We're here at St. Paul's Cathedral in London, England. St. Paul's is on the top of Ludgate Hill, which is the tallest hill in the city. Over the years, this cathedral has been struck by lightning on countless occasions. And in 1561, a lightning strike actually caused a large portion to burn down. In this unit, we'll learn not only why this cathedral is such a prime target for lightning strikes but also how to prevent lightning strikes from causing such disastrous fires.
Being alive today, you probably know that lightening is a form of electricity. But this wasn't obvious in the 18th century. If you were this green-haired person here watching houses get struck by lightening, you'd probably think, "What is this thing?" Let's go back to the professor to get some more context on this situation. [Professor Lucio Fregonese, University of Pavia] Before the explosion of electrical studies in the 18th century, lightening was interpreted as an explosion of sulfur, sulfurous matter coming from the earth. But people started to realize some analogies between lightening and electricity. Benjamin Franklin was not the first to think about that analogy. It was already present in science. For example, a French scientist wrote down a list of analogies between lightening and artificial electricity, but it was Benjamin Franklin to stress the analogy. One of the most evident effects you'll see studying electricity are attraction and repulsion. So, there are interactions between electrified bodies. There is a quantity called electrical charge, which is one of the quantities involved in the phenomenon. The bigger the charge, the stronger the effect in the same conditions. The analogy with gravity is very clarifying. It looks like we have our work cut out for us, but with the help of Benjamin Franklin, it looks like we may be able to answer this question--what is lightening? And we might even be able to prevent it from hitting our churches, houses and other buildings. Now, if you've ever rubbed your feet on the carpet and then touched your finger to your friends, you might have noticed a little spark. That spark is electricity. It was Franklin's idea that this spark was the same as this giant spark in the sky and that both were a form of electricity.
In the 18th century, it was all the rage to study electricity. Everyone was doing it, and the thing they were storing their electricity in was known as a Leyden jar. Now, we don't need to go into the details of how this jar worked just yet, but the key thing to know is that if there is a process which involved friction this jar could become charged. And for now, let's say that charged means the jar possesses electricity in some way. Well once it was charged, the electrodes of this jar could be connected to wires and by attaching these wires to various objects you could see things like sparks or you could even start a fire. Now remember, Benjamin Franklin's idea was that lightning is somehow the same thing as the electricity that scientists have been playing around with in these Leyden jars. So my question is, which of the following options would be the most convincing demonstration to show that lightning is actually the same thing as the electricity in these Leyden jars? Would we want to show that lightning, like a Leyden jar, can actually somehow cause a fire? Would we want to show that we can use lightning directly to charge a Leyden jar? Would we want to use lightning to destroy a Leyden jar? Or would we want to see if lightning somehow increases friction? The thinking being that Leyden jars were somehow charged by a process that involve friction. Which of these four options should Benjamin Franklin do if he wants to convincingly prove that lightning is electricity?
Well, I don't think this first one is good. Lots of things cause fires that are not electricity. The second answer seems like the best to me. If we can take an uncharged Leyden jar and somehow use lightening to charge it and then have a Leyden jar that's charged just like any other,
To test this hypothesis that lightning was actually electricity, Benjamin Franklin did something--well, something incredibly stupid. Now, it's not entirely certain if Franklin actually did this experiment but what's believed is that he took a kite out into a windy, raging thunderstorm and as the kite flew and the string got wet, well he tied a key to that string. His thinking being that, well if this lightning is somehow electricity there's got to be a ton of this electricity in the sky. And so he probably didn't actually allow the kite to get struck by lightning because that could've been fatal. Instead, he let the kite fly close to the clouds where he hoped it would collect electricity. That electricity he hoped will be transferred somehow along this wet kite string into the key, which could then be touched to this--what's called an electrode of the Leyden jar, thus charging the jar. When he did the experiment, it worked. What he set out to do actually happened. He showed that since lightning can be used to charge a Leyden jar, lightning must be electricity. For the rest of this unit, we're going to learn about electricity. Now I have to say this is usually a subject that's covered over an entire course. So what we're going to do here is learn the very basics enough to protect our buildings from being struck by lightning but this is really just a teaser. We're really just skimming the surface of what there is to learn about electricity.
So in order to answer the question what is electricity, we're going to look at a lot of the contributions made by Benjamin Franklin. Franklin gave us the idea of charge both positive and negative. He gave us the notion of conservation of charge, which is very similar to conservation of energy, which we talked about in Unit 4. He described the properties of conductors and insulators. We're going to learn about all of these and more in this unit, but one thing I want to point out is that in some sense we might be historically inaccurate at some points. I'm going to use vocabulary that we would use today when talking about electricity. Some of the words Benjamin Franklin used might have been a bit different. So let's start with this idea of charge. Well, what is charge? Charge--and I'm going to use the convention way I label charge with the variable Q-- Well, it's a property of matter. Well, that's all fine. But what does it mean to be a property of matter? Well, we've gotten used to in our force diagrams that described the motion and forces on an object to writing the mass on that object. Because the mass was such an important property of the matter. Well, let's think about mass. Why was mass so important? We need to think about this and answer the following question. Why is mass so important? Is it because mass causes friction? Is it because mass tells us how much space an object occupies? Or is it because mass is somehow relevant to gravity? Think about this and choose what you think is the best answer.
Well the reason why mass is so important is because it is relevant to gravity, and it's not just relevant in the sense that a mass feels the effects of gravity. Masses actually cause gravity. The reason why a person standing on the earth doesn't fall off--well there's 2 reasons. One is because the mass of the earth is producing gravity, and the second is that the mass of the person is feeling the gravitational force. Without both of these masses, there would be no force. Charge is very similar except that charge causes the electric force, and that force is felt by other charged objects.
It's not like there are some real similarities between charge and mass. Specifically, similarities between the electric force and the gravitational. Let's do some comparison to see just how similar or how different these forces are. First, let's analyze the cause of each force. Well, the electric force is caused by charged objects whereas the gravitational force well it's caused by massive objects. Charge and mass are the causes of these forces. What about the effect? What kind of object feels the effect of the electric force? Well once again it's an object with a charge. Likewise, gravitational force is felt by objects with mass. Notice that we already see one similarity. The thing that causes the force is the same as the thing that feels it. What about the force law? And by force law I mean what's the equation that describes these forces? Well with gravity we knew the force of gravity was proportional to 1 over your distance away from the mass of object that's causing the force. In the case of the earth and the moon, r would be the separation between the two bodies. With the electrical force, it turns out the force law is almost identical. It's still proportional to 1 over r². So doubling the distance will decrease the force by a factor of 4. What about the direction of force? Well for gravity, objects always attract each other. In fact, it's this attraction that allows large bodies like the earth to form because every little tiny chunk of rock is attracted to every other little tiny chunk of rock and together they coalesce and form this wonderful beautiful sphere. What about with electricity? This is where things get interesting. With electricity, the direction is not always attractive. Sometimes it's repulsive. And this one key difference is responsively for many of the fascinating aspects of electricity which well we can learn about now.
How is it that charge can be both attractive and repulsive? How does it know when to behave in which way? Well, charged objects can either be positive or negative. This is totally different from mass, which when we described an object's mass we said 5 kg. We didn't have to say +5 or -5. It doesn't make sense to talk about a negative mass. And the key thing to remember with charge is that opposite charges attract each other but like charges repel. Now this is really amazing. Now the key thing with charges is that opposite charges attract and like charges repel. Let's say you have these two charges and you are somehow able to hold them in your fingers. Right now, there exists some force between these two charges. If I let go and allow these charges to move, I want to know what will the charges look like after I allow them to move. Will they look exactly the same like nothing happened? Will they come together and be really close? Will they fly apart from each other? Choose the best answer.
Well these charges are opposite. One is a positive and one is a negative. Opposite charges attract so they'll come together. This is actually deeply fascinating and has some serious implications for well everything from the structure of matter to--well-- lightning because a lone positive charge and a lone negative charge when left their own devices pair up. Let's take a look at the consequences of this pairing up.
Here we have our two charges - a positive and a negative. And let's assume they're equal in size so the positive charge is as positive as the negative charge is negative. Now might be a good time to introduce the Coulomb, which is the unit of charge. We could say that this is a charge of +1 Coulomb and this is a charge of -1 Coulomb. Now let's make things interesting. Let's say that another charge, a third mystery charge arrives on the scene. I'm not going to tell you if this is a positive or a negative charge. I want to know what direction is the net force on this mystery charge. Is it up? Is it down? Maybe there's no force at all. Or maybe it depends on whether this mystery charge is positive or negative? Think about this one and give me your best guess. I warn you it is a bit tricky.
Now, I suspect you may have chosen this one. It's so tempting. And actually technically it's a little bit correct. I encourage you to go to the forums to talk about why this is a little bit correct. But I think the best answer is that there's no force because— Let's say this was positive. Well then it's going to feel a repulsive force from this positive guy. And an equal attractive force from the negative since these are the same sized force. These are going to exactly balance out and so no force. If this guy was negative, same thing except now the repulsion comes from the negative force and the attraction comes from the positive. Now why did I bring this up? This is just some weird coincidence. Okay. In this situation, this guy didn't feel any force. No. It's not a weird coincidence. In fact, you almost never find isolated charges like this in nature. And why not? Because electricity is really, really, really strong. It's a super strong force compared to gravity. Man, gravity is so weak compared to electricity. What that means is if this guy were to exist, this lone negative charge, and somewhere off in the distance there was a lonely positive charge they would find each other and they would pair off. And it seems like in our universe there's more or less an equal amount of positive and negative charges. Let's take a look at the human body for example.
When we look at the human body we see a series of sticks because that's all I can draw. But that's not really what we see. We see a human body. If we take a magnifying glass to a part of this and really zoom in on this region what do we see? We see cells. In fact, we see something like 10¹³ cells. That's a 1 followed by 13 zeros. That's a massive number. Well let's not stop there. Let's zoom in on a cell. That's a magnifying glass by the way. If we zoom in on the cell, we see that it's made up of molecules and those molecules are made up of atoms. And here I've drawn a single atom. This atom has three interesting parts. Here in the center we have the nucleus. The red and the blue dots. I'm using the red dot to represent the proton, and the proton has a charge of +1.6x10⁻¹⁹C. Also in the nucleus we have the neutrons which have a charge of 0 so we call them neutral. And orbiting around outside the nucleus we have electrons. And electrons have a charge of -1.6x10⁻¹⁹C. Same as the proton but negative. Each of these cells— Each of the 10¹³ cells in the human body has about 10¹⁵ protons, So my question is, using all of these data you have here of these numbers, I want you to tell me what is the net or total charge and remember Q is charge on the human body. Enter your answer here in Coulombs.
Did I trick you? Because this is not as tricky as it may look initially. Okay, so this 10¹³ cell. Let's figure out what the net charge on this cell is. What each cell has 10¹⁵ protons? Okay, that will contribute some charge 10¹⁵ times the charge per proton as 10¹⁵ neutrons, they don't contribute at all in 10¹⁵ electrons which will contribute the exact same charge that the protons contributed but negative. The positive charges in the protons will cancel the negative charges in the electrons The net charge on the human body will be zero. This explains why you don't feel the electric force everyday. You're much more familiar with gravity because your body doesn't have a net charge. You could stay in pretty close to a charged object and you wouldn't feel much of anything. This may have just raised more questions than it answered because well, let's see, if everything is neutral, why do we even care about charge? How can we make something non-neutral? How can we give it a charge? If lightning has electricity, well it seems like there's a whole lot of it moving around. Where does that come from? Let's answer those questions.
Let's take a look at the conservation of charge, very similar to conservation of energy. Conservation of charge means that the total charge in the universe never changes. Now, this doesn't mean it's impossible to, let's say, create a positive charge. It just means that when we do create a positive charge, we better create a negative charge to go along with it. In fact, we can refine this definition. Let's make it a little more specific. Let's say that the total charge in a closed system never changes Well, what does this mean? What's a closed system? Well, for the purpose of conservation of charge, a closed system means that there's no charge being added to or removed from the system. For example, let's imagine a metallic sphere. This would be, in this case, a closed system. Nothing is touching it. It's just hanging out somehow and there's no charge being introduced to it and no charge being removed from it. Now in reality, this sphere would have to be held by something. Let's say it's held by some stand and the only important thing is that this stand be what's called an insulator. An insulator is something which doesn't allow charges to move around inside of it. But we'll get to that in a bit. Now, this metallic sphere, just like the human body, is made of atoms. And those atoms contain positive protons and negative electrons. And let me get rid of some of this stuff, so we can focus on the problem at hand. I mentioned before that our stand has to be an insulator, something in which charges are stuck and can't move. The other end of the spectrum is a conductor in which electrons are free to move. Now in the case for our conducting sphere, of course, the sphere is a conductor and the positive and negative charges in this neutral conductor are perfectly balanced. I've drawn seven, in reality, they'd be trillions and trillions but what I want to know is, let's say, we're somehow able to find a positively charged object. This is a net positive charge and we could bring it close to this conducting sphere. Can you think about this problem and tell me what would the charge distribution in this sphere look like when we bring this charge close? Which of these pictures best indicates what the charge distribution in this sphere will look like once we've brought a positive charge close to the right-hand side? Now, you have to think about this for a minute. Think of what it means to be a conductor. Think of what sorts of charges are attracted and repelled? I think you can probably get this one right. Good luck.
And the correct answer is that the charge distribution will look like this. The positive charge will attract the negatives over to this side but this negative has to come from somewhere. Well, previously they were hanging out positive charges over here. Once they leave those positive charges, that leans a deficit of electrons on this side, and so this left side becomes positively charge as the right side becomes negatively charge. What we have just discovered is the phenomenon known as polarization, and that's what we call when charges separate--positive on one side and negatives on the other.
At the heart of polarization, we have a charge attracting opposite charges. We found something very similar happens when a lightning cloud comes overhead. These clouds tend to have a lot of negative charge built up at the bottom of them. We haven't talked about how yet, but this negative charge gets there. Well, what happens is this negative charge in the clouds causes some of the negative charges in the ground to be upheld--leaving a deficit of electrons and excess of protons. This causes the ground to actually become slightly positively charge. This concept of polarization is essential to the functioning of what we're going to find-- this Benjamin Franklin's solution to saving buildings from lightning strikes. Let's actually think about what would happen if ??? a perfect sphere, we change the shape of our conductor, because ??? with a sphere where the negative charges have a large surface over which they can distribute themselves. What if we made this a pointier shape, not a sphere but a cone--do I still expect polarization to happen. But qualitatively, is there any way difference between what happen with the sphere and what happen with the cone. At the tip of this cone, is the concentration or density of negative charges higher than it was with the sphere, lower or the same, and I admit this is quite a tricky question. Think about it and take your best guess but don't worry if you're wrong.
Well, these negative charges all want to get as close to the positive charges they possibly can-- which means all packing in to this one tiny little tip, which means the concentration will be higher. This will turn out to be very important when we design a tool to save our buildings from lightning strikes, and this is something that some people call the effect of points, mainly that pointed objects tend to have higher concentrations of negative charge accumulating in them in these situations than rounder objects or flat objects, but there's still huge question to be answered--namely, where did this guy come from, how do we get a positively charge object to begin with. Far all we've seen are how an object can become polarized, how the charges can separate. I want to know how to get a charge object.
How do we charge an object? Well, there are actually several ways. One way is we can charge by friction. And if you've ever rubbed your feet on the carpet and then touched your friend who was standing nearby and giving them a shock you have charged yourself by friction. And what's going on here, the rubbing between two objects actually causes one to steal the electrons of the others. Now, it doesn't steal the protons because protons are well relatively gigantic compared to electrons. Electrons are tiny, tiny little guys. And so it turns out that just simple rubbing can actually cause an exchange of charge leaving one object positive and one negative. In fact, this sort of charging happens in cumulonimbus clouds and these are the sorts of clouds that cause lightning. And what happens is little drops of ice or water are constantly moving around in this cloud and as these droplets pass through the cloud rubbing against each other and passing through different regions of the cloud they gradually either accumulate or lose electrons depending on what they're moving on and the details of the actual situation but what this does is it creates a motion of charge. Whether this is positive or negative. Whether it's going up or down. It doesn't really matter. What happens is charge separates and what that usually leads to is chaotic motion of particles. There's a buildup of minus charges in the bottom of the cloud and positive charges at the top. Now we've already shown that these minus charges lead to corresponding positive charges building up in the ground. We're starting to really understand lightning here as well as electricity. We can use charging by friction to create a charged object. Let's say we've created a positively charged ball. A good way to do this is by rubbing something metallic with let's say rabbit fur. Anyways we have this positively charged ball. and we know that if we bring it near to this ball we'll induce some polarization. Negative charges on this side and positive on that side. Fine. But what happens if this ball touches that ball? We bring this over and let them touch and remember they're both conductors. All in all, what do you think will happen when I touch this ball to that? Do you think nothing will happen? Do you think that some positive charges will flow from ball B to ball A? Do you think that some negative charges will flow from A to B? Or do you think that all the positive charges on ball B will flow to ball A? Think about what it means. There will certainly be a conductor, and then give this question a shot.
Well, being a conductor means the electrons are free to move, not protons. Protons like I said before are really quite big. Electrons are tiny. Electrons are easy to move around. So positive charges aren't going to do any flowing. But what will happen is some electrons will flow from A to B. Remember, electrons have a negative charge and they'll do that because this positive charge is attracting them. And that is our second method of charging. Charging by conduction. It's when you touch a charged object to an uncharged object, and the uncharged object becomes charged. There's one more very clever method of charging an object that involves polarization.
Now as a reminder, polarization occurs when we bring a charged object next to an uncharged conductor and allow the charges to separate because the negatives are charged to the positive and the positives are repelled. Now, I want to do something a little different, something that we haven't done before. I want you to really think creatively here and tell me how can we use this idea of polarization to create a charged object or maybe to create two charged objects? You can start to see here that it looks like there should be a way to create something that's charged here. Maybe one, maybe two objects that are charged but I leave it up to you to enter into this box what you think would be the best way to create charged objects using this polarization idea. If you think you have a particularly clever method, you should go to the form and share it there. Since I'm so confident that you can tell me this answer on your own, I'm not going to tell you at all but if the anticipation is just killing you and you need to know if your method is right, which I bet it is, you can go ahead and look up charging by induction. Go ahead and enter your answer here. Don't worry, you'll be marked correct regardless of what you put but I hope put some time to this and I'll be going over and looking for some clever ways to charge an object using this idea of polarization.
Okay, so I lied. I am going to tell you how charging by induction works. But I hope you did put some thought into it. One way you can charge by induction is by exchanging your single sphere for two connected by a detachable conducting rod. In this case, negative charges will be attracted to this end of our little dumbbell and positive charges will be left in this end, then we can just detach our connection and tada, we have two charged objects--one positive and one negative.
It turns out this actually another method to charge by induction. This method, just like the first method, also uses two spheres but here, one of those spheres is actually the earth. Let's say you have your conducting sphere and it's attached to the ground by a conducting rod. Let's also add a bunch of wires that extend into the ground and then let's hold a positive charge over our conducting sphere. What's going to happen is that we're going to actually draw electrons from the earth. If we then detached this sphere, we can even remove the positive charge and now here we have it, a negatively charged sphere. And this negative charges somehow came from the ground. Now, of course, this must mean that throughout the earth, there must be a few extra positive charges lingering around. They've lost their electrons. It seems like if we were to do this experiment over and over and over, well, eventually we'd have a positively charged earth and that might be a problem. It turns out that this is a non-issue and I want you to tell me why you think this works and why it's a non-issue? Maybe you think the earth is somehow able to create electrons create this negative charges, so that actually there's no residual positive charge leftover. Maybe it has something to do with the fact that the earth is huge. Maybe that has something to do with the reason why this never becomes a problem where we actually wind up charging the earth with some noticeable amount. Or maybe you think the earth is an insulator, something in which charges cannot move and that this somehow saves us and allows this whole process to work. Check what you think is the best answer.
Well, the first thing I want to clear up is that the earth is not an insulator. The only reason this method works at all that we can draw this electrons up from the earth is because the earth is more of a conductor than an insulator. That was a bad answer. Also the earth is not able to create electrons. Nothing can create an electron without also somehow creating a corresponding positive charge. The truth is part of the reason why we can do this is because the earth is just gigantic. What if I take a few negative charges from the earth. Eventually, they'll probably wine up back in the earth. The truth is, the earth serves as an infinite source and sink of electrons. Source means for all affective purposes, we can count on the earth to provide us with whatever electrons we need in this situation. Likewise, we can also deposit electrons into the earth, essentially infinitely. This idea that the earth is an infinite source and sink of electrons, well that's what the word grounding means. Let's talk to Lucio Fregonese to see what he has to say about the topic. We say that the body is grounded when it is an electrical communication with the earth, and so there is an electrical conductor and electrical path connecting it to the earth, and making it one conductor together with the earth. And it is a good situation sort to say because the earth is a big conductor, and so quantities of charge if ones eat little. This thing might be a useful concept, this idea of grounding when we have a lighting strike and we need somewhere to put all of that electricity.--Looks like we're making some serious progress.
Well, we've already learned a lot about electricity. We know that negative charges like to be with positive charges. We know four methods to charge an object, and we've learned that the earth is both a source and a sink for electrons. But one thing we haven't talked about at all— one of the most important concepts in physics is energy. Why don't we go back to Professor Fregonese and see what he has to say about energy as it relates to electricity. One of the most evident effects of electricity are attractions and repulsions of electrified bodies and this is important because you can use these forces to produce work, to produce energy. We can start understanding it with an analogy with gravity, which is simple because we have only attraction and electricity is much more complicated because you have also this complication of repulsion. If I have a body of mass, there is an attraction between the body and the earth and there is potential energy. If I drop this body, it has the capacity to produce some work maybe to break a neck down there. It goes down and the potential energy diminishes and it acquires kinetic energy, movement, velocity, and which is proportionate to the square of velocity. With electricity, it's more complicated because of repulsion but the idea is similar. You can use the interactions between electrified borders between charges to produce work so to have energy to produce something.
To talk about electric potential energy, let's imagine a universe that only has two charges in it and let's say they're both positive. And the separation between these charges we'll call r. And what I want to know is when do you think electric potential energy which I'm using a big U with the subscript E to indicate--when do you think that's highest? Do you think it's highest when r is big? when it's small? Or maybe it doesn't matter what r is. Now when you're thinking about this question, I want you to think okay there's two positive charges. Are they going to attract or repel? Given whatever that tendency is, if I move them closer well is there going to be more energy stored in them or less? Are they going to have more capacity to do work or less?
And you think of this as compressing a spring. When I compress the spring more and more and more, I'm storing more and more energy in it, likewise, with these two charges. When r is really small or those charges really want to fly apart, they want to fly off into the distance and acquire kinetic energy. That is when the electric potential energy is highest. Now, we should probably quantify this mathematically.
Looking back at our universe where there's only two positive charges. I'll call them q1 and q2 and in this case they're both positive, but they can be negative or one of each. It turns out that the electric potential energy is equal to some constant Kq1q2/r. Now K is just a constant. Its value is 910⁹ and maybe you can tell me by doing your dimensional analysis skills what the units are, but that's for the forums. What this equation tells us is that well if the charge is bigger either this charge is the potential energy increases proportionally. If the distance of separation is bigger, the potential energy decreases proportionally. The derivation for this equation is actually really fascinating, something we won't do here, but it basically comes from the idea that there's a certain amount of work required to move these charges from very, very far away into this configuration and that work happens to be equal to this. Let's do some quick practice, let's imagine that q1 is actually a minus charge of -1c and q2 with a +3c, and let's say the separation between them is 2 m. You need to tell me the potential energy. I've already filled in the x10¹⁰ because that's what your exponent is going to want to be when you convert this to scientific notation. You can you just fill in this part here with the potential energy ought to be and be very careful with the sign.
Well let's plug into this equation. When we carry out this multiplication, we get a result of -1.35 x10¹⁰ J. Now notice that this is a negative number and in fact, if r were smaller, so these were closer together, it would have been a more negative number. It would have been a lower potential energy. Now in genuine physics, objects like to be in a low energy state. Balls like to roll downhill and positive charges like to be with negative charges. And we can see in this equation that if one charge is positive and the other negative, well this energy will be negative, and this r want to be as small as it possibly can.
Now, what happens if there is more than two charges--for instance three. How do we use this equation to find the potential energy of this system. We have three charges all separated by 1 m and this one is +2, this one -3, and this one is +4c. One thing not to be confused by is the fact that even though this is q1 and q2 that is not saying that this formula exclusively applies to q1 here and q2 there. I just happen to label this charge q1 and this charge q2. I could have labeled this one q7 and this one q? and this one q smiley face, but I didn't. This equation just means that for any pair of charges, there's potential energy stored and this one and two just referred to the two charges in that pair. If we want to calculate the potential energy of this system, we have to calculate the energy associated with this pair of charges, this pair, and that pair. We'll have to make three calculations. Could you tell me what is the potential energy stored in this system of three charges, and you can enter your answer here and I've already included the x10¹⁰, again, be careful with your sign.
Okay. Let's see. Here's the factor in all three pairs. The potential energy is just the sum of KQ1Q2 over this distance plus Q1Q3 over this distance plus Q2Q3 over this distance. Now, if we plug in our numbers, Q1 is +2, Q2 is -3, and Q3 is +4, we find that the answer is -910¹⁰ J. Now, a very interesting question is where is this energy stored.
Where is the energy stored? In the previous example we have three charges 2+ and 1-, and we want to know, well is the energy stored in the charges? Somehow in the space between? And the answer is that the energy stored in something called the electric field. Now the concept of the field is a strange one. So don't worry if this is intuitive at first. We actually could have talk about this concept of a field when we talk about gravity. So for example, if you look at the earth, we can draw this imaginary arrows pointed towards the center of the earth and these arrows somehow indicate what would happen if I put a mass near them. If I put a mass in this arrow, well it will a feel force into the direction that the arrow is pointing. These arrows are somehow representing the gravitational field. The electric filed is very similar in the same way that gravity is caused by mass, electric fields are created by charges, and just as gravitational fields are felt by mass, electric fields are felt by charges. Both created and felt by objects with charge. Interesting! Now, how are we going to measure the electric field. Well it must have some strength associated with it. The way we measure that strength is by putting a small test particle with a charge let's say +q somewhere and if there's an electric field, this object will feel a force. Electric fields cause forces, and of course if this charge were bigger, the force will be bigger. But it seems like there's something more fundamental going on than the force on this particular charge. Actually, what we want to do is to find the electric field in the following way as being equal to the force but we divide by whatever the charge of the particle we're putting in this. If we find that there is some force in this direction that means it must also have been an electric field in this direction at this point. As a quick example of how to use this equation, E=F/q. Let's say we take our +1c charge, set it down somewhere and note that it feels a force to the right of 4N. Well the electric field is just force over charge 4/1 and both of those numbers are positive. In this case the E field or electric field would be 4N/c and maybe I'd want to say something like to the right because electric field is a vector. It has both the size and the direction. Now what if I gave you a different problem. Let's say I have a negative charge that when placed in a certain electric field fills a force of 10 N to the right. Can you fill this out for me? Can you tell me what's the strength of the electric field is? And that strength should be a positive number and can you tell me whether it's an electric field to the right or to the left.
When I do my F/q like 10/-0.2, I get a value of -50, but the negative actually just means that the electric field is to the left. Negative charges fill forces opposite the direction of the electric field whereas positive charges fill forces in the same direction.
All right, so we've learned that the electric field exerts a force on particles. If I have an E-field that looks like this and I put a positive charge there, well, it's going to feel force to the right and a negative charge would feel force to the left. All right, but how do I know how to draw these lines? Where did they come from? Where did they go? Let's learn about that. The field line himself. Well, I mentioned before that electric field is not just felt by charges, it's created by charges. If I have a positive charge, well the associate electric field will look like this. The field lines will be evenly spaced and radiating outwards from the charge. This makes sense because I know if I put a positive charge here, well it better be repelled from this guy and according to this, it will. Likewise, a negative charge looks very similar but the field lines point inwards. Again, this makes sense. I know that a positive charge better be attracted to this negative charge and according to this electric field line, it will be and a negative charge, if I put it here, will be repelled since negative charges go opposite the direction of field lines. Now, knowing what you know about field lines, maybe you can tell me if I have a positive and a negative charge and they're next to each other, what would the electric field look like? I'm going to give you a few options and you pick the best one. Which of these four options do you think best describes the electric field that exists when you have two charges, a positive on the left and a negative on the right. Do you think it's this one? Do you think maybe there's no electric field. Do you think it's this one, where there is no electric field but it bends in this weird way, or maybe this one or that one. Think about it, think about maybe what would happen if you put a positive test charge somewhere and what direction you'd expect the force to be? Good luck. This is a tricky question.
Why we really love thinking about these sort of things? This option is not right. The reason this is not right is this has no electric field anywhere. Clearly, if I put a positive charge in the middle somewhere, it will go to the right towards the negative charge so that can't be right. There must be some electric field, but on this one, this one has a weird shape. According to this one, if I put a charge here, it would fill a force upwards, it looks like. Now, that doesn't make sense. It should be attracted more towards the negative charge. There's no reason for to go up so that's wrong. These two look very similar. It's just the matter of what they point to the positive or point towards the negative, and the correct answer is they should point towards the negative. One thing that's really interesting is to look at the strength of the electric field and how we see that with these pictures. So for example, right between these two charges, the field would be very strong. You can see there's a high density of field lines here. In this one little drawing I made, this little shape, three field lines have gone through. They are all tightly packed together. Tightly packed field lines mean a strong field. Way out over here, I can draw a similar area, and no field lines are going through. The electric field would be very weak over here.
We're very close to understanding how to solve our problem-- how to prevent buildings from getting struck by lightning. Let's take a look. Here's our cloud overhead. And the bottom of that cloud is negatively charged. That induces some positive charge on the ground, and this leads to some complicated pattern of electric field. Okay, so we've got these buildings. We know that they're at risk of being struck by lightning. In fact, well, there's a lot of ways to explain what's going on with this lightning. It's a very complicated subject. But one thing that's going to happen is a little bit of charge due to this negative charge will be induced on the roof. And since the tip of this roof is a little closer, a little more charge will be induced there and a little less over here and that's going to modify the electric field. It's going to make the electric field around here a bit stronger and quite a bit stronger here and even a little bit stronger over this building. Now, can you tell me which of these three buildings is most likely to get struck by lightning?
Well, you might know this from experience--personal experience. And remember, physics always has to be in line with your personal experience, right? This building is the most likely. It's the tallest. The electric field around here is stronger than the electric field around here. And in fact, the reason why lightning actually occurs is because the electric field exceeds some threshold strength. Once the electric field is sufficiently high, that's when lightning can strike. And a lightning strike can lead to fire and other disasters. That's what we want to avoid.
We're basically there. We need to install some object let say that was Benjamin Franklin's idea. And I think you could probably tell me what property this object ought to have if we want it to get struck by lightening or to sort of discharge these clouds in order to prevent the lightening from hitting the building. So using everything we know about electricity, should the object we install here should it be tall or should it be short. Also should it be conducting as in should charge be allowed to flow along it or should be an insulator. Should it be grounded or should it not be grounded? This is the sort of thought process that I'm sure Benjamin Franklin went through when solving this problem. For each of these options, can you select one of the two radio buttons. Good luck.
Well first of all it's got to be tall. If it's not tall, the building will be hit before our object is. It's got to be conducting, if it isn't conducting, well, no charge will flow through it and will be pretty difficult to entice lighting to strike our object, and finally it's got to be grounded. We got to disperse all of this electrical charging energy somehow, and the way we're going to do that is by dumping it into the earth to the ground, and so there you have it. We've basically solved the problem, so let's go to Professor Fregonese one more time and see what he has to say. Franklin Benjamin idea was to discharge clouds as there is an effect called the effect of points. Points have the property of discharging electricity, so this was Franklin's idea. It was put in practice, but it doesn't work this way. It catches the lightning, so to say. The explanation is a bit complicated. It produces modifications of the electrical field and then it is important that it conveys the electricity through a conductor avoiding the circuit through the building. It conveys electricity to the earth so discharge it to the earth. The earth receives the electricity of lighting because it is a very big body, and so it can receive an extra amount of electricity. At the time of Benjamin Franklin, it was thought as a sort of general receiver of the electricity. There you have it. We've invented the lighting rod. Good work! And all the lighting rod is a large conducting pole placed in your building or on top of your building with a wire running along the side, and it must be properly grounded, and what happens is when a storm cloud comes over head, it draws but we can think of this as drawing positive charge up. Really what it's doing is forcing negative charge into the earth, but it creates a really strong electric field in this region, and the lighting instead of striking the house--it will strike our pole and life is good. No more buildings get burn down. Amazing! Good work Benjamin Franklin and good work to you.
Well, congratulations. We talked about a lot in this unit. In fact, you learned all the basics of electricity. You've learned about the two different types of charge and how they interact. You learned several methods for charging a neutral object and how this method relate to lightning. We learned a bit about the cause of lightning and discovered that a tall conducting pole connected to the ground can effectively catch lightning and safely redistribute both the charge and electrical potential energy into the ground without destroying any buildings. Next unit would be a bit about many unit on the future of physics as well as the final exam. See you next week.