The best way to think of this idea is the concept of aperture: the pupil of your eye, a few millimeters, vs., e.g. the aperture of the Hubble Space Telescope (HST), about 2.4 meters. HST is about 300 times wider, about 90,000 times more area than the human eye's pupil.

The HST is about the size of a school bus.

(Hubble being transferred from the Vertical Assembly Test Area (VATA) to the High Bay at the Lockheed assembly plant in preparation for transport to the Kennedy Space Center (KSC) after final testing and verification.)

We will conclude Ch. 26.4 with this example, then bypass the remainder of Ch. 26.4

Notice that, in this diagram, the rays are almost parallel coming out of the eyepiece to the eyeball. If the rays are parallel, your eye does not have to strain to focus the image on your retina

Or just one in a simple microscope

Always a big proviso.

An understatement. When we view a star in the night sky, our retina collects very small numbers of Roy G. Biv photons per second.

One refractive interaction, an approximation to the two physical interactions.

Most of this section is bypassed. However, we discussed LC circuits extensively in terms of oscillation, e.g., in Fig. 5.

We discussed "phase" a little bit differently than this.

Bypass or skim the diagrams. We talked about oscillating circuits from the standpoint of energy, but we did not get into any detail of this section, 23.11.

Study this secrion, 23.10. We discussed inductance and RL circuits in Session 27 and other places.

Bypass. It won't be on Exam 3, although Florida residents would do well to read about the GFI technology, which many major appliances and pool pumps have.

Bypass

Bypass

We mentioned generators and motors in general terms, but all of the materials in this section we bypassed.

Bypass

We discussed this briefly in Session 26 in the context of the navy's "rail gun."

Other material in this chapter is bypassed.

Brain burner deluxe....

Brain burner!! Attempt this diagram at your own risk!! :D

Nice mental exercise.

Basic calculations.

I like this question. You can work it out with typical values of indices of refraction, \(n_{air}=1.00,\, n_{water}=1.33,\, n_{glass}=1.5\)

You will have a small table like this on the cover page of Exam 3

Similar to the headless body situation.

VIP, very important principle.

You can also use the marching band effect with a diagram like this.

Here, the left wheels move more slowly on the thick grass, while the right wheels move more rapidly when they hit the sidewalk. Net result: lawn mower turns left, line of travel cuts away from the normal (dotted line).

Left wheels move more rapidly on the sidewalk, and right wheels move more slowly on the thick grass. Net result: lawn mower turns right, line of travel close to the normal (dotted line).

Example: for many types of glass, \(n=1.5\) or so.

!

100% reflected

Very nice simulation of refraction. "More tools" can even produce total internal reflection. It is an HTML file. Download it then click it open -- runs good.

"Not steep enough to permit transmission and refraction."

Good rule of thumb.

Like molecules and crystals, with grid spacings on the order or nanometers.

E.g., using silicon, opaque to Roy G. Biv, but fairly transparent to 1200 - 7000 nm infrared.

By far, our dominant sense, for which our brains are amazingly well developed to analyze and understand.

One of the mirrors on the James Webb Space Telescope, to be launched in 2021, we hope.

Image is as far behind the mirror as the object is in front of the mirror.

I also like this problem: will the electrons in the antenna circuit of the typical radio oscillate enough to an electric field of this intensity? Enough to provide an audible, uninterrupted signal without having to compete with too much random noise in the background? Because I have noticed, while driving around Orlando, that some of our Orlando AM radio stations really fade out in various locations, especially at night.

I like this calculation because lasers are frequently used to move electrons and ions around, with the E field. So knowing, for example, the size of the molecule or metallic lattice, you can tune the laser intensity to get the molecule or ion or electron to dance exactly the way you want it to dance.

Deceptive statement, in my opinion, because saying one field is weak is completely relative to the two scales we have for \(E\) and \(B\). For the electric field the author uses \(\frac{V}{m}\) but for the magnetic field, Teslas. Perhaps a different scale should be used for magnetic field?

It would be interesting to work out a system of constants and so forth so that E and B have the same unit and in radiation are the same size.

Fairly simple plug-in, for the definition, \(I=\frac{P}{A}\)

I like this part of the calculation.

This reminds me of something that astronomers calculate: the "solar constant,", which, it turns out is not quite constant because the Sun's output varies on a daily time scale and slowly over its 11-year sunspot cycle. Currently, the observed value is about \(1360.66\frac{W}{m^2}\).

Oscillation, like the square \(x^2\) in a spring system and the "kinetic term" with a \(v^2\) in it

The electromagnetic wave equation: $$c=\lambda f$$ ...simple yet powerful.

One of the best Interactive Simulations. I completely recommend it. Download the java file, then open it. Try the "radiated field" option -- it is spectacular.

Another way to look at this quotient, \(\frac{E}{B}=c\) involves Newtons of force.

enhance

They carry energy \(E\) and momentum \(p\).

Stated as an aside, but this is a critical concept. The source of electromagnetic radiation is accelerating charge, like the northern lights

In fact, the intensities of radiation in each direction is controlled primarily by the shape and dimensions of the antenna.

Profound. Why should lightning and lodestones have this affinity, i.e., that the \(\vec{E} \perp\vec{B}\)? Lightning Magnetite

One-time exercise, to get over the strangeness of \(\epsilon_0\) and \(\mu_0\).

Discussed in Session 28.

Now we can see where the mysterious constants, \(\epsilon_0\) and \(\mu_0\) come in and combine for the speed of light, $$c^2=\frac{1}{\mu_0 \epsilon_0}$$

WAY beyond

Oscillation analogy, similar to the diagram in Session 27. https://youtu.be/T_2R9JBu89E

Nice!

I.e., tons of trig and calculus

Blackout!

Can lead to huge arcing of current

ANother significant dependence

Significant: \(\mathcal{emf}\, \propto \, \frac{\Delta I}{\Delta t}\) is going to lead to oscillation

A dodge. The average field value requires a ton of calculus and trig!

The coil gains RIGHTWARD field lines, do the coil's induced current produces leftward field lines, \(\vec{B}_{coil}\)

Images (b) and (c) show induced fields \(\vec{B}_{coil}\) consistent with Lenz' Law.

Another big understatement!

If we were to make a full general definition, accounting for shapes of circuit and of the field, then there'd be

• a ton of trig, and
• a ton of calculus

The flux must now be dealt with!

Like Grand Coulee Dam on the Columbia River.

Mentioned in Lecture 22. https://youtu.be/ZJOsVs0kzgw

Mentioned in Lecture 22. https://youtu.be/ZJOsVs0kzgw

Nifty YouTube of sound waves Doppler shifting, about 0:40. https://youtu.be/w0AadZ1bs78

"Complicating factor," yes, but this Doppler shifting is something we understand, and it gives us basic leverage to extract more information:

1. "blue shift" meaning a λ wavelength shift to shorter than normal λ, and you can extract the speed at which the object approaches the observer;
2. "red shift" in which the observed λ wavelength is shifted to a longer λ, plus you can extract the speed at which the object is moving away from the observer.

Here is an interesting diagram of Doppler shift information uncovering currents underneath sunspots!:

Because the speed of light c is a constant, and because the electromagnetic wave equation is c = λf,

• when the wavelength increases (redshift), the frequency decreases, but
• when the wavelength decreases (blueshift), the frequency has to get bigger.

The arrow of Observer C's wavelength is slightly off, too short. It should go from the top edge of the dark red circle to the top edge of the next circle in (reddish pink).

As I always say, "What does the observer see?"

Will mention in Session 20 or 21.

Needs a third sub diagram that shows the reversed current.

Would be a restoring force, leading to oscillation, if current continues in the initial direction.

...using tons of trig and calculus!

Important diagram

We will try this demonstration in Friday's session 23.

Cf., The Hunt for Red October.

https://www.imdb.com/title/tt0099810/

Will review this in Session 23.

We viewed this force effect in Session 21, with the big horseshoe magnet and the thick copper strip between the poles of the magnet.

We will work out an example from this set up in our Session 21.

Bypass

For Exam 2, we will bypass the aurora and other examples past this point.

Like in CSI

Cosmic rays are protons and other particles blown out by supernova detonations and big galactic black holes.

I severely hate this version of the right hand rule. However, other semingly normal people might like it, so I will include it in the textbook without mass crossouts.

"relatively simple" ← nice, but do not forget the appearance/disappearance of the magnetic field depending on the motion of the observer.

This is a good set of questions to ask of the magnetic field of Earth. Theoretical image of field lines:

Actual field lines:

Very important diagram.

As reviewed in Session 20.

Always true, unlike electric field lines. There are electric monopoles, e.g., proton and electron, with porcupine and anti-porcupine field lines. There are looped \(\vec{E}\) field lines starting with a dipole array.

Ditto with \(\vec{E}\) field lines

Flux again.

Good -- similar to our idea about electric field lines.

NOT

crude indeed. As far as we can tell, electrons have no structure, so saying that it spins on an axis like a planet is very crude. We make do, saying that the electron has intrinsic spin angular momentum, \(\plusmn \frac{\hbar}{2}\)

Moving charge is the source of the magnetic field.

Any large structure built of steel, like a building of steel girders or a warship, can be magnetized by pounding the steel: pile drivers, riveters, etc. Liberty ship, keel plates

This topic should follow "Electromagnets" because we understood electromagnets a century earlier than we savvied ferromagnetism (iron atoms as tiny electromagnets).

Check for paired white-and-black spots on the Sun's magnetogram. The Sun is pretty quiet now, however.

So the magnetic pole up in arctic Canada is actually an S!!

Might be no such thing as a magnetic monopole. Magnets seem only to come as dipoles.

We can thank Michael Faraday for these developments.

WHat an understatement! Transistors on various electronics chips are on the order of a few dozen nanometers!

Check the Session 18 extension in YouTube.

The circuit's "time constant" \(\tau = RC\) is related to the half-life of the circuit. Both terms are used by scientists in exponentially growing or decaying systems.

Will be helpful when working on HW 2.

We will work out a few like this on Friday, 10/4.

idealization

So after an amount of time \(\Delta t\), all of the energy of a battery will dissipate at the circuit element, e.g., the light bulb, where stored Joules from the battery are dissipated as light and heat. At that point, the bulb goes cold.

Conservation of current.

better

NO! NO! NO! Voltage is measured in \(\frac{Joule}{Coulomb}\) but power is different, \(\frac{Joule}{second}\)!!

Nice definition

We will have discussions about these diagrams on Friday, 10/4.

This term traces way back to the 1800s, before we had figured out everything and unified the electromagnetic theory. So calling it a force is anachronistic, but we still use it for the sake of custom. The common symbol is an upper case script E, \(\mathcal{E}\)

This is what scientists and engineers call \(I^2R\) heating, a.k.a., Joule heating. Cf., Ch. 21.3

Mentioned in Lecture 14, Fall 2019

This was as far as the reading went to prepare for Exam 1. The sections after this will be on Exam 2!

We will work out this exercise in Session 13, if possible

a pipe filled with gravel

more current that gets through to the device, less resistance.

Dissipation of energy into the metallic lattice of the conductors, not to the hair dryer or other device hooked up to the circuit.

For instance, in the solar corona, positive ions, protons and electrons are flying around in "current sheets" blazing through the corona, and we have a hard time figuring out the Ohmic resistance for such complicated currents. YouTube

Will work this out in Session 13

Good problem to try out.

also out of place

This problem is slightly out of place... might be better in a later section of Ch. 20

information....

Big number, \(8.342\times 10^{28}\), but a few feet of 12 gauge wire is not nearly one cubic meter.

A specification of manufacture.

We will work through a calculation like this in Session 13, 9/25/19.

a lot like water, which is pretty much an incompressible fluid

less than 1 millimeter per second!

$$c=3\times 10^8 \frac{m}{s}$$

We can do all of our calculations etc. with conventional current \(I\left(t\right)\), but when actually trying to understand what is physically moving so that you can capture it or track it, you have to think about electrons, if you are in a regular circuit. Electrons require "reverse psychology."

and everyone else until about 1899

E.g., Kenmore 81422 washer/dryer, minimum circuit rating: 20 Amps.

Cf., for example, the BP-ATM-15-RP fuse for Ford F-150,

rated with amperage 15 Amps.

refer to Fig. 1

"...rate at which charge flows" past a given point in a conductor, $$\frac{\Delta q}{\Delta t}$$

although the photo is a water current! 🤦🏻‍♂️

The authors should title this section, "19.7 Energy Stored in Defibrillators" ; )

basic

A basic question

This and the following few sentences are describing a calculus equation using words instead of formulas.

This formula, \(E=\frac{1}{2}\frac{1}{C}Q^2\) is actually related to oscillating currents in a circuit, as we shall see in Ch. 23.

Energy delivered from a defibrillator's cap. E.g., "At 200 J, the ZOLL RBW delivers more average current to high-impedance patients than any other biphasic waveform."

Zoll makes all kinds of defibrillators, rated in Joules.

aka, sinus rhythm,

Hmmmmmm...This would make a lovely iClicker item.

Uh oh

A brain burner.... work this out before Monday lecture if you can!!!!!!

First two capacitors are parallels: \(10\mu F\) and \(2.5\mu F\), so they simply add up the preliminary combo capacitance: \(C_{12}=12.5\mu F\). Easy.

However, there is one cap in series with those first two, so now you employ the reciprocals formula for the total equivalent capacitance \(C_{eq}\), viz.

$$\frac{1}{C_{eq}}=\frac{1}{C_{12}}+\frac{1}{0.30\mu F}$$

So the common denominator is semi-nasty, \(cd=\left(12.5\right) \left(0.3\right) \longrightarrow 3.75 \)

The rest is fractions. Don't forget to flip your \(\frac{1}{C_{eq}}\) fraction to get \(C_{eq}\) itself.

We will get into this kind of brain burner on Monday, plus in a lab this coming week.

Easier

The top of three capacitors are equivalent to one big plate, and same for the bottoms.

must use common denominators!

For \(n\) capacitors in series, $$\frac{1}{C_{eq}}=\frac{1}{C_1}+\frac{1}{C_2}+\cdots+\frac{1}{C_n}$$

...or in Dr. Brueckner's parlance...

$$\Delta V=\frac{Q}{C_{eq}}=\frac{Q}{C_1}+\frac{Q}{C_2}+\frac{Q}{C_3}$$

• First capacitor, \(\Delta V_1=\frac{Q}{C_1}\)
• Second capacitor, \(\Delta V_2=\frac{Q}{C_2}\)
• Third capacitor, \(\Delta V_3=\frac{Q}{C_3}\)

Note that the assumed charge load at the top of the first capacitor and at the bottom of the third capacitor are assumed to be the same size, \(\pm Q\). This is an application of the conservation of charge: the number of electrons stolen from the top plate is the same as the load of surplus electrons pushed into the bottom plate.

Total voltage drop = \(V\) of the battery! But this time it is split up between three separate capacitors

A single equivalent capacitance, \(C_{eq}\)

First mentioned in Session 8.

Nice

Household size units for capacitors. Go into Radio Shack and check them out.

This property, permittivity, is related to a substance's ability to be polarized. You can look up the specs for permittivity for many substances, e.g., for muscle fiber. However, the vacuum also takes a value, denoted \(\epsilon_0\) and used here for parallel plates, even though the vacuum has no substance.

I detest this description, but it sort of makes some sense.

...from the battery

Fried dielectric time!

Many studies of dielectric properties, biological and otherwise.

Breakdown:

1. Sparks if vacuum or air filled capacitor;
2. fried dielectric if filled with a dielectric material like paper or paraffin.

For a singly ionized sodium atom, the time to cross this membrane is about \(\Delta t = 0.02\: ns\)... pretty quick!

As mentioned in lecture. For those of you studying biology, this is an important application

This is why the authors show the rolled up capacitor in Fig. 1

flux concept

Can be approximated as parallel plates, with an insulating layer in between.

They also store energy in the electric field. This is the first time we have had something other than a Sir Isaac Newton \(F=ma\) style object with mass that can carry energy.

A great paragraph about what a capacitor is and how it works

The ancient Greeks could not measure with this precision, nor could the great Tycho Brahe. Kepler and Galileo, Newton and Halley: nope. But by the 1800s, yup, it started becoming possible, with better telescopes and measuring devices.

This is the end of the material in Ch. 19 needed for Exam 1.

True, but astronomers still use both pc and LY!

Parallax angle P, in the diagram

Actually, a successful parallax measurement would've satisfied Plato, Aristotle et al., in their day, that Earth orbited the Sun. Unfortunately, they did not have good enough technology. But neither did Kepler and Galileo. Bessel bagged 61 Cygni 200+ years after Galileo.

This is essentially what astronomers do when they make pallalax measurements. But for stars, it is a much larger triangle.

I like this question. It is not a calculation, but it would be very nice to ask in class.........hmmmmm

A lot of sketching.... for after Exam 1!!

Very interesting

We talked about this a lot in Session 9.

A nice sketching exercise, equipotential lines of a dipole field. We might go through this in our first session after Exam 1.

Huge amount of difficult calculus behind this paragraph, enough to choke Sir Isaac Newton's horse.

Correct. In a conducting material, the surplus charges will redistribute themselves into dynamic equilibrium, equal distances from each other.

from PHY2053!!