析1. 麦克斯韦方程组的推导和物理意义。

lecsup222

麻省理工学院-物理系物理学8.02 2002.02.22电介质与极化二月二十二日星期五的课程#8的一些笔记同学们不要孤立地学习这些笔记。

大家应该结合我讲的课程来“消化”这些笔记。

我们曾经两次遇到过绝缘体在外加电场的作用下会被极化。

有外电场存在时，有些分子和原子将变成偶极子。

电场越强，极化的程度越强。

我们把这样的物质叫做电介质1。

在这里我们不考虑所有理想导体，即外电场作用下内部电荷能自由有序运动的导体。

现在我们要学习的电介质不再是那么有规律，甚至有点混乱。

没有箭头的符号代表数量。

现将一平行板电容器（两板为导体）接到一节电池（电压为V）的两端。

因此，两极板带有电性相反但数量相同的电荷。

我们把每个极板上的电荷叫做，表面电荷密度叫做free Q free σ（即由除以平板表面积所得）。

我们把由该电荷激发的电容里的电场称做。

注意，即在GIANCOLI 第625页提及的“自由电荷”，但是那里我们用的是Q 和free Q free E σ（而没有下标“free”）。

E=0E=0电容器充完电后，我们断开给极板提供电势差为V 的电池。

现在极板上的电荷将“不再改变”。

现在我们将电介质插入两极板之间。

此时电介质上激发出两层感应电荷。

（记住笔记中标明的“+ -”）。

我们把这些感应电荷密度用ind σ表示。

这就是电场作用下电介质的极化。

一般地，与“自由电荷”相对应，我们也把感应电荷称做“束缚电荷”。

1某些电介质的分子即使在没有外电场的情况下也存在着固有的偶极矩。

当将这类电介质放到电场E中，这些偶极矩会努力沿着电场线方向排成一队一队的形式。

其和电场线拟合程度的高低和场强大小成正比。

本章所讨论的电介质也包括这类电介质。

E=0E=0感应电荷“自己”也激发电场，ind E ，此电场方向与原电场free E 相反。

所以，净电场为因此从数量上看，E 比小（即电场变弱了）。

freeE在“一般”情况下，，因此free ind E E ∝free ind bE E =，这里b 是一个只依赖于电介质物质本身的常数。

麻省理工电磁课系列

14
Magnetic Field Above/Below a Sheet of Current
… flowing in the
uniform DC surface current
direction with current density
As seen “end on”, the current sheet may be thought of as a combination of parallel wires, each of which produces its own field. These fields combine, so that the total field above and below the current sheet is directed in and direction, respectively.
Magnetostatics (Free Space With Currents & Conductors)
Suggested Reading - Shen and Kong – Ch. 13
Outline
André-Marie Ampère, 1775-1836
Review of Last Time: Gauss’s Law Ampere’s Law Applications of Ampere’s Law Magnetostatic Boundary Conditions Stored Energy
Gauss’s Law encompasses all observations related to Coulomb’s Law…
3
2nd Observation: Force and Potential Energy

Mawell教学讲解课件.

Mawell教学讲解课件.一、教学内容本课件基于《电磁学》教材第四章“麦克斯韦方程组及其应用”，详细内容涵盖：麦克斯韦方程组的数学表达形式及其物理意义，边界条件的应用，以及静态电磁场和时变电磁场的分析和计算。

二、教学目标1. 理解并掌握麦克斯韦方程组的四个基本方程及其衍生形式。

2. 能够运用麦克斯韦方程组分析和解决实际电磁问题。

3. 掌握电磁波的产生与传播，理解电磁波在现代科技中的应用。

三、教学难点与重点教学难点：麦克斯韦方程组的理解与应用，特别是时变电磁场问题的分析。

教学重点：麦克斯韦方程组的推导，以及各个方程的物理意义。

四、教具与学具准备1. 电磁学实验器材：电流表、电压表、导线、电容和电感元件。

2. 多媒体教学设备，用于展示电磁场模拟动画。

3. 学生用计算器、笔记本、教材。

五、教学过程1. 实践情景引入：通过简单的电磁感应实验，引导学生思考电磁场的变化规律。

2. 理论讲解：详细讲解麦克斯韦方程组的四个方程，每个方程通过例题进行讲解。

例题1：计算一个简单闭合回路的磁通量变化。

例题2：分析一个平面电磁波的传播特性。

3. 随堂练习：布置与例题难度相近的练习题，学生现场解答，教师及时反馈。

4. 互动讨论：针对麦克斯韦方程组的应用，组织学生讨论其在现实生活中的应用案例。

六、板书设计1. 麦克斯韦方程组的四个基本方程。

2. 例题的详细解题步骤。

3. 随堂练习的关键步骤提示。

七、作业设计1. 作业题目：计算给定线圈中的感应电动势，并分析其与线圈半径、线速度的关系。

描述一个均匀磁场中平面电磁波的传播特点。

2. 答案：作业答案将提供详细的计算步骤和最终结果。

八、课后反思及拓展延伸1. 反思：通过学生作业和随堂练习的反馈，调整教学方法，加强学生对难点的理解。

2. 拓展延伸：鼓励学生探索麦克斯韦方程组在现代通信技术中的应用，例如无线充电技术、光纤通信等。

组织课外阅读和小组讨论，拓宽学生视野。

重点和难点解析：1. 麦克斯韦方程组的理解与应用。

2024年Mawell教学讲解课件.

2024年Mawell教学讲解课件.一、教学内容本节课我们将学习《Mawell》教材第四章“电磁感应”部分，详细内容包括：电磁感应现象的发现与理解，法拉第电磁感应定律，以及楞次定律的应用。

还将探讨闭合电路中电磁感应的应用实例。

二、教学目标1. 让学生理解电磁感应现象的产生原理，掌握法拉第电磁感应定律和楞次定律。

2. 培养学生运用电磁感应知识解决实际问题的能力。

3. 培养学生的实验操作能力和团队协作能力。

三、教学难点与重点教学难点：法拉第电磁感应定律和楞次定律的理解与应用。

教学重点：电磁感应现象的产生原理，以及闭合电路中电磁感应的应用实例。

四、教具与学具准备1. 教具：电磁感应实验装置，演示电磁感应现象的动画，PPT课件。

2. 学具：学生分组实验器材，包括线圈、磁铁、电流表等。

五、教学过程1. 导入：通过展示磁铁穿过线圈的实验，引发学生对电磁感应现象的兴趣，提出问题：“为什么磁铁穿过线圈时，线圈中会产生电流？”2. 基本概念：讲解电磁感应现象的发现，引导学生理解法拉第电磁感应定律。

3. 例题讲解：分析一道应用法拉第电磁感应定律的题目，让学生跟随讲解思路，逐步解题。

4. 实践操作：学生分组进行电磁感应实验，观察并记录实验现象，探讨楞次定律的应用。

5. 随堂练习：布置几道有关电磁感应的练习题，让学生当堂完成，及时巩固所学知识。

六、板书设计1. 电磁感应现象2. 法拉第电磁感应定律3. 楞次定律4. 闭合电路中电磁感应的应用实例七、作业设计1. 作业题目：（1）简述电磁感应现象的产生原理。

（2）运用法拉第电磁感应定律，计算一道题目：一个长为0.5m，宽为0.3m，磁感应强度为0.2T的平面线圈，在匀强磁场中以10rad/s的角速度转动，求线圈中产生的电动势。

答案：（1）电磁感应现象产生原理：当导体在磁场中运动或磁场发生变化时，导体中会产生电动势，从而产生电流。

（2）电动势E = NBAω = 0.2 × 0.5 × 0.3 × 10 = 0.3V八、课后反思及拓展延伸本节课通过实践情景引入、例题讲解、随堂练习等多种教学手段，使学生较好地掌握了电磁感应现象及其应用。

电磁学04

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电磁学04-07: 再论恒稳电流电场
恒稳电流过程已经touched的一些性质： E dl 0 L I j dS 0 1 S E dS Q0 & Q 0 S 0 S内 d ( x, y , z ) 0 D dt dS Q0 S S内在此基础上再延伸一些性质 (1) 如果闭合面 S 上各点不变，则： 1 J dS E dS 0 E dS
电磁学04-02: 电流连续性方程
有限空间被闭合曲面包络电荷守恒； I j dS Q(t ) Q(t dt ) Idt
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电磁学04-06: 金属导电的经典微观理论
载流子：很多实验证实是自由电子 Richard Chace Tolman experiment 导电的电子气理论：
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电磁学04-01: 电流的几个概念
电流密度 j ：某点的电流密度数值上等于和该点正电荷定性移动方向垂直的单位面积上的电流强度；方向：该点正电荷定向移动的方向，即电场的方向。
电流密度 j 与电流强度 I 的关系：矢量与通量的关系！