 Hi, I'm Zor. Welcome to Unisor Education. Today we will talk about voltage as a very important characteristic of electric field. It's a characteristic actually of two different points in the electric field. We are talking about voltage between them. Now this lecture is part of the course called Physics for Teen presented on Unisor.com. This is the website. I do suggest you to watch the lecture from the website because, well, first of all, all lectures are presented in a logical sequence. It's a course, right? So every lecture has a textual detail explanation besides this video which you are watching right now. And textual part is basically like a textbook. So you can always read it. It might be in some cases complimenting what I say or don't say during the lecture. Now, for instance, some sophisticated calculations. I'm just doing it in writing in the text, but I don't do it on the board. Plus the website has many problems solved and exams for you to check yourself. And the site is completely free. There are no advertising or anything like that. So we are talking about voltage. Now, first of all, voltage is a derived characteristic. And the primary characteristic is something which we have already learned before. It's called potential. Every point of electric field has a characteristic called potential. Potential is by definition amount of work to bring a probe object of plus one Coulomb from infinity to that particular point in the electric field. We were also talking about moving an object from one point to another as something which, well, the work to move from one object to another, we were talking about this. It's independent of the trajectory. Why? Because electric forces are conservative. That's the term, conservative forces. So the field of conservative forces and electric forces are conservative. It has such a property that to move from one place to another, a charge is really independent on the trajectory. Which means that the most important part is what's the potential here, what's potential there, or even more important, what's the difference between potential. So whenever we are talking about, let's say we are talking about a centrally symmetrical field of point charge of certain, let's say, q Coulons. And this is our probe object plus one Coulomb. Now, this is point A and this is point B. So no matter how we move from one point to another, we have to spend exactly the same amount of work, which actually corresponds to the difference in potential. Because I can move it from here to infinity and then from infinity to B, so it will be minus potential of this plus potential of that, right? So we're always talking about VB minus VA as something which is amount of work which we have to really spend. Now, that's amount of work which we have to spend for one particular probe object which has a unit charge. So when we want to measure amount of work, we usually measure it in the C system of units. We are measuring it in joules, right? Now, in this particular case, amount of work is per unit of charge. So it makes sense to measure the difference between potentials, which is actually the work which should be performed to move a unit charge from point to point. In units which are actually units of work, which is joules, by units of charge, which is coulombs. So one volt, and this is the new unit which we are using to measure the difference of potentials, is equal to basically amount of, it's a difference in potentials such that amount of work to move from point to point of one particular unit charge of electricity is equal to one joule. So one volt is a difference in potentials between two points such that to transfer amount of electricity equals to one coulomb requires amount of work, one joule. Now, obviously it's very important to have design properly here. So amount of electricity is positive. Amount of work, which is one joule, can be either plus one joule or minus one joule, right? Depending on whether you're moving it from A to B. Now let's say this is the central field of the point charge, then whatever is closer would have a stronger potential, right? Because if you remember for the central point, our potential is equal to K Q divided by R, right? Q is the source of electric field and R is the radius. So the further we are R, the smaller the potential, the closer we are, the bigger the potential. So if we are moving, now let's say A is closer than B. So let's say R1 or RA is less than RB. What happens in this case? Well in this case the potential of B A is greater than potential of B B, which means to move from B to A would be positive, to move from A to B would be negative, right? So it all depends on the sign, but in from the magnitude standpoint, again, the difference in potential of one volt is such a difference, which means that one coolant of electricity moved from one point to another would require one joule of work, positive or negative, depending on the game, to closer or to further. So this is the definition of a new unit, unit of the difference of potential. Well, do we have to invent the new unit? No, we can say that it's just measured in joules by coolants, but physicists decided to have it a new unit, which is called one volt, in the same way as what is joule. Joule is basically Newton times meter, right? So they could have used Newton times meter, but they decided to have a new unit in honor of some physicists. Now this is also volt is a new unit, which is named in honor of Italian physicist Alessandro Volta. So the volt is a new unit of difference of potential between two points. Now, and the voltage is actually the quantitative value between two points. So let's say we're talking about that the voltage between A and B is 100 volts. What does it mean? Well, it means that to transfer one coolant of electricity from A to B would require 100 joules. That's what it means, basically. Okay, now we will talk about two particular examples of electric field and we will talk about what exactly is the voltage between two points in each of these cases. Okay, so the first example is basically as I just displayed right now. We have a central field with a point charge of Q and we already basically know that the potential V A is equal to K Q divided by R A. Potential at point B is equal to K Q R B. K is a coolant constant of this. So the difference in potential is V is equal to K Q 1 over R A minus R B. Now again, or R B minus R A, it all depends on which direction we are moving from A to B or from B to A. Well, I think this is from B to A, but if it's from A to B, it should be reversed. In some way, it's actually similar to lifting in the gravitation field, lifting at one kilogram by one meter. So we are changing the potential energy of this particular object by one Newton times one meter, which is one joule. So that's exactly the same thing because, and the word actually, potential in electric field and potential in gravitational field are basically, they do mean exactly the same thing. It's certain amount of energy which should be either spent as work or the object actually already has, if it's already positioned in the field, gravitational field or electric field. So it's just a potential energy. All right, so this is the voltage between two different points. One is at radius R A, another is at radius R B from the centrally located point charge. So this is one particular example. Now another example is it's related to the problem which was considered, I think it was problem number two. When we were talking about infinite plane, which has certain density of electricity sigma, it's infinitely thin and infinitely large plane. It's charged with a density sigma and we have actually came up with a very interesting result that intensity of the field at any point is the same and it's equal to 2 pi k sigma. This is intensity of the field. Now from the potential standpoint, if I have a constant intensity and constant force, intensity is a force applied to a unit electricity of electricity, of electric charge. Now that means that if I will bring this particular probe charge of plus one coulomb from infinity to this point, I have to spend an infinite amount of energy, right, because the force is exactly the same. Force times distance and distance is infinite. So in this case the term potential doesn't make any sense at all. It's just an infinite amount of work. However, however, the difference in potential between two different points, let's say this is point A and this is point B, the difference in potential does make sense. Why? Because we are actually lifting from one point to another or lowering down from one point to another and we know exactly what is the force acting against us or helping us. So it's positive or negative, but in any case the difference is just the height. Because again, to horizontally move we don't really spend any energy, no work is done because the force is perpendicular to the trajectory, but to moving up or down perpendicularly to the plane does make sense and does change something and it requires work. Now we have a constant field, constant intensity, which is a force. So the difference in height is important. So if A has height HA and B has a height HB, then we can talk about the distance as HA minus HB. Now this is the distance and multiplied by force that gives me amount of work. So this is the voltage between A and B. So it depends on the height about the plane. So this is just another example how to calculate the voltage if we know, you know, whatever we know about about electric field. So in case of a central electric field it's one formula and it depends on the distance from the center. In case of a flat plane as the source of the field it's a different formula. For any case there is something which we can calculate as a numerical formula which gives you exactly the voltage. So let me just summarize. This lecture is not about anything new basically. Whatever I'm talking about right now is you knew from the previous lecture. I have just introduced a new terminology, the voltage and the new unit how to measure it, which is basically a joule per calorie, one volt. That's a potential difference between two different points. And again it always makes sense to talk about the difference in potential rather than potential of every point separately. The same way as I was explaining if I'm lifting something from one place to another doesn't really matter how far it is from the center of the earth. The matter is by how much I lifted. Well that's it. Nothing extremely new here except as I was saying terminology in the unit of measurement. However we have to really understand that this is a very important unit of measurement because the voltage is something which is used in electricity everywhere. So whenever you are using your outlet you know that there is some kind of an electric current which will start working if you will turn on the lamp or something like this and the voltage is very important. So in the United States you have main voltage in all the houses 110 for instance, 120. In Europe it's 220 etc. So people should know their voltage because from the voltage depends the next thing which we will talk about which is the current but that's in the future. Okay that's it. Thank you very much and good luck.