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Knight Physics
John Denker

Here are some notes concerning the book

 Randall D. Knight Physics for Scientists and Engineers

This is just a collection of notes that I have accumulated. It should not be considered a book review. It is not by any means complete. Perhaps gradually it will become more complete and more balanced.

## *   Contents

1  Some Observations
2  References

## 1  Some Observations

1.
On page 117 it asks, «What is a force?» Among other things, it says «A force requires an agent.» It insists on distinguishing the roles of the agent «that acts or exerts power» from the object that is acted upon by the force.

This violates the letter and spirit of the third law. A force is just a force. It is not just unnecessary but actively misleading to introduce the notion of «agent».

2.
On page 118 it calls for drawing force vectors with the tail of the vector anchored on the particle.

First of all, this embodies a fundamental misconception about vectors. In reality, a vector has a direction and magnitude; it does not have a direction, magnitude, and location.

Secondly, you get into all sorts of trouble if you insist on anchoring vectors by their tails. Sometimes it is better to anchor them by their middles, or to move them somewhere else entirely.

3.
On page 129, it defines and describes an «inertial frame». It then illustrates this with an example that contradicts everything that has been said. In accordance with Einstein’s principle of equivalence, the only difference between Figure 5.21(a) and 5.21(b) is a different value of g. Either both frames are valid, or neither is.

4.
On page 181, the traction setup is fake and impractical.

5.
On page 219, it says that momentum is conserved «under the proper circumstances».

That is a terrible thing to say. In fact, momentum is conserved, period.

6.
On page 407, it says Bernoulli’s equation is «a statement of energy conservation».

In fact, though, all fluids are compressible to some extent, and when we take that into account, we find that Bernoulli’s equation has more to do with enthalpy than energy.

7.
On page 427, it suggests blowing across the top of a strip of paper, to demonstrate Bernoulli’s principle. This is, alas, demonstrates nothing of the sort.

8.
On page 477, it says «Thermal energy is an energy of the system due to the motion of its atoms and molecules.»

Authors should be allowed to define their terms however they like, within reason, but this is unreasonable. To the extent that «thermal energy» can be defined at all, it needs to include the potential energy as well as the kinetic energy of the atoms and molecules. In a solid, half the heat capacity comes from potential energy, and half from kinetic energy.

9.
On page 477, definition of «heat».

10.
On page 518, it says «It is often said that entropy measures the amount of disorder in a system.»

Gaaack!

11.
On page 720, it introduces the idea of electric charge by saying «There are two kinds of charge.»

There are definitely not two kinds of charge. If there were, we would need two variables: one to keep track of the “resinous electricity” and another to keep track of the “vitreous electricity”. In fact, we keep track of a single charge variable, which can be positive or negative. For details on this, see reference 1.

This was figured out by Watson (1747) and independently by Franklin (1747). Indeed, Franklin introduced the terms “positive”, “negative”, and “charge” for precisely this reason, to indicate a surplus or a deficit of the one type of electricity. See reference 2.

12.
All of chapter 29 assumes the voltage is a potential.

13.
On page 826, figure 28.27 shows four ways of visualizing the 1/r potential. This is a good thing in principle. However, the contour map is not quite right. The V=1 and V=3 contours are to scale; so far so good. However, the contour in between surely must represent V=2, but its radius is not what it should be. It should be half as big as the V=1 contour. Why not just compute all the contours quantitatively, as in figure 1?

Ironically, in the book, the 3D diagram – which is harder to draw – is drawn much more accurately.

 Figure 1: Equipotentials V=1, V=2, and V=3 for the 1/r Potential Figure 2: Equipotentials V=1 through V=5 for the 1/r Potential

It would be even better to show more contours, as in figure 2.

Secondly, in the elevation graph, it would be better to use a louder color and/or a heavier line to emphasize the contours of constant V. As it is, they are hard to untangle from the contours of constant x and y. Also, given that the plot goes higher than V=4, the fourth contour really should be shown.

14.
On page 826, in figure 28.27, the 3D plot would look better if an entire octant were cut away. This would also greatly facilitate plotting more contours.

15.
On page 827 in example 28.10, it shows a proton (not a test charge) initially at zero distance from the surface of a charged sphere. We have to assume the sphere is made of conducting material, because the exercise speaks of “the” potential of the sphere, and it would be impossible for a non-conducting sphere to remain an equipotential under the conditions of the experiment.

The text says «The potential outside the charged sphere is the same as the potential of a point charge at the center.» That’s quite wrong. That’s the worst sort of equation-hunting, i.e. applying an equation in a situation where it is not valid. It leads to getting an answer that is wrong by a factor of infinity.

There is a theorem about a spherically-symmetrical static distribution of charge, but that’s not what we have here, because of the image charge induced by the proton. At zero distance, the induced-dipole interaction is infinitely stronger than the first-order Coulomb interaction. The text ignores this infinitely-large contribution.

16.
On page 847 and again on page 893: Kirchhoff’s law is not equivalent to conservation of energy. Energy is always conserved, but Kirchhoff’s law is not always valid.

One familiar counterexample is any electrical transformer, which depends on the voltage not being a potential. Another example is a betatron. This is perhaps less familiar, but it makes the basic physics particularly obvious.

17.
Contrary to what it says near the bottom of page 893, it does not make sense to define ΔVres = VdownstreamVupstream. This does not make sense for batteries, where ΔV is independent of the direction of the current. It does not make sense for resistors, capacitors, inductors, and similar devices, where for many many decades Ohm’s law has been written in terms of the voltage drop.

Similarly in the un-numbered equation in the middle of page 894: it does not make sense to define things in such a way that a minus sign appears in the statement of Ohm’s law. This misbegotten minus sign crops up again and again throughout the chapter.

18.
Also on page 893, defining ΔVR = − ΔVres does not solve the problem mentioned in item 17; it just adds a layer of needless complexity. The complexity turns into ambiguity if not outright contradiction when ΔV is used without a subscript as in the «stop to think 31.2» box at the bottom of page 895. In contrast, Ohm’s law is invoked without a minus sign on page 899.

19.
Near the bottom of page 893 it says «Ohm’s law gives only the magnitude ΔVR = IR of the potential difference across the resistor.»

We are reminded of this at the top of page 898.

This will come as a surprise to every electrical engineer in the world.

20.
On page 895: An escalator is not a good model of a battery. An ordinary escalator moves at a constant rate, independent of load. There is no reasonable way to arrange escalators so that the “stronger” one will force something to run the wrong way on the other one.

21.
Near the bottom of page 892 and again on page 896: In reality, electrical current is not conserved. The alleged «conservation of current» should not be mentioned in the same breath as conservation of charge. The latter is quite fundamental and important.

I suppose it is “legal” for an author to define a notion of «conservation» as applied to current that is not parallel to the notion of conservation as applied to everything else ... but it’s amazingly bad pedagogy.

• For starters, you might think it makes the subject twice as difficult as it needs to be, because now students need to learn two different notions of «conservation» rather than just one.
• Really, though, it’s much worse than that. If students had to learn two separate definitions (conservation of charge and blorkivation of current) that would be twice as much work as necessary ... but if they have to learn two ideas that share the same name it imposes the additional burden of confusion ... utterly needless confusion.

This is on top of the pre-existing painful confusion involving the physics notion of conservation as opposed to endangered-wildlife conservation.

A major goal of the course is for students to develop a solid understanding of conservation. This is immediately applicable to charge, energy, momentum, and angular momentum. It can eventually be extended to other things such as lepton number. It can be approximately extended to yet other things, such as the conservation of the number of carbon atoms during a chemical reaction.

The idea referred to in the previous paragraph cannot be extended to current, not even approximately. Here’s a counterexample: the current in an RC circuit just dies away. It doesn’t flow away into some nearby region; the current just stays in place and decreases. Momentum cannot do the analogous thing, because momentum is conserved.

Here’s another counterexample: Consider a photodetector or perhaps a Geiger-Müller tube. It contains some substance subject to an electric field. Initially there is no current. Then a photon comes in and ionizes the substance. Now there is a current, because the negative ion goes one way while the positive ion goes the other way. This current did not come in from outside; it just appeared in place, violating any reasonable notion of conservation of current.

It is a serious disservice to students to speak of «conservation of current» in the same breath as conservation of charge. It seriously undercuts one of the major goals of the course.

The idea that the current is the same everywhere along a given wire already has a perfectly good name, Kirchhoff’s Current Law. This is a corollary of conservation of charge, in the DC limit. The existence of a good name makes it all the more insane to use an abusive name such as «conservation of current».

22.
On page 896: It says «It’s not current that the bulbs use up, it’s energy

In other words, we are told that current is conserved and energy is not. That’s two misconceptions in a single sentence.

In my universe, conservation of energy is of the utmost importance. It is hard to imagine anything more fundamental, more emblematic of the the unity and grandeur of physics.

We already have a problem because students are confused by the ambiguity and contradiction between the physics energy and the “DoE energy”. The latter is some kind of loosely-defined “useful energy” or “available energy”. If the physics teacher starts throwing around the word “energy” in such a way that it does not refer to the physics energy, things get real ugly real fast.

Even if we pretend the statement on page 896 refers to conservation of charge, it amazes me that anyone could make such a statement without noticing that energy is conserved, just as strictly as charge. So it seems off-the-wall to use conservation ideas to assert that energy is used up whereas charge (or current!?!) is not.

The thousand-pound moose on the table is entropy. The only thing in this scenario that is irreversibly used up is the non-entropy. This is not mentioned – not even hinted at – in Knight or in Chabay & Sherwood.

When the DoE-energy gets used up, it is not for reasons having anything to do with the physics energy. The physics energy is still there. It may perhaps become less-available and less-useful, but that’s because of entropy, to the extent that it can be quantified at all.

The true physics is very easily explained by saying that the electrical resistor is creating a lot of entropy. This is incomparably better than replacing one wrong idea (current used up) with another wrong idea (physics energy used up).

23.
At the bottom of page 897 it says «Most household appliances, such as 100 W lightbulb or a 1500 W hair dryer, have a power rating. [...] and their rating is the power they will dissipate if operated with a potential difference of 120 V.» That may be approximately true for light bulbs and hair dryers, but it is not true for «most» household appliances. It is not true for mixers, can-openers, refrigerators, clothes washers, dish washers, vacuums, heating/ventilating/air-conditioning, or anything else that has a motor in it. It is also not true for audio or video equipment, phones, or computers.

24.
On page 898, some amplifiers are specified according to «maximum» i.e. instantaneous peak power, while others are rated according to average power (RMS voltage) averaged over the whole cycle. Some are rated even more modestly than that. As a result, the maximum current can be dramatically greater than what is calculated in EXAMPLE 31.4.

25.
On page 899: A junction is properly the joining of two or more things (not three or more things). It is quite silly to speak of two resistors with no junction between them.

This is important, because there is value in applying Kirchhoff’s Junction Rule – aka Kirchhoff’s Current Law – to the junction between the two resistors.

26.
On page 899, anybody who thinks Req = 2R for the two-bulb circuit in FIGURE 31.13 has obviously never done the experiment. See also item 30.

27.
On page 899, it emphasizes that «A battery is ... not a source of current.»

A more correct statement appears on page 900.

28.
On page 900, there is an emphatic bold-face statement about battery behavior: «fixed and unvarying emf (potential difference)».

The part about fixed and unvarying potential differences is contradicted on the next page. The part about fixed and unvarying EMF is repeated on the next page, but is not true in real life.

Statements that are restricted to ideal batteries should say so.

29.
On page 901, it asserts that the terminal voltage is always less than the battery EMF. This make wildly unwarranted assumptions about the sign of the current and/or the sign of the EMF. Even if you stuck in a bunch of absolute value bars it wouldn’t be true.

Hint: Rechargeable battery.

30.
On page 917, exercise 36 calls for wiring two incandescent bulbs in series. It asks «How much power is dissipated by each bulb?»

There is no chance that students will be able to answer this question correctly. Incandescents are infamously non-Ohmic. See also item 26.

31.
On page 1064, Galileo’s principle of relativity is discussed for the first time. I suppose it is better late than never, but this seems remarkable to wait so long to discuss a principle that has been at the heart of physics since Day One of modern science (1638).

What’s worse, on page 1009, it says the calculations «aren’t quite right» because they «are based on Galilean relativity». Let’s be clear: There is nothing wrong with Galileo’s principle of relativity, as he stated it in 1638. Indeed the calculations on pages 1008-1009 are not quite right ... but that’s for reasons having nothing to do with Galileo.

32.
On page 1075, the book introduces the modern (post-1908) idea of proper time, but greatly undervalues it. It is used only as a stepping stone to calculate pre-1908 quantities such as the dilated time.

33.
On page 1088, equation 36.32 is a formula for the four-dimensional velocity.

p =
 Δx Δτ
(1)

We remark in passing that it would make a lot more sense to use an actual derivative, rather than a ratio of finite deltas.

However, the main point is that the book doesn’t do anything useful with this formula. Instead, it immediately converts it to an expression involving the 3-velocity and a factor of gamma, namely equation 36.33. The rest of the discussion emphasizes the latter.

34.
On page 1228 the periodic table shows La under Y, with an asterisk linking to the rest of the lanthanoids. It would be better to show a no single element under Y, just a blank space with an asterisk, and then to show the entire lanthanoid series in the inset. The entire series consists of 15 elements, from La to Lu inclusive. This is standard good practice, for excellent reasons. All theory and all data agree that La and Lu have an equally-good claim to sit directly under Y. It is important for students to see all 15 lanthanoids together. Ditto for the actinoids.

Furthermore, explicitly labeling the transition metals as «d» and the lanthanoids as «f» is a step in the wrong direction. A lot of people who ought to know better think there should be 14 “f block” elements, but there is no data to support this. The set of integers from 0 through 14 inclusive has 15 members. People who cannot reliably count to 15 should not be telling other people how to do quantum mechanics. For details on this, see reference 4.

## 2  References

1.
John Denker,
“One Kind of Charge”
www.av8n.com/physics/one-kind-of-charge.htm

2.
Steven Weinberg,
The Discovery of Subatomic Particles Revised Edition

3.
John Denker,
“Equipotential Shells : 1/r Potential” js/equipotential-shells.html

4.
John Denker,
“Periodic Table of the Elements – Cylinder with Bulges”
www.av8n.com/physics/periodic-table.htm
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