Philosophers. Let's think about philosophers for a second. Philosophers ask difficult questions that nobody really cares about the answer to. One of the most famous philosophical questions I think, is if a tree falls in the woods and no one is there to hear it, does it make a sound? So the philosopher might say, well maybe sound is a communal experience between the tree, and the answer is no. Physicists would say, of course, it makes a sound. When a tree falls in the woods, it releases energy into the air, that energy vibrates, the air molecules creates a pressure wave, and that pressure wave is sound, and it's there whether your ears are there to hear it or not. So we have something similar with electromagnetism. So let's think, instead of a tree, let's think about a charge, a big charge Q sitting here. Let's imagine what if there's a little charge, q here, and let's say they're both positive. What's going to happen is you're going to have a force, a force on q. It's the force we calculated before. That Q would apply to q. I could put q here, and you'll also have a force. It'll be bigger because we're closer, as we learned from Coulomb's law. I could put q way over here, q right there, and it would have another force, the force is always going to point away, as we learned with Coulomb's law and it would be smaller. I could put q anywhere around Q , and I would generate force vectors, and in fact I would have a force-field. So that's a case of a vector field. All the vectors as you move around, will get smaller as you move away from Q, and they'll always point away from Q. So that's an example of a force field. But now let's think about the philosopher's question. What if q isn't there? Okay? So the Q is creating a condition, where if q is there, it feels the force. But what if it's not there? What is it doing? Is it doing anything? Well, just like sound exists anyway, it is doing something there, it's creating an electric field. That's how we think of these forces when only one of the charges is there. There's no charge to experience the force, but it's modifying space there and creating a condition which will lead to a force. So our simple definition is the electric field could be called, what a charge does to space, is a interesting way to put it. What a charge does to space. Let's think about it mathematically now. One reason we want it to find it mathematically is because physicists are actually lazy, is because we don't want to have to calculate the force every time we have a different value q here, we want a general number that always tells us the force. So that's why we calculate E, the electric field. The electric field created by Q doesn't actually care what size q is there. It's just doing something to space. So the way we do that mathematically is we define the electric field. So I'll use three bars, which means we've defined it that way, is the force that Q would apply to q, divided by the quantity of q. So really the electric field is just the force per unit charge, the force per unit of this little charge here. In books, this will often be called the test charge, and the reason is we're moving q around to test the force that you would get in each location. Here what it's doing is giving you a number that's a value that's useful, that doesn't care what q out here. Any q you put out here, no matter what its quantity, you can now get the force just by multiplying by the electric field. The unit for this is Newton per Coulomb. So the unit of the electric field has no fancy name, hasn't been named after anyone, it's just a newton per coulomb. You'll often see plots of the electric field and they're often very complicated, but you can actually generate them yourself just by thinking about the force. So here we have, say, a positive charge and a negative charge. If you want to start drawing the field, you just have to imagine how you have a test charge. What if I put a test charge here? What forces are going to feel? It's going to feel a force that way, right? A positive charge would fly away from the other positive charge, or a repulsive force, an attractive force towards that charge. A little test charge would feel a force like that. So I just drew the force, but I also drew the field, the vectors point in the same direction. All you're doing is dividing the force by a scalar number, which is the quantity of the test charge. If I put it here, put the test charge there, normally the force would just be straight up. Be straight up because we just apply Coulomb's law. However, it's also attracted this way. So you do a little vector addition in your head, a big force pulling it up, slightly smaller or somewhat smaller force pulling it that way. Therefore it's like that, and then down here it'd be the same thing, be like that. What if I put it here right in the middle? Then it's going to feel a positive, the positive charge is going to push it that way, the negative charge is going to pull it that way and you get a force like that, and you get a similar one down here, and if it's here it's going to get pulled straight towards minus q, but then pushed away a little bit, it's going to be like that. If you start to fill these in, you can actually draw the electric field. Since it's the force on a positive charge, it's always going to point away from a positive charge and towards a negative charge. This one would go out and I'm running out of room and it would come in like this. Then here, a positive charge there would go this way and it will actually never come back. So the field goes away from that charge and it goes towards that charge. So you can actually generate these plots just by thinking about forces and thinking about vector addition. So that when we may add a demo later when the humidity is low enough.