《光与物质》系列：免费基础物理学教材-4.电磁学

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"4.electricity_and_magnetism_crowell.pdf" 这本《Electricity and Magnetism》是Benjamin Crowell所著的《Light and Matter》系列物理学教科书的第四册，旨在提供免费的初级物理学教程。该系列还包括其他五本书：1. Newtonian Physics（牛顿物理学）、2. Conservation Laws（守恒定律）、3. Vibrations and Waves（振动与波）、5. Optics（光学）以及6. The Modern Revolution in Physics（现代物理学革命）。作者Benjamin Crowell是一位居住在加利福尼亚富勒顿的物理学家，他通过www.lightandmatter.com网站分享这些教材。该书的版本为2.3，修订日期为2007年3月5日。它遵循了创作共享 Attribution-ShareAlike 1.0 许可证，这意味着读者可以在尊重原作者权益的前提下自由复制、分发和改编内容。此外，书中的一些照片和插图由其他作者提供，并在图片信用中列出，这些作品不受此许可证约束。同时，读者也可以选择根据GNU Free Documentation License version 1.2来复制这本书，但需遵守不包含不变部分、封面文本的规定。《Electricity and Magnetism》这本书涵盖了电学和磁学的基础知识，可能包括以下主题： 1. **静电学**：电荷的基本性质，如库仑定律，电场的概念，电势能和电势，电场线，电容，电容器的工作原理，导体和绝缘体的行为。 2. **电流和电路**：电流的定义，欧姆定律，电阻，电压，电源（电池和发电机），简单电路分析，串联和并联电路，电阻的温度系数。 3. **电磁感应**：法拉第电磁感应定律，自感和互感，变压器的工作原理，电动机和发电机的原理。 4. **磁场**：磁现象的起源，磁力线，磁矩，安培环路定律，地球的磁场，磁介质中的磁性。 5. **电磁波**：电磁波的产生，麦克斯韦方程，电磁波的传播特性，光的电磁性质，电磁谱。 6. **电磁场的统一理论**：引入电场和磁场的相对论性解释，如洛伦兹力，詹姆斯·克拉克·麦克斯韦对电磁理论的贡献，以及电磁波的统一描述。 7. **量子电动力学**：量子化电荷和电磁相互作用的初步介绍，如电子的自旋，光电效应，康普顿散射。这本书通过清晰易懂的语言和实例解释复杂的物理概念，适合初学者或对电学和磁学感兴趣的读者自学使用。通过阅读这本书，读者不仅可以掌握基础的物理原理，还能了解到这些原理在日常生活和技术应用中的实际意义。

Suppose we pick cat fur rubbed on rabbit fur as a representative of

type A, and glass rubbed on silk for type B. We will now ﬁnd that

there is no “type C.” Any object electriﬁed by any method is either

A-like, attracting things A attracts and repelling those it repels, or

B-like, displaying the same attractions and repulsions as B. The two

types, A and B, always display opposite interactions. If A displays

an attraction with some charged object, then B is guaranteed to

undergo repulsion with it, and vice-versa.

The coulomb

Although there are only two types of charge, each type can come

in diﬀerent amounts. The metric unit of charge is the coulomb

(rhymes with “drool on”), deﬁned as follows:

One Coulomb (C) is the amount of charge such that a force of

9.0 ×10

N occurs between two pointlike objects with charges

of 1 C separated by a distance of 1 m.

The notation for an amount of charge is q. The numerical factor

in the deﬁnition is historical in origin, and is not worth memoriz-

ing. The deﬁnition is stated for pointlike, i.e., very small, objects,

because otherwise diﬀerent parts of them would be at diﬀerent dis-

tances from each other.

A model of two types of charged particles

Experiments show that all the methods of rubbing or otherwise

charging objects involve two objects, and both of them end up get-

ting charged. If one object acquires a certain amount of one type of

charge, then the other ends up with an equal amount of the other

type. Various interpretations of this are possible, but the simplest

is that the basic building blocks of matter come in two ﬂavors, one

with each type of charge. Rubbing objects together results in the

transfer of some of these particles from one object to the other. In

this model, an object that has not been electrically prepared may ac-

tually possesses a great deal of both types of charge, but the amounts

are equal and they are distributed in the same way throughout it.

Since type A repels anything that type B attracts, and vice versa,

the object will make a total force of zero on any other object. The

rest of this chapter ﬂeshes out this model and discusses how these

mysterious particles can be understood as being internal parts of

atoms.

Use of positive and negative signs for charge

Because the two types of charge tend to cancel out each other’s

forces, it makes sense to label them using positive and negative signs,

and to discuss the total charge of an object. It is entirely arbitrary

which type of charge to call negative and which to call positive.

Benjamin Franklin decided to describ e the one we’ve been calling

“A” as negative, but it really doesn’t matter as long as everyone is

16 Chapter 1 Electricity and the Atom

consistent with everyone else. An object with a total charge of zero

(equal amounts of both types) is referred to as electrically neutral.

self-check A

Criticize the following statement: “There are two types of charge, attrac-

tive and repulsive.” . Answer, p.

202

Coulomb’s law

A large body of experimental observations can be summarized

as follows:

Coulomb’s law: The magnitude of the force acting between point-

like charged objects at a center-to-center distance r is given by the

equation

|F| = k

||q

where the constant k equals 9.0 ×10

N·m

. The force is attrac-

tive if the charges are of diﬀerent s igns, and repulsive if they have

the same sign.

Clever modern techniques have allowed the 1/r

form of Coulomb’s

law to be tested to incredible accuracy, showing that the exponent

is in the range from 1.9999999999999998 to 2.0000000000000002.

Note that Coulomb’s law is closely analogous to Newton’s law

of gravity, where the magnitude of the force is Gm

, except

that there is only one type of mass, not two, and gravitational forces

are never repulsive. Because of this close analogy between the two

types of forces, we can recycle a great deal of our knowledge of

gravitational forces. For instance, there is an electrical equivalent

of the shell theorem: the electrical forces exerted externally by a

uniformly charged spherical shell are the same as if all the charge

was concentrated at its center, and the forces exerted internally are

zero.

Conservation of charge

An even more fundamental reason for using positive and nega-

tive signs for electrical charge is that experiments show that charge

is conserved according to this deﬁnition: in any closed system, the

total amount of charge is a constant. This is why we observe that

rubbing initially uncharged substances together always has the re-

sult that one gains a certain amount of one type of charge, while

the other acquires an equal amount of the other type. Conservation

of charge seems natural in our model in which matter is made of

positive and negative particles. If the charge on each particle is a

ﬁxed property of that type of particle, and if the particles themselves

can be neither created nor destroyed, then c onservation of charge is

inevitable.

Section 1.2 Charge, electricity and magnetism 17

b / A charged piece of tape

attracts uncharged pieces of

paper from a distance, and they

leap up to it.

c / The paper has zero total

charge, but it does have charged

particles in it that can move.

Electrical forces involving neutral objects

As shown in ﬁgure b, an electrically charged object can attract

objects that are uncharged. How is this possible? The key is that

even though each piec e of paper has a total charge of zero, it has at

least some charged particles in it that have some freedom to move.

Suppose that the tape is positively charged, c. Mobile particles

in the paper will respond to the tape’s forces, causing one end of

the paper to become negatively charged and the other to become

positive. The attraction is b etween the paper and the tape is now

stronger than the repulsion, because the negatively charged end is

closer to the tape.

self-check B

What would have happened if the tape was negatively charged? .

Answer, p. 202

The path ahead

We have begun to encounter complex electrical behavior that we

would never have realized was occurring just from the evidence of our

eyes. Unlike the pulleys, blocks, and inclined planes of mechanics,

the actors on the stage of electricity and magnetism are invisible

phenomena alien to our everyday experience. For this reason, the

ﬂavor of the second half of your physics education is dramatically

diﬀerent, focusing much more on experiments and techniques. Even

though you will never actually see charge moving through a wire,

you can learn to use an ammeter to measure the ﬂow.

Students also tend to get the impression from their ﬁrst semester

of physics that it is a dead science. Not so! We are about to pick

up the historical trail that leads directly to the cutting-edge physics

research you read about in the newspaper. The atom-smashing ex-

periments that began around 1900, which we will be studying in this

chapter, were not that diﬀerent from the ones of the year 2000 —

just smaller, simpler, and much cheaper.

Magnetic forces

A detailed mathematical treatment of magnetism won’t come

until much later in this book, but we need to develop a few simple

ideas about magnetism now because magnetic forces are used in the

experiments and techniques we come to next. Everyday magnets

come in two general types. Permanent magnets, such as the ones

on your refrigerator, are made of iron or substances like steel that

contain iron atoms. (Certain other substances also work, but iron

is the cheapest and most common.) The other type of magnet,

an example of which is the ones that make your stereo speakers

vibrate, consist of coils of wire through which electric charge ﬂows.

Both types of magnets are able to attract iron that has not been

18 Chapter 1 Electricity and the Atom

magnetically prepared, for instance the door of the refrigerator.

A single insight makes these apparently complex phenomena

much simpler to understand: magnetic forces are interactions be-

tween moving charges, occurring in addition to the electric forces.

Suppose a permanent magnet is brought near a magnet of the coiled-

wire type. The coiled wire has moving charges in it because we force

charge to ﬂow. The permanent magnet also has moving charges in

it, but in this case the charges that naturally swirl around inside the

iron. (What makes a magnetized piece of iron diﬀerent from a block

of wood is that the motion of the charge in the wood is random

rather than organized.) The moving charges in the coiled-wire mag-

net exert a force on the moving charges in the permanent magnet,

and vice-versa.

The mathematics of magnetism is signiﬁcantly more complex

than the Coulomb force law for electricity, which is why we will

wait until chapter 6 before delving deeply into it. Two simple facts

will suﬃce for now:

(1) If a charged particle is moving in a region of space near where

other charged particles are also moving, their magnetic force on it

is directly proportional to its velocity.

(2) The magnetic force on a moving charged particle is always

perpendicular to the direction the particle is moving.

A magnetic compass example 1

The Earth is molten inside, and like a pot of boiling water, it roils and

churns. To make a drastic oversimpliﬁcation, electric charge can get

carried along with the churning motion, so the Earth contains moving

charge. The needle of a magnetic compass is itself a small permanent

magnet. The moving charge inside the earth interacts magnetically with

the moving charge inside the compass needle, causing the compass

needle to twist around and point north.

A television tube example 2

A TV picture is painted by a stream of electrons coming from the back

of the tube to the front. The beam scans across the whole surface of

the tube like a reader scanning a page of a book. Magnetic forces are

used to steer the beam. As the beam comes from the back of the tube

to the front, up-down and left-right forces are needed for steering. But

magnetic forces cannot be used to get the beam up to speed in the ﬁrst

place, since they can only push perpendicular to the electrons’ direction

of motion, not forward along it.

Discussion Questions

A If the electrical attraction between two pointlike objects at a distance

of 1 m is 9×10

N, why can’t we infer that their charges are +1 and −1 C?

What further observations would we need to do in order to prove this?

B An electrically charged piece of tape will be attracted to your hand.

Does that allow us to tell whether the mobile charged particles in your

hand are positive or negative, or both?

Section 1.2 Charge, electricity and magnetism 19

1.3 Atoms

I was brought up to look at the atom as a nice, hard fellow, red or

grey in color according to taste. Rutherford

Atomism

The Greeks have been kicked around a lot in the last couple of

millennia: dominated by the Romans, bullied during the crusades

by warlords going to and from the Holy Land, and occupied by

Turkey until recently. It’s no wonder they prefer to remember their

salad days, when their best thinkers came up with concepts like

democracy and atoms. Greece is democratic again after a period

of military dictatorship, and an atom is proudly pictured on one of

their coins. That’s why it hurts me to have to say that the ancient

Greek hypothesis that matter is made of atoms was pure guess-

work. There was no re al experimental evidence for atoms, and the

18th-century revival of the atom concept by Dalton owed little to

the Greeks other than the name, which means “unsplittable.” Sub-

tracting even more cruelly from Greek glory, the name was shown

to be inappropriate in 1899 when physicist J.J. Thomson proved ex-

perimentally that atoms had even smaller things inside them, which

could be extracted. (Thomson called them “electrons.”) The “un-

splittable” was splittable after all.

But that’s getting ahead of our story. What happened to the

atom concept in the intervening two thousand years? Educated peo-

ple continued to discuss the idea, and those who were in favor of it

could often use it to give plausible explanations for various facts and

phenomena. One fact that was readily explained was conservation

of mas s. For example, if you mix 1 kg of water with 1 kg of dirt,

you get exactly 2 kg of mud, no more and no less. The same is true

for the a variety of processes such as freezing of water, fermenting

beer, or pulverizing sandstone. If you believed in atoms, conserva-

tion of mas s made perfect sense, because all these processes could

be interpreted as mixing and rearranging atoms, without changing

the total number of atoms. Still, this is nothing like a proof that

atoms exist.

If atoms did exist, what types of atoms were there, and what dis-

tinguished the diﬀerent types from each other? Was it their sizes,

their shapes, their weights, or some other quality? The chasm be-

tween the ancient and modern atomisms b e com es evident when we

consider the wild sp e culations that existed on these issues until the

present century. The ancients decided that there were four types of

atoms, earth, water, air and ﬁre; the most popular view was that

they were distinguished by their shapes. Water atoms were spher-

ical, hence water’s ability to ﬂow smoothly. Fire atoms had s harp

points, which was why ﬁre hurt when it touched one’s skin. (There

was no concept of temperature until thousands of years later.) The

20 Chapter 1 Electricity and the Atom

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