 Hi, I'm Zor. Welcome to Unizor Education. Today we will talk about fields, primarily electromagnetic fields. Now, this lecture is part of the course called Physics 14 presented on Unizor.com. And that's where I suggest you to watch this lecture from, because this lecture is part of the course. The Unizor.com website contains a menu which can lead you in logical sequence to all the lectures which are participating in this course. Plus, every lecture has detailed notes on the website which basically can serve as a textbook. There are exams, problem solving, etc. And it's totally free as no strings attached. So, the field waves, that's the theme of this particular lecture. Well, let's talk about fields first. Well, we used to have to deal with material objects. Something which we can just see and touch and basically feel what these objects are using our senses. Well, fields are different. In some cases you can feel the, let's say, electric field. If you touch some charged electrode, you probably will feel it in your tactile or your hair might actually go up because of electrostatics. But that's rarely. Right now the electromagnetic waves are all around us. But we don't feel them, we don't see them. So what exactly they are? And how can we study something like this? Well, let me go back to mathematics. Maths for teens, by the way, is a prerequisite course for this physics for teens. And it's presented on the same website. So let's go back to mathematics. In mathematics we are studying certain objects like number or n-dimensional vector space. Well, these are abstract objects, they do not exist. There is no number. There are five sheep, but there is no number as a concept. It's something which we have come up with to study certain groups of objects. And then we came up with irrational numbers, for instance. And we are considering them as numbers and we study them, but what are they? In decimal representation they have an infinite number of digits. So it's kind of difficult to deal with in material sense. Still we are dealing with these abstract objects. Now, how? Well, based on properties. So we basically are abstract ourselves from material representation of some kind of entity or abstraction, which we are talking about, and we concentrate on the properties of this object. We don't really care what n-dimensional vector space is, but we do care about properties of this particular object which we have created in our minds. And if two different things have the same properties, and we have a theory which kind of predicts new properties, both will have them. So our abstract thinking helps us to understand the properties of all objects which correspond to our abstract model. But the same thing with fields basically. We don't know much about what is a material kind of background, what is the base, material base of fields. Well, it's part of a space where certain properties can be demonstrated. For instance, if you will place an electron in magnetic field, it will probably turn from its trajectory, depending on where exactly the magnetic field is directed. So basically we are talking about properties of these fields, not about their material substance. And that's very important. We don't really, well, not that we don't care, but we don't really want to talk about what stands behind some kind of an object, which is a subject of our theory. But we do care about the properties of these objects, and that's how our theory can develop. Now, in physics we have experiments, and if our model which we have developed based on certain old experiments doesn't correspond to a new experiment, well, we change the model, we update it, we modify it, we do something with this model, or completely abandon it and come up with a new model. And based on that model, we learn what exactly the properties are, what new properties might actually be, and then the new experiments come to either confirm or reject our conclusions. So that's what I would like you actually to think about fields in this particular direction. So forget about what exactly field is in the material sense. Think about the properties of the field. Again, the properties are something which we can learn, which we can build some formulas about. You remember the Coulons, for instance, formula about two charged particles, or two charged object or point object, whatever, and they have certain either attraction or repulsion based on their charges and their distances. Well, that's a theory. We can start explaining it well. There are electrons and there are excess of electrons, deficiency of electrons, positive, negative, etc. That's our theory. When we developed that thing, we didn't really know much about what are the electrons. Alright, so that's kind of an introduction into concept of a field. So you don't really feel lost when somebody is asking you what exactly field is. Well, it's just part of space where certain properties can be demonstrated. But based on these properties, we built a model. And the model actually allows us to put some formulas around, some predictions, maybe, for new properties, and they might or might not be wrong or right or whatever. Okay. Now, we will talk about, this lecture is only about electromagnetic fields. Yes, there are other fields like gravitational field right now. And they might or might not have certain waves. Well, I know there are certain experiments which kind of indicated that maybe gravitational field also has certain waves and that's how it propagates. Whether it's right or wrong, I don't know. But for electromagnetic fields, we do know that there are waves and we really have a very well-developed theory about these waves. And in particular, it explains why, for instance, we see the stars, light, even if there is no carrier between us and the stars. The light from the stars somehow comes to us and we see it. And so that's kind of a propagation without the real material in the usual sense of this word, carrier. If you have a rope and you are moving up and down one end, then you see how the waves are propagated and the rope is exactly the carrier of these waves. In case of electromagnetic field, since there is no medium, there is no carrier of these waves, there is a vacuum in space, right? So how come they actually reach us? Well, the theory explains it and I'll just try to explain it in my own words. Again, not perfect explanation but still reasonable. Okay, so talk about electromagnetic field and let me start from something which we have experimentally observed, but not personally, but I mean people experimentally observed and we have learned in the chapter which is called electromagnetism of this particular course. Now obviously I will relate to electromagnetism chapter very heavily when talking about the field so I suggest you if you didn't really study that particular part, please do it. It's a previous to this one. The waves is secondary and electromagnetism was before that. Okay, so the experiment which is kind of one of the first experiments was as follows. If you have a straight line, wire and there is certain electric current in it, well, if you put some kind of a table here and put some small metal parts and you will do some kind of a vibration a little bit, just knock a little bit so they will form circles. Now what does it signify? Well, our theory says that this is the flow of electrons and as electrons are moving around them exists a magnetic field and magnetic field acting on these metal particles on this table makes them magnetic. So they are kind of sticking to each other and magnetic field has certain direction so at any point there is a force which actually acts and the force are concentric circles. Well, the experiment shows this so our theory follows the experiment and our theory is that around moving electrons you have the perpendicular to it magnetic field. Well, why electrons are moving? Well, we can say that maybe there is a plus and minus in both sides, charges so electrons are moving from negative to positive. Well, the current by definition moves from positive to negative but that's historical kind of a deviation but in any case moving electrons. So moving electrons are causing the magnetic field and electrons are moving because there is a difference in potential, electro potential plus and minus. Well, what does it mean that there is a difference in potential? Well, there is an electric field actually. There is something which forces the electrons to move. Why do they move? Because there is an electric field. So electric field causing electrons to move and moving electrons are causing the magnetic field around it. Well, but let me just drop the electrons from this picture because what happens is that its electric field produces the magnetic field so to speak. Yes, through the electrons in this particular case. But now, next logical step is the following. What if magnetic, what if electric field is not constant? So it's not a direct current here for instance but alternate current. So the electrons are moving back and forth. Well, then magnetic field also will be changing directions. It will be either this direction or that direction, the forces. Forces here. Okay, so the variable electric field produces, is causing the existence of variable magnetic field. Okay, fine. Now, let's go to another experiment, the electromagnetic induction. So if you remember, if you have some kind of a wire in the loop and you have a magnet which you move in and out of this loop, you can observe the electric current. And why electric current? Well, because obviously it must be electric field. Only because of electric field exists with different potentials and two sides, that's what makes electrons moving. So in this particular case, variable magnetic field and it's variable because we are moving it up and down. So the variable magnetic field is creating electric field inside this loop and that's why electrons are moving. So we have two different things actually which are, well, reversing each other. We have a variable electric field is producing variable magnetic field around it and variable magnetic field is producing variable electric field around it. Do we need conductor here and here, these loops where electrons are actually moving? Well, apparently not. I mean, if you will have it, electrons will move. But if you don't have it, electric field or magnetic field will exist by themselves. So this is the property of the concept of this thing which we call a field. The field is just piece of space, part of the space where certain forces exist but they exist independently of whether we put some kind of into this field or not. Field exists by itself. So here it's not really necessary. As long as we have some kind of a variable electric field, it will produce the variable magnetic field and variable magnetic field will produce variable electric field. So what happens is the following. Let's say initially you have a real electrons which are actually moving, let's say in a circle, it doesn't really matter. Now these electrons will produce magnetic field which is inside it. Remember that's how electromagnet actually is done, right? You have some kind of a core and then you have wire around it. You put electric current into the wire and the score will be magnetized, right? So there is a magnetic field inside this. Now how this field is arranged? Well, it's arranged actually in loops as well. These are magnetic lines, right? Now these are loops of magnetic lines and again if this is variable, this will be variable. Now if this is variable, this is magnetic, now if this is variable then it will produce perpendicularly to this electric field also variable. Now we don't have even the wire loop. The field will exist by itself. And then since this is also a variable, I think it will produce another E, another electric field. So this is E electric field. So as you see, once created the variable let's say in this case electric field, variability is very important. Now the constant electric field is producing constant magnetic but constant magnetic doesn't really produce any electric. So we need the variability. So as long as we have initial variable electric field, it will produce the variable magnetic, which in turn will produce variable electric, which in turn will produce variable magnetic and it will propagate into all directions basically. And that's how the light from the stars come to us because what happens in the star or in our sun is just huge kind of flows of elementary particles. Electrons, protons, whatever, it's a big mess. And obviously there is a huge amount of electricity and magnetism which are in this mess and it propagates because every little piece of variable, every little part of the space where variable electric field exists will produce the magnetic field and it will produce variable electric field and variable magnetic, etc. and it goes in all directions. And it's so strong because the stars are so bright and there is so much going on over there that the power of this radiation, let's use the word radiation, that's basically a propagation of electromagnetic waves. So it reaches us regardless of how far they are. Now obviously it's getting weaker and weaker with the distance and it's inversely proportional to square distance obviously as everything else we know in this three-dimensional space because it goes through this spherical kind of surface and on each real piece of the surface it goes proportionally to, inversely proportionally to square of distance. Okay, so that's how the light propagates, that's how radiation propagates, electromagnetic waves are propagating. Now we probably can reasonably safely consider that the variability is kind of sinusoidal. It's kind of sinusoidal because obviously these up and downs they do not represent a clearly defined sinusoid curve with their ups and downs. However, to a very certain degree we can actually consider this to be based on sinusoid or a combination of different sinusoids. Now in mass you can learn that basically with combination of different sinusoids we can approximate any function. So it's indeed the fact that any kind of complex radiation is actually a combination of more elementary radiation of different sinusoids with different amplitudes and different periods. Okay, now what else? What else is important is, as you see, whenever it goes, directions go this way, the loops of magnetic field and loops of electric field are perpendicular to each other. And also all of them are perpendicular to the direction of propagation. Let's go back to the initial thing. Now the initial with a direct current, there's no propagation so to speak, but you can see that this is a direction of the electric current. This and this is tangential to a loop. It will be perpendicular. So now if you have a variable thing here, like here for instance, the propagation is this way, but our magnetic field will be in this particular plane and it will be perpendicular to the propagation and this will be in the horizontal plane and it will also be perpendicular to propagation. So what I would like to say is that vector E is always perpendicular. This is intensity of the electric field, this is intensity of the magnetic field and they're both perpendicular to the vector of speed of propagation of this particular radiation. And it goes to this direction, to all directions and in all directions we have different directions of intensity of the electric field, the magnetic field and the vector of propagation, vector of speed. So in the notes for this lecture I have kind of nice picture of how the waves are going. I do suggest you to go to the website to this particular lecture and notes contain this picture where in one color I represent the waves of propagation of electric field and I think blue one are magnetic field or vice versa and they all go to a three dimensional like x, y and z axis. One axis goes to propagation, another axis are the amplitude of the electric field and the third axis is amplitude of magnetic field. So it's a nice picture which kind of explains how the whole thing is going. And the last thing which I would like to touch is the speed of propagation. Now, when we were talking about electricity and magnetism in the electromagnetism chapter of this course, we were talking about characteristics of space or some kind of conductor or whatever it is called electric permittivity. And we were talking about magnetic field, we were talking about permeability. Now, both of these concepts are basically playing the same role as resistance for electric current. Well, you know, the greater the resistance, the more difficult it is for the electric current to go through. Okay, this is the same thing, but for the space. Now, the electric or magnetic field, there are fields, right, so they are kind of part of space. Now, what's inside that space? Well, it can be vacuum, it can be air, it can be glass, it can be water. Because the electromagnetic field actually is going into all different kind of, through all different kind of substances, but differently. And these two characteristics, they're called epsilon and mu, are characterizing the environment where electromagnetic field is actually acting. Now, with an index zero, it indicates the properties of the vacuum. So everything is related to a vacuum, and then if you would like to have this same characteristic, let's say, for water, well, usually it's characterized by relative permittivity or permeability relative to vacuum. So, if you would like to say it's relative, it's equal to epsilon times mu relative is equal to real mu. So these are real permeability of the environment, and they are usually measured in vacuum times certain coefficient. Now, what's interesting is that the speed of propagation of, let's say, light or any other electromagnetic wave related to the environment where they are actually propagating. And there is a very nice formula. And the formula is... Now, I'm not deriving this formula in this lecture, and I might actually put it as notes, I'm not sure, but it's an interesting nice looking formula which gives you basically the speed of propagation based on properties of the environment. Now, if you would like to have the speed of light in the vacuum, you obviously have to put epsilon zero and mu zero here. So these are vacuum, these are relative, these are actual for any kind of environment, and this is how the speed of light actually is related to permeability and permeability of the space. By the way, these are kind of the same thing, but the meaning of these words is the same. I don't know why they have decided to call it differently. I think nowadays they're just changing it to electric constant and magnetic constant for vacuum or for any other environment. So with this nice formula, I would like to finish this particular lecture. It's supposed to give you some kind of a taste of what exactly the field's electromagnetic field primarily is and how it propagates. Well, that's it. I would suggest you to read the notes for this lecture. So you go to Unison.com, Physics for Chains is your course, and there is a chapter called Waves, and this is the topic which is called Field Waves, which contains, probably will contain more than one lecture, but right now there is one lecture which is this one, ready. Alright, thank you very much and good luck.