Electric Field Lines - Online Tutor, Practice Problems & Exam Prep

Electric Field Lines

Hey, guys, with this video, I want to talk more about electric field lines, what they represent and how we actually construct them in arrangements of charges. There's not a whole lot of calculations that we will do in this video, but it definitely is a conceptual point that you need to know. So let's go ahead and check it out. So just remember that electric field lines always point from whoops. They always point from positive charges and towards negative charges. Now, if you've seen our video on parallel plate capacitors, you saw what happened when we have a positive plate and a negative plate separated by some distance; we would just end up with a uniform electric field that points from the positive plate towards the negative plate. If you haven't seen our video, that's perfectly fine, because you should remember that positive charges always produce electric field lines that point outwards, whereas negative electric charges always produce electric field lines that point inwards. All right, so another way to visualize these electric field lines is that they give us the direction that a positive charge would go now. Just remember that the force of any charge that we put in an electric field is just related to Q times the electric field. But just remember that these EFS and these are actually vectors. And what do we know about vectors? Vectors always have magnitudes, and they also have a direction. So how does something like a positive or negative sign of this Q affect that direction? Well, basically, if you have a Q and that's a positive number, then that means that all of these things over here end up being positive. So what I mean by that is that if you have this positive charge here with some Q, then it's going to experience a force that goes in the same exact direction as the electric field. So that means that F points in the same direction as E and any positive charge. An electric field will just point towards the right. It'll go. It'll go with the flow, whereas if you have a negative sign that's out here. So if you have Q equals negative, then basically this negative sign serves to reverse the direction of F and E right. So if we ever have a negative sign, negatives and positives in physics usually associate with the direction. So that means if you have a negative charge, it's actually going to want to go against the flow. So that means the force is going to point in the opposite direction as E. So if you have an electron or a group of electrons or anything like that, they're always going to want to go against that flow. All right? Does that make sense? So for the rest of this video, we're going to go ahead and construct these electric field lines, and basically just doing one long example. But it's definitely something that you might run into on a test or homework or anything like that. So we're supposed to draw the electric field lines for an electric dipole. So that's going to be part A. And I've got all these points of interest. All these black dots represent just points of interest that we're going to look at the electric field lines. So what I'm going to do is I'm just going to use Red to mark positive lines, and I'm going to use blue for negative field lines. And then I'm going to use green for the Net electric field lines. Now, the other thing we have to remember is that the electric fields due to any charge is just k Q divided by R squared, which means that it gets weaker with distance very, very quickly. All right, so let's go ahead and just start. Start off with all the positives. So we know that the electric field from this positive charge is just going to produce outward vectors in all of these cases right here. All of these points of interest, the electric field lines. You're just going to point away from that positive test charge from that from that positive charge? Right? So we've got that's and then they start to get a little bit weaker over here and then here, and then it's going to be strong over here. It's going to be weak and then even weaker. And then over here points away, actually should be smaller, like that's and then here it's going to be very, very, very small, then, yeah, cool. So that's it for the positive lines. Let's go ahead. Do the same thing for the negative lines. The negative lines actually have electric field lines that will point towards it. So that means that these guys will actually be very strong because remember this distance right here between this point of interest, and this charge is going to be way bigger. Sorry, way smaller than this distance with this positive charge. So that means, essentially, that this blue line is going to be overpowering the red one. So that's why these electric field lines were stronger over here. These really, really strong over here. Kind of like how these were strong. And then they start to get weaker over on the left side. Okay? And a couple more on these get really, really weak. Something like that's okay and done. Great. So now what we can go ahead and do is construct what the net electric field is going to be the easiest place to start is going to be in the middle because these two field lines basically just point in the same exact direction. So it means that the Net electric field is going to point towards the rights. And now we can see that anywhere that we look along the midline right here we can use another property of electric fields and electric charge that we've used before, which is called symmetry. Remember that along this midline here, which is directly between these two positive charges anywhere you look, the electric fields are going to have a cosine of the angle with the horizontal direction, we can always use the cosines and sines basically set up the components of that vector. And we know that the vertical components are always going to cancel out. So what that means is that the electric field, the net electric field anywhere along the midline is going to be pointing towards the rights and it gets weaker with distance. So it's going to look something like this, and then this one is going to be a little bit weaker. So this is the easiest one because we know there's always going to point towards the right. Now over here, anywhere off of the midline. You can't exploit that symmetry. So we're just going to have to take a look at the vectors right here. We can just group up these vectors like that. We could group these vectors like this. They're going to look something like that. And then over here it's going to look something like this and then this, and that's basically it. Great. So now we've constructed all the net electric field lines. We can start to see a pattern between some of these some of these points of interest. So basically, we have this electric field going up. Then it goes to the right, and then it goes down towards the negative charge. So basically, what happens is that you can sort of trace the swooping lines, these arcs that travel through those points from the positive charge towards the negative charge. Now, you could do this basically with any points. So basically curves outwards like this and then goes down towards the negative charge similar to over here and then basically this whole process or this whole sweeping arc thing is symmetrical. So the same thing is going to happen over here. You're going to have an arc like this. It's going to go towards all the charges and go towards the negative. And you basically could just draw all of these arcs over here. So basically, we see how these how these swooping arcs go from the positive towards the negative. But on either side, what happens is that the electric field lines basically dominate from the charge that it's closest to. So basically, these lines start to look like how they normally would for electric fields. Except there's a little bit of a curvature to these lines. So it's basically like that and like this and like this. So all these lines go in words like that because of the negative charge. And then the same thing happens on the left side, but to the opposite. Now, these electric field lines, we're going to go outwards like this, and it's going to be like that just like that. And these electric field lines will point outwards. So this is basically what the electric field of an electric dipole looks like. It's very interesting. So we figured out what part a is and now in part B, what we're supposed to do is figure out where an electric where an electron would be accelerated inside directly between this electric dipole. So, in other words, if I were to drop a little electron over here, which the queues equal to negative e, which way would it go? Remember that negative charges always want to go against the flow of the electric field. In this case between the electric dipole, it always goes from the positive to the negative points in this direction. So that means this charge right here will experience a force that points in the opposite direction, so it's going to point to the left, and that's the answer. Another way to think about this is we do know that negative charges will repel each other. So if this is an electron, a negatively charged particle, it's going to want to repel from the negative and go towards the positive. So everything makes sense. All right, guys, that's it for this video. We're going to go ahead and do another example. Let me know if you guys have any questions.

Draw the field lines for a pair of identical, positive charges.

Alright, guys, welcome back. So, using the last video, we're going to go ahead and figure out what the field lines are for two identical positive charges. Now, if you're going to work this thing out together with me, go ahead and just draw these black dots in case you haven't already because it's going to help us visualize what the electric field lines are. We know that the electric field lines for positive charges? I'm just going to go ahead and stick to that convention of using the last video and use them in red, and then we have no negative charges. So there's no blue lines and then the net lines, they're just going to be in green. All right? So just go ahead and pick these dots right here, and we're just going to go ahead and start solving them one by one. So from this positive charge, we're going to have electric field lines that point outward like this, and then we're going to draw them everywhere. Right? So we've got strong electric field lines over here that always point away, and then over here, we've got some weaker ones like that. And then we've got even weaker ones over here, and then we've got even weaker ones all the way out here. Right? So this is what the electric field lines would look stronger, closer to the positive charge and then weaker, the further you go away. So now we have the same electric field lines from the positive charge, we have red lines, but these were going to point in the opposite direction. So they are going to cancel out and actually directly in the middle right here. They're just going to go ahead and draw them everywhere. Here, they're going to be strong here. They're going to be like that like that. And then we've got strong field lines this way. And then over here, strong field lines this way, strong field lines that way. And then it gets weaker a little bit over time. So you get slightly weaker lines and these are going to be really weak all the way out here. Okay, I think that's it. I got all of them. Awesome. So we know that along the midline here, if we pick these dots that are symmetrically placed, we know that the horizontal to the vertical components are always going to cancel. So right here, directly in the center, we actually have the same exact vectors even though they possibly don't look the same. They are equal and opposite and magnitude if they are positioned if this dot is positioned right in between them. So we know that \(E = 0\) right here. There is no electric field, whereas anywhere that you go away from this there is going to be some component of the electric field. We know these two things. The horizontal components. Sorry, the horizontal components are going to cancel, actually, So you see how we have this symmetry right here. If you were to break this up into the angles and use sine and cosine to break this up into its horizontal and vertical components, these things would have the same exact vertical components. Which means that the horizontal component which just add up in this direction and produce a field like that way and the same thing would happen all the way over here. Now, anywhere else, we basically had just go ahead and add these vectors together, tip to tail, sort of like, you know, just like this. So we've got these electric field lines like that. And then we've got over here. They're going to point in this direction and in this direction, and then over here, it's going to go in this direction like that. Okay, so let's see what's going on here. We've got these two electric. You have these two positive charges and they're basically their electric field lines. Want to push off of each other? So we know that anywhere you go along, this midline here, the electric field is going to point upwards anywhere over here. But then when you get downwards, it's going to point in the downward direction. And what happens is that the closer you get to this midline, it's sort of like approaches. The swooping arcs sort of start to approach this asymptotic vertical direction. So it's like these lines are trying to smush each other in so that they smear vertically like that. So that's what these swooping arcs will do. And you can sort of draw them for anywhere, along or anywhere that sort of going alongside that midline. So these things, basically their electric field lines are almost like getting crammed in together, and they're like trying to push off of each other. And so they sort of group up and do that. So they get smushed along this midline right here. And this is where the electric field lines are going to point. Whoops. That's not downwards. And the same thing is going to happen over here. All right, And then anywhere outside of those outside the middle, you're basically going to have these electric field lines that start to push off of each other just like this. We've got a charge right here. If you have a point of interest, the electric field lines would point this way from the positive charge. And also away from this positive charge, these lines would actually swoop away from this positive charge. And the same thing happens over here. What sweeps away like that and the same exact thing happens here, but just reversed. So now you have this effects right now like this, and then you have the opposite. All right. So hopefully you guys understood what these electric field lines will look like for these two positive, identical charges. By the way, if these were two negative charges, this would look exactly the same except all of the directions would be reversed. So you would have literally the exact same field lines, the exact same swooping arcs, except all of these things would just point towards instead of away. All right, let me know if you guys have any questions with this.

Field Lines of Electric Quadrupole

Hey, guys, let's do another example of drawing electric field lines. Okay, draw the electric field lines for the four charges shown below. This arrangement is known as an electric quadrupole. Okay, so just like we had an electric dipole, which was two charges, we have an electric quadrupole, 'quadrupole' being four charges arranged as shown.

Okay, the important thing to remember here is that the electric field decreases pretty rapidly with distance. Okay, the electric field is what we call directly proportional to one over R squared. That means that when R doubles, the two is actually squared, so E becomes 1/4. When R triples, E becomes 1/9. So, it's not just that it drops off linearly; it drops off very, very rapidly like this. This is the electric field versus R, basically what I'm getting at is that only nearby charges affect the electric field lines. So, what we can do is we can actually look at this as a collection of multiple dipoles and our electric field lines. They're going to look like that.

Okay, so let's start these dipole lines. They're going to go from the positive to the negative. It's the other direction. Okay, these dipole lines are going to go from the positive to the negative; these dipole lines are going to go from the positive to the negative and these dipole lines are going to go from the positive to the negative with very, very little influence.

Now, the closer we get to the center, the more it looks like a dipole; sorry, the less it looks like a dipole, while the more we get away from the center, the more it looks like a dipole. The further away, this actually looks even more like a dipole. The further away, this looks even more like a dipole. This one looks even more like a dipole. Yeah.

Okay, now what happens as we get near the center? Well, at the very center, we have an electric field down due to the top positive charge, we have an electric field up due to the bottom positive charge, we have an electric field to the left due to the right negative charge, and we have an electric field to the right due to the left negative charge. Okay? Because all these charges are the same and because we're looking at the direct center, so they're all the same distance from the center, we know that all of these electric fields cancel. So the electric field is just going to be zero at the center of the quadrupole. Okay, so this is what it looks like. It looks like a collection of dipoles with a zero electric field at the center.