Subtitles section Play video Print subtitles - [Instructor] Okay, so we know that electrical charges create electric fields in the region around them but people get confused by electric field problems so you got to get good at at least two things here if you wanna proficient at dealing with electrical field. You should get good at determining the direction of the electric field that's created by a charge. If you've got some charge and you wanna know which way does that charge create an electric field, you should get really good at that. And if you know the direction of the field, you should get good at finding the direction of the electric force exerted on a charge. If there's some charge floating around in an electric field, you should be able to say, oh, okay, I can determine the electric force. Not too bad. If you get good at these two things, these problems are gonna be way easier and the whole process is gonna make a lot more sense. Let's figure out how to do this. How do you do these things? We'll do the first one first. Let's try to tackle this one. Let's try to figure out how do you determine the direction of the electric field that's created by a charge. Let's say we didn't know, this is what the electric field look like around a positive charge. I just gave this to you but how do we know that this is what the electric field's supposed to look like? What we can do is this. We can say that we know the definition of electric field is that it's the amount of electrical force exerted per charge. In other words, if you took some test charge, think of this Q as the test charge and we usually just make this a positive test charge so this is easier to think about. If you took some positive test charge into some region let's do that, let's put some positive test charge in here. We take this test charge, we move it around. All we have to do to figure out the direction of the electric field, since this Q would be positive, we can just figure out what direction is the electric force on that positive test charge. In other words, the direction of the electric field E is gonna be the same direction as the electric force on a positive test charge. Because if you know about vector equations, look at this electric fields vector, this electric forces vector. This electric field is just gonna adopt the same direction as the electric force as long as this Q is positive. If this Q were negative it would flip the sign of this electric force and then the E would point the opposite direction. But if we keep our test charge positive then we know, okay, the electric field's just gonna point the same direction as the electrical force on that positive test charge. Here's what I mean. We take our positive test charge. We move it around. If I wanna know the electric field at this spot right here, I just ask myself, which way does the electrical force point on that test charge? The electric force would point to the right since it's being repelled by this other positive charge over here. I know that the electric force points to the right, these charges repel each other. And since the electric force points to the right, that means the electric field in this region also points to the right. It might not have the same magnitude. The electric force might be 20 newtons and the electric field might be 10 newtons per coulomb but they have the same direction. And I can move this charge somewhere else, let's say I move it over here. Which way would the electric force point? Well, these positive charges are still repelling. I'd still have an electric force to the right. That electric force would be smaller but it would still point to the right and that means the electric field also still points to the right, it would be smaller as well but it would still point to the right. And if we wanna determine the electric field elsewhere, we can move our positive test charge, I'll move it over to here. I'll ask which way is the electric force on this positive test charge? That would be in this direction since these positive charges are repelling each other, they're pushing each other away so this positive always gets pushed away from this other positive charge. And so, that also means that the electric field is pointing in that direction as well. We keep doing this. I can move this somewhere else. I can move this positive charge down here. The charges repel so the electric force would point downward. And that means the electric field would also point down. If you keep doing this, if you keep mapping what's the direction of the electric force on a positive test charge? Eventually, you realize oh, it's always just gonna point radially out away from this other positive charge. And so we know the electric field from a positive charge is just gonna point radially outward, that's why we drew it like this. Because this positive charge would push some positive test charge radially away from it since it would be repelling it. Positive charges create electric fields that point radially away from them. Now what if the charge creating the field were a negative charge? So, let's try to figure that one out, let me get rid of this. Let's say the charge creating the electric field were negative, a big negative charge, how do we determine the electric field direction around this negative charge? We're gonna do the same thing, we're gonna take our positive test charge and we're gonna keep our test charge positive, that way we know that the direction of the electric force on this positive test charge is gonna be the same direction as the electric field in that region. In other words, the positivity of this test charge will just make it so that the electric field and electric force point in the same direction. And if we do that, I'll move this around. We'll just put it at this point here, we'll move this test charge here. Which way is the force on that test charge? This time it's getting attracted to this negative charge. Opposite charges attract so the electric force would point this way and since it's a positive test charge and it preserve the direction in this equation, that means the electric field also points in that leftward direction. And we can keep mapping the field we'll move the test charge over to here. The electric force this time is gonna point up because this positive test charges is attracted to this negative charge. And if the electric force points up, that means the electric field also points up in that region. And you'd realize the electric force is always gonna pull a positive test charge toward this negative creating the field around it. And because of that, the electric field created by a negative charge points radially inward toward that negative charge. This is different. Positive charge created a field that pointed radially away from because it always repelled the positive test charge. But a negative charge creates an electric field that points radially into because it's always attracting a positive test charge.