SPEAKER: This is a production of Cornell University.
ROBERT RICHARDSON: Hello, today our subject is the propagation of electromagnetic radiation. It gives us an opportunity to use some of the most interesting 19th century lecture demonstration apparatuses in the Physics Departments collection. I'll be doing things that make lots of sparks. And in fact, one way that you'll know that electromagnetic radiation is being propagated is that sometimes there will be interference lines on the television pick-up of the monitor.
My first experiment is going to be one very similar to that which was done by Hertz to propagate the first radio waves, or what were called Hertzian waves. I have here my transmitter, which is going to consist of a coil of wire, which is an inductor, and a capacitor, called a Leyden jar, and a source of voltage, and a spark gap.
Spark breaks down as soon as the electric field becomes large enough to ionize the gas in between the gap, so that there is a sudden current flow. And following that, there's a transient frequency oscillation in my circuit.
Let me talk about the capacitor for a minute because they are very interesting things that were devised in the 19th century. These are called Leyden jars. Early thoughts about the storage of electrical charge, conceptually the idea that occurred to people was that it should be stored in a way very much like the way they would choose to store tomatoes or peaches, in a jar.
The container has a metal foil in the interior and then another metal foil on the outside. So there is an electric field between the metal foil on the outside and the metal foil on the inside. And the dielectric medium in between is just the glass of the jar.
We make contact with the inner conductor with a spring-loaded device that has an electrode on it. We make contact with the outer conductor by just letting this rest on a metal plate.
In this circuit, then, I have one Leyden jar from a capacitor in my inductor. The characteristic resonant frequency, then, is determined by 1 over the square root of the inductance times capacitance. That's the angular frequency 2 pi times f.
When I turn on my electric potential, the spark gap breaks down.
And I have an alternating current in my coil. And now, I can pick this up in a second coil, which I have here. There are no other wires attached to this coil.
When the current's flowing this way in the loop, there's going to be a magnetic field pointing that way. When the current flows this way in the loop, there's going to be a magnetic field that way. And this alternates at a rather high frequency.
Over in my second loop, this alternating magnetic field-- and there's also an electric field associated with it around it. The alternating magnetic field produces an EMF in the loop. And that's picked up. And it can cause a discharge in a neon bulb that we see down here.
If I rotate the plane of the loop in my second coil-- which is really an antenna. And this you can think of as being something like an unusual radio station. If I rotate this to be 90 degrees away, there is no flux changes in the loop, and the loop doesn't work.
But the total flux change in the loop is not the only thing that determines the strength of the signal that can be propagated in my second coil, picked up by my second coil, it has to have a frequency, a resonant frequency that's close to the resonant frequency of my transmitter.
For instance, if I change the dimensions of my pickup coil by just making the loop bigger, if the only thing that were involved is the change in the magnetic flux in the second loop, you might expect it to have an even brighter glow in my neon bulb, but that's not the case. When I increase the area of this loop, I increase the inductance. And it's no longer near the resonant frequency of my source. You'll see that when I lower this again, I can get the neon bulb to glow.
Well, this is basically the type of apparatus that Hertz discovered that he could use for the propagation of waves in the frequency range around 1 megahertz a million cycles per second.
Let me turn this off. And we will go on to an apparatus that looks like one used by Dr. Frankenstein for his experiments. And that's the set of experiments that I'm going to do with another tuned circuit. But this time, I'm attached to a very strong voltage source.
I have over here a transformer with enough turns in it so that the voltage that's on the output of this transformer is 60,000 volts when I hook it up to the 110 volt mains. And now I'm going to connect that to another LC circuit that also has a spark gap. And you'll see a very bright spark when this is running. And the frequency of this one is around a megahertz.
All right, for my first experiment that I will be doing in this circuit, I have here three of these capacitors. I have an inductor in the circuit and a spark gap. You will see the bright spark when it's activated. And I'll have a coil that I'll attach in the circuit. So I'll have a very strong alternating magnetic field in this loop when I activate the circuit. And we'll do several experiments in it.
Why don't you go ahead and turn it on then, please.
This first experiment is one similar to one we've seen before. I have a loop with a light bulb in it. And I place this in front of my circuit. And you'll notice that the light bulb glows. This is very similar to an experiment that we demonstrated earlier for Faraday's law. The alternating magnetic field in here is picked up in my second coil, and I get an alternating electric field in the loop, which causes the light bulb to glow.
The second demonstration with this is a little more unusual. Here I have a glass bulb that has a low pressure of air in the bulb. Watch what happens when I place this within the coil. You notice a ring.
Now, what happened there? The gas in the tube was ionized. And you saw a circular ring of ions. The reason that we had the breakdown in that pattern is because we had alternating magnetic field this way. That, according to Faraday's law induces an EMF and a circle around the outside, where it's going to be the strongest there. And the electric field in that region was sufficiently large to cause a breakdown in the gas, in that region in the glass bulb.
I can cause a breakdown in gas in the air with another apparatus that I'm going to next demonstrate. And that's called a Tesla coil.
And I'm going to construct another form of transformer, and this time to an even larger voltage. I'm going to attach a coil similar to the one that we used before to the same terminals, but place within it a second coil that has a much larger number of turns, so that the potential that's generated in the second coil is close to a megahertz. And then we will do several experiments with it. I'm going to change the tuning of my circuit for coupling into this coil.
And now, at the top of the coil, there is a small wire. And that's a region in space in which I'll have the largest electric field. And when the experiment begins, you will see a lot of blue sparks coming off. And that's the actual breakdown of the gas in the air, which is called corona. I will do several experiments with the corona discharge from the Tesla coil.
The first one will be that I will hold this glass bulb, which is just a bulb with a wire attached to it, up in the air. And I will, in fact, then cause the bulb to be lit. And in this experiment, my body will be the return path that completes the circuit for the electricity in the coil.
I will feel a tingle, and you might see me flinch, but it's not particularly dangerous because at this frequency-- it is a megahertz-- the electricity does not penetrate into my body very deeply. It just flows on the surface. And it will flow back down to ground potential on my body.
Then I will also hold up several other glass bulbs. And you will see a fluorescent light glow. And you will also see the breakdown of hydrogen gas in another tube. For this segment, I'm going to take off the microphone because of the interference from the spark noise.
Our next demonstrations come from a vintage in time, 50 years more modern than the million volt Tesla coil we demonstrated. And we will be studying now the properties of a dipole antenna.
Let's consider an electric dipole. That is, we have a positive charge and a negative charge. And let's hook them up in a wire. There's an electric field line that will go-- a set of lines that will go from the positive charge to the negative charge.
Now, if I arrange to change the potential on each end of my wire so that this end becomes minus and that end becomes positive, the electric field lines that come out will reverse in direction. So they go in the opposite direction. And that's the basic way that we can transmit with a dipole antenna electromagnetic radiation.
During part of the cycle, we have the top end positive and the bottom end negative, electric field lines coming out like that. And when we reverse it, if we look out here at a certain distance, we'll see electric field lines that are up for part of the cycle and down for part of the cycle.
Let's consider, then, what happens to the magnetic field at the same time. Because when we reverse the direction of the polarization, the electric potential in my rod, I have to change the current that's flowing in the rod. And I will have a maximum current flowing in the middle of my cycle change. And there will be a magnetic field going radially around the rod.
Consider this rod. If I have an alternating electric field in the rod, there's going to be current going down the rod. And there's going to be a magnetic field going radially around the rod. The current's going up. The magnetic field is making a circular loop like this.
So each time I have current flow in my rod, I have a magnetic field associated with that. And it's going to be in circular loops around the rod. And as I go out here further and further in space, I'm going to have a magnetic field perpendicular to my electric field. So during part of the time I'll have a magnetic field that's coming out, and the other part of the time a magnetic field that's going in.
Let's demonstrate some of this with an apparatus here. Here I have a tube transmitter for my source and an antenna that's coupled to the source oscillator. So I have an alternating [BUZZING SOUND] electric potential placed across this antenna.
And now, I will use for a receiver just this rod and a light bulb. And you'll notice that the light bulb glows, and quite a distance away from the source there.
It glows most brightly when I go closer and closer to it, when I get closest to the source, of course, because the strength of the electric field that's radiated decreases as I move further away from the source.
I also get, at a given distance away from the source, a maximum amount of signal that I can receive if I have this rod parallel to that rod. And that's because the electric field lines that are coming out of that source are parallel to the rod. If I make this perpendicular to the direction of the electric field lines, the light bulb doesn't glow, even if I go quite close to the source. On the other hand, if I turn it back so that it's parallel to it, I can make the bulb glow bright enough to actually burn out the bulb.
There's another aspect to this, is the length of the antenna is important. If I make the antenna very much longer, I have to go quite a bit closer to the source to get the same amount of brightness. This, once again, is a resonance phenomena like the one that we had in Hertz's experiment.
Let's look, in fact, at the strength of the electric field along such an antenna rod by having an antenna that has lots of light bulbs on it. And now you'll notice that as I go close to the transmitter so that they're glowing bright enough, the ones near the center are glowing quite brightly, and the ones on the ends are barely glowing at all. That's because the strength of the electric field or the amount of current in the circuit is largest in the center and falls off on each end.
This, in fact, is then a half wavelength of the light going from here to there for my electromagnetic radiation. I have my maximum amplitude of electric field in the middle. And I have a node on each end.
You can see qualitatively why that is the case, because in my antenna source-- and now I could demonstrate in my antenna, the fact that it's hooked up to some alternating source by having this hooked up to an amplifier box, it has alternating signal. In my alternating source, during part of the cycle, this is positive and that's negative. And then I reverse that. The characteristic distance between, then, the maximum and the positive direction and the maximum in the negative direction is roughly the dimensions of my antenna.
The speed of light is 3 times 10 to the 8th meters per second. And now we say that this distance is approximately, then, a half wavelength, is the dimension between the most positive and the most negative. And it sort of means the wavelength here is roughly 2 meters. So you can, in fact, calculate the frequency associated with this electromagnetic wave that's being propagated.
There's several other possible modes that an antenna could have. We could have an antenna in which we have several nodes in the middle so that there are several places in which I have maxima and minima if I want to drive it at a higher and higher frequency. And my next demonstration, in fact, is one in which we do that.
I have, in this case, a rod of glass that has a wire wrapped around it. And so it's quite a long length of wire wrapped around the rod. And I place this in my antenna source. And we will test the strength of the electric field along the rod by moving a neon filled bulb beside the rod. And [CLICK SOUND] [BUZZING SOUND] if the electric field is strong enough, we can cause the neon to break down.
Watch what happens as I move the neon bulb along the rod.
Let me readjust the position of this in the source.
There you have the neon breaking down at that point, which means I have a strong electric field there. And as I move further down the rod, it goes off. I should come to a place again later where it comes on again. So when I move down further, it goes off. It comes back on again. It glows weakly. It goes off. It comes back on again.
So characteristic distance about like this is the distance between nodes for the radiation. In this case, that would be a half wavelength. And this would be a wavelength for the standing wave in my antenna. Of course, that's all coiled up. Characteristic distance is still roughly the same as this for a half wavelength.
Our next demonstration is in a different frequency range yet. This is a shorter wavelength than the ones that I've just done. And this is at the microwave frequency range. I have here a dish antenna source with a dipole in the center that sees a high frequency oscillation on this little metal rod in the center. So the characteristic wavelength is roughly something like this, of order 3 centimeters. Once again, you should make a calculation to estimate the frequency of this radiation.
And because the dipole is pointed this way, we know the electric field polarization is in the up and down direction, and it's propagating outward from that dish source.
We have a receiver here, which is a very simple device. It's a meter with a little diode attached to it. And as the electric field alternates across a diode, it produces a current that can be detected in the meter. So we have a deflection on the meter due to the microwave radiation that's coming to it.
We can do some simple experiments with the radiation. One thing, let's see what happens when I place a piece of metal in the path of the microwave radiation. And what you should observe is that the amplitude of the electric field intensity at this point is very much weaker. And that's because the metal is a very good reflector for light at the microwave frequency, as well as it is for visible light.
I have a piece of Bakelite here, which of course completely is opaque to visible light, that is, no visible light gets through it very easily. Now, watch what happens when I put this in the path of the microwave radiation-- very little. This is invisible, or practically invisible, at the microwave frequency, so that if you and I had our eyes tuned to work at microwave frequency, we could see through all sorts of walls and other things if it behaved in a way that it does for this Bakelite demonstration.
My next demonstration is related specifically to the polarization of the radiation that comes from this source. We know that we have the dipole antenna in the up and down direction, so the electric field is in the up and down direction.
Now, this object is just a disk with a bunch of parallel conductors, wires, in a grid. And the question that I want you to think about is which orientation will disturb the microwave propagation most when I place it so that the wires are parallel to the electric field or perpendicular to the electric field.
Let's try it with this direction. Let me put the grid so that it's perpendicular to the electric field lines in the propagation in this direction. Well, you see that very little happens.
On the other hand, when I rotate this 90 degrees-- we have an experiment similar to this that you will be doing in the course-- you see that the radiation is absorbed.
Well, part of one of the experiments you'll be doing is to understand that phenomena. But the answer is not that the radiation is polarized with the electric field in that direction. The electric field is, in fact, in the up and down direction.
I want to conclude with a vector that relates the magnetic and electric field in a traveling wave. You'll remember in my dipole I had an electric field amplitude that was oscillating in the up and down direction. And I had, then, in the plane perpendicular to that, a magnetic field that was oscillating. That's a general result in a set of equations called Maxwell's equations. When the electric field is at a maximum, I also have a maximum in the magnetic field, which is represented by this blue arrow.
There's a vector relation, in fact, between the direction of the electric field in a wave, the magnetic field in the wave, and the velocity of propagation, which is that way. It's another one of the right-hand rules. The velocity of propagation is in the direction of e cross b. So you turn e into b with a right-hand, and a thumb points in the direction of propagation.
So all this radiation one should imagine as being such that I have these oscillating electric and magnetic fields that are moving along at the speed of light.
We want to talk now about the instruments that are used for measuring voltages and currents. There are two classes of these instruments. There's a modern solid state set of instruments that typically have digital readouts that are for voltage and current reading. And then there's another group of instruments that are based upon measurements of electromagnetic forces in an instrument called a galvanometer. And the discussion today is going to be about instruments based upon the principle of a galvanometer.
And the basic idea here-- and this is the raw elements of such a galvanometer-- is that we have usually a permanent magnet, which is this weird horseshoe magnet that I have here, and a coil. When I pass a current through the coil, it produces a magnetic moment that interacts with the permanent magnet, and I get a force which can cause a deflection of my meter.
And I have current going one way. And you'll notice that the pointer goes in one direction. If I reverse the current by just changing the terminals on the battery, the torque is in the opposite direction, and I have the meter deflection in the opposite direction.
So I have a magnetic moment that's proportional to the current passing through this coil that produces a torque when it's in this permanent magnet. And the size of the torque is proportional to the current through the loop.
So the galvanometer is intrinsically an instrument that gives us a deflection that's proportional to the amount of current that goes through it. The amount of the deflection depends upon the spring constants. And if we look at some of these meters that we have over here-- for instance, this one, you will see that there is a tight spring that looks very much like a watch spring that controls the balance in the torque. And the motion of the meter can be used for damping the meter, and so forth.
All right, this one basic instrument can be used to measure a variety of currents. And also it can be used to measure potential differences. And let's look at how we modify the instrument by addition of extra elements in order to make it a ammeter with a specified current range or a volt meter.
Suppose this instrument had for its basic deflection full scale, that is that the meter deflected full scale, with one milliamp, and that the electrical resistance of my coil is 1 ohm. That means, without doing anything else to it, I'll get a full scale deflection of my meter with 1 milliamp current passing through it.
And the thing that I will understand to mean when I write the symbol a in some sort of a circuit through which I want to pass current is that I have a device that has a resistance of 1 ohm. And there will be full scale deflection with a 1 milliamp here current passing through it.
Suppose I wish to modify that in order to have the current be 1 ampere for full scale. Well, the way this is done is to actually place a very low resistance element in parallel with the meter so that most of the current passes through this shunt-- is the name of this element-- instead of through the meter. We just bleed a little bit of current in parallel through the meter.
So I have 1 ampere going into a network that will contain the meter and my parallel resistance element. This will be my resistor, R, in parallel, the shunt resistance. And now I have 1 ohm for 1 milliamp going through the galvanometer.
And now, in order to calculate how much resistance I have to put in parallel, I observe that I have 1 amp here going into the system, and it wants to split, with a certain fraction of the current going through the shunt resistor and 1 milliamp going through the meter itself.
Well, the current obviously has to split so that 999 milliamperes go through the resistance R. And that has to be a much smaller resistance than the resistance of the meter itself. And the size of that resistance is just proportional to the ratio of the currents. That is, 1 milliamp divided by 999 milliamps-- current going through the upper branch-- must be equal to the resistance R divided by 1 ohm. So that evidently R should be equal to-- if I say this is 10 to the minus 3 amperes, to put that in resistance, it's going to be equal to 1.001 times 10 to the minus 3 ohm.
So I can make this meter into a meter that reads 1 ampere full scale by adding a very small resistance in parallel approximately 10 to the minus 3 ohms.
Now, there is a correction that one sometimes has to worry about with meters. In the case of my ammeter here, it has a finite resistance, and it can change the amount of current that flows in the circuit when I install it.
For instance, back as a milliammeter let's see how it would change the current flowing in a simple circuit. Suppose I have a 1 volt battery, and I install my milliammeter here in series with that and 1,000 ohms. If I have no resistance in my meter, if it's perfect, or if I just put a short circuit around it for the time being, then the current flowing in this circuit, i equal v/r would be equal to 1/1000 would be equal to 1.000 times 10 to the minus 3, or 1 milliampere.
But with a real meter where I have a real resistance of 1 ohm, when I'm making my measurement, the total resistance in the circuit now is going to be 1,000 ohms plus 1 ohm, so that I will have 1001 here, and then the current that will flow through the circuit will be 0.999. And I will have a small correction because this is not a perfect meter.
An ideal ammeter is one with zero electrical resistance. Of course, we can only approach the ideal case.
Suppose I wish to make this instrument into a volt meter. Now, a volt meter is an instrument that is used to measure the potential difference between two elements in a circuit. And we can arrange this so that some of the current in the circuit is bled off to pass through the galvanometer to cause a deflection that's proportional to the voltage.
For instance, using the same meter again, suppose I wanted to measure the potential drop across a resistor. Here's a resistor R. And there's a current i flowing through it. And I want to know what the potential drop between this point and that point might be. And the way I achieve this is by placing a resistor in series with my galvanometer so that I have the desired calibration features.
For instance, suppose I wish this galvanometer to have a full scale deflection when there is 10 volt potential difference between here and there, that is, when the potential is v is equal to 10 volts. Once again, the current i in the circuit there would be 1 milliampere so that the resistance that we have to add in is going to be determined by Ohm's law again. v equal i times R.
So for this example I said that the potential was 10 volts. The current for that particular meter is 1 times 10 to the minus 3 amperes. And the total resistance will be my extra resistance that I add in series R plus the 1 ohm for my meter.
We can solve this. So R plus 1 is equal to 10 to the 4th ohms. And now R, the extra series resistance that I need to add to my galvanometer to make it into a volt meter, will be equal to 9,999 ohms, so that if I do that, add this resistance in series with my meter, it can then be used as a volt meter. Pretend that that's in the box.
And this is typical of the series resistors that were designed to be added to these delicate galvanometers.
This will work perfectly well until I have to measure the potential drop across large resistors. For instance, if I had a resistor here of a million ohms and I tried to use this instrument as we've designed it here for a measurement, the current would primarily go through my meter itself because it would have only a resistance of 10 to the 4th ohms, so that, once again, we'll have a serious correction that I have to apply when I use this instrument in measuring potential drop across large resistors.
The ideal volt meter, then, should have as large an apparent resistance as possible. Another statement is so that the correction comes about because we want to have the minimum amount of current drained from the circuit in making the measurement. The ideal volt meter should have an infinite apparent resistance. The ideal ammeter should have zero resistance.
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Sparks fly--literally--as CU physicist Bob Richardson lectures on the propagation of electromagnetic radiation for PHYS 101/102 (1981).
Richardson is the Floyd R. Newman Professor of Physics, senior science advisor to the President and Provost, and director of the Kavli Institute at Cornell. His collaborative research with David M. Lee and Douglas D. Osheroff led in 1971 to the discovery that helium-3, a rare isotope of helium, can be made a superfluid, that is, flow without resistance at temperatures close to absolute zero. The importance of this discovery, which has transformed research in low-temperature physics, was recognized in 1976 with the awarding of the Sir Francis Simon Memorial Prize in Low-Temperature Physics by Britain's Institute of Physics, and in 1981 with the Oliver E. Buckley Solid State Physics Prize from the American Physical Society. In 1996 Richardson, Lee, and Osheroff shared the Nobel Prize in Physics.
Richardson's 30 years of teaching college physics culminated in his co-authoring of College Physics with Alan Giambattista and Betty Richardson (McGraw-Hill, 2003).