Thu., Oct. 6 notes

First we need to review a couple of rules concerning static electricity and learn something about electric field arrows.

The static electricity rules are found at the top of p. 59 in the photocopied ClassNotes

Two electrical charges with the same polarity push each other apart. Opposite charges are attracted to each other.

Electric field arrows (or just the E field) show you the direction and give you an idea of the strength of the electrical force that would be exerted on a positive charge located at that point.

In this figure (p. 59 in the ClassNotes) a positive charge has been placed at 3 locations around a center charge. The electric field arrow shows the direction of the force that would be exerted on each of the charges. The force arrow is shown in blue.

The E field arrows tell you what will happen to a + charge. You can use the arrows to determine what will happen to a - charge also.

For a negative charge the force will point in a direction opposite the E field arrow.

I tried a short "static electricity" demonstration that consisted of blowing bubbles toward a Van de Graaff generator. The metal ball at the top of the generator gets charged up with electricity (I'm not sure what polarity it is but let's assume it is positive). Some of that charge leaks off into the air. I thought that this charge would stick to the bubbles floating by. Then since the bubbles would have the same charge as the generator, the bubbles would be pushed away from the generator. What happened instead was that the bubbles seemed to be attracted to the dome of the generator. After doing a little research (after trying the demonstration in the MWF section last Friday) I found that the people blowing the bubbles and the dome of the Van de Graaff were oppositely charged.

Trying the demonstration with the bubble blowing tool connected to the Van de Graaff generator seemed to work better. But it still wasn't very impressive. Still after seeing my attempt at the demonstration you'd be able to appreciate better this video showing how the demonstration is supposed to work.

Here's a figure to test your understanding of electric field arrows. This figure wasn't shown in class.

The direction and strength of the E field near the ground during fair weather and under a thunderstorm are shown. Show the directions of the forces that would be exerted on the charges shown in the figure. Click here when you think you have the answer.

We're learning about E fields so that we can understand how electromagnetic radiation can transport energy from one place to another. You'll find most of the following on p. 60 in the photocopied ClassNotes. What follows is a little more detailed explanation than was shown in class.

We imagine turning on a source of EM radiation and then a very short time later we take a snapshot. In that time the EM radiation has traveled to the right (at the speed of light). The EM radiation is a wavy pattern of electric and magnetic field arrows. We'll ignore the magnetic field lines. The E field lines sometimes point up, sometimes down. The pattern of electric field arrows repeats itself.

Note the + charge near the right side of the picture. At the time this picture was taken the EM radiation exerts a fairly strong upward force on the + charge (we use the E field arrow at the location of the + charge to determine the direction and strength of the force exerted on the + charge).

Textbooks often represent EM radiation with a wavy line like shown above. They don't usually explain what the wavy line represents.

The wavy line just connects the tips of a bunch of electric field arrows.

This picture was taken a short time after the first snapshot aftere the radiation had traveled a little further to the right. The EM radiation now exerts a somewhat weaker downward force on the + charge.

The + charge is now being pushed upward again. A movie of the + charge, rather than just a series of snapshots, would show the charge bobbing up and down much like a swimmer in the ocean would do as waves passed by.

The wavy pattern used to depict EM radiation can be described spatially in terms of its wavelength, the distance between identical points on the pattern. By spatially we mean you look at different parts of the radiation at one particular instant frozen in time.

Or you can describe the radiation temporally using the frequency of oscillation (number of up and down cycles completed by an oscillating charge per second). By temporally we mean you look at one particular fixed point and look at how things change with time.

EM radiation can be created when you cause a charge to move up and down. If you move a charge up and down slowly (upper left in the figure above) you would produce long wavelength radiation that would propagate out to the right at the speed of light. If you move the charge up and down more rapidly you produce short wavelength radiation that propagates at the same speed.

Once the EM radiation encounters the charges at the right side of the figure above the EM radiation causes those charges to oscillate up and down. In the case of the long wavelength radiation the charge at right oscillates slowly. This is low frequency and low energy motion. The short wavelength causes the charge at right to oscillate more rapidly - high frequency and high energy.

These three characteristics: long wavelength / low frequency / low energy go together. So do short wavelength / high frequency / high energy. Note that the two different types of radiation both propagate at the same speed.

The following figure illustrates how energy can be transported from one place to another (even through empty space) in the form of electromagnetic (EM) radiation.

You add energy when you cause an electrical charge to move up and down and create the EM radiation (top left).

In the middle figure, the EM radiation that is produced then travels out to the right (it could be through empty space or through something like the atmosphere).

Once the EM radiation encounters an electrical charge at another location (bottom right), the energy reappears as the radiation causes the charge to move. Energy has been transported from left to right.

This is really just a partial list of some of the different types of EM radiation. In the top list, shortwave length and high energy forms of EM radiation are on the left (gamma rays and X-rays for example). Microwaves and radiowaves are longer wavelength, lower energy forms of EM radiation.

We will mostly be concerned with just ultraviolet light (UV), visible light (VIS), and infrared light (IR). Note the micrometer (millionths of a meter) units used for wavelength for these kinds of light. The visible portion of the spectrum falls between 0.4 and 0.7 micrometers. UV and IR light are both invisible. All of the vivid colors shown above are just EM radiation with slightly different wavelengths. When you see all of these colors mixed together, you see white light.

Here are some rules governing the emission of electromagnetic radiation:

Unless an object is very cold (0 K) it will emit EM radiation. Everything in the classroom: the people, the furniture, the walls and the floor, even the air, are emitting EM radiation. Often this radiation will be invisible so that we can't see it and weak enough that we can't feel it (or perhaps because it is always there we've grown accustomed to it and ignore it). Both the amount and kind (wavelength) of the emitted radiation depend on the object's temperature.

The second rule allows you to determine the amount of EM radiation (radiant energy) an object will emit. Don't worry about the units, you can think of this as amount, or rate, or intensity. Don't worry about σ either, it is just a constant. The amount depends on temperature to the fourth power. If the temperature of an object doubles the amount of energy emitted will increase by a factor of 2 to the 4th power (that's 2 x 2 x 2 x 2 = 16). A hot object just doesn't emit a little more energy than a cold object it emits a lot more energy than a cold object. This is illustrated in the following figure:

The cool object is emitting 2 arrows worth of energy. The warmer object is 2 times warmer and is emitting 32 arrows (16 times more energy).

The third rule tells you something about the kind of radiation emitted by an object. We will see that objects usually emit radiation at many different wavelengths but not in equal amounts. Objects emit more of one particular wavelength than any of the others. This is called λ_max ("lambda max", lambda is the greek character used to represent wavelength) and is the wavelength of maximum emission. The third rule allows you to calculate λ_max. The tendency for warm objects to emit radiation at shorter wavelengths is shown below.

The cool object is probably emitting infrared light so the 2 arrows of energy are colored red. The warmer object will also emit IR light but also shorter wavelengths such as yellow, green, blue, and violet (maybe even some UV if it's warm enough).

If the cool object were warm enough to be emitting a little visible light it would probably appear red or orange. In that case the warmer object would emit some of the shorter wavelengths of visible light and would probably appear white.

The graphs at the bottom of p. 65 in the photocopied ClassNotes also help to illustrate the Stefan-Boltzmann law and Wien's laws. We're really beating this topic to death.

Notice first that both and warm and the cold objects emit radiation over a range of wavelengths (the curves above are like quiz scores, not everyone gets the same score, there is a distribution of grades)

Lambda max has shifted toward shorter wavelengths for the warmer object. This is Wien's law in action. The warmer object is emitting lots of types of short wavelength radiation that the colder object doesn't emit.

The area under the warm object curve is much bigger than the area under the cold object curve. The area under the curve is a measure of the total radiant energy emitted by the object. This illustrates the fact that the warmer object emits a lot more radiant energy than the colder object.

An ordinary 200 W tungsten bulb connected to a dimmer switch can be used to demonstrate these rules (see p. 66 in the photocopied ClassNotes). We'll be seeing the EM radiation emitted by the bulb filament.

The graph at the bottom of p. 66 has been split up into 3 parts and redrawn for improved clarity.

We start with the bulb turned off (Setting 0). The filament will be at room temperature which we will assume is around 300 K (remember that is a reasonable and easy to remember value for the average temperature of the earth's surface). The bulb will be emitting radiation, it's shown on the top graph above. The radiation is very weak so we can't feel it. The wavelength of peak emission is 10 micrometers which is long wavelength, far IR, radiation so we can't see it.

Next we use the dimmer switch to just barely turn the bulb on (the temperature of the filament is now about 900 K). The bulb wasn't very bright at all and had an orange color. This is curve 1, the middle figure. Note the far left end of the emission curve has moved left of the 0.7 micrometer mark - into the visible portion of the spectrum. That is what you are able to see, just the small fraction of the radiation emitted by the bulb that is visible light (but just long wavelength red and orange light). Most of the radiation emitted by the bulb is to the right of the 0.7 micrometer mark and is invisible IR radiation (it is strong enough now that you could feel it if you put your hand next to the bulb).

Finally we turn on the bulb completely (it was a 200 Watt bulb so it got pretty bright). The filament temperature is now about 3000K. The bulb is emitting a lot more visible light, all the colors, though not all in equal amounts. The mixture of the colors produces a "warm white" light. It is warm because it is a mixture that contains a lot more red, orange, and yellow than blue, green, and violet light. It is interesting that most of the radiation emitted by the bulb is still in the IR portion of the spectrum (lambda max is 1 micrometer). This is invisible light. A tungsten bulb like this is not especially efficient, at least not as a source of visible light.

You were able to use one of the diffraction gratings handed out in class to separate the white light produced by the bulb into its separate colors.

When you looked at the bright white bulb filament through one of the diffraction gratings the colors were smeared out to the right and left as shown below.

Some of the gratings handed out in class behaved a little differently and spread out the colors horizontally, vertically, and diagonally.

We had time for one more page of notes.