 In this video, we're going to figure out how the equipotential surfaces are going to look like when we have multiple charges. Say positive and another positive or a positive and a negative or a negative and negative charges. Now just a quick recap, we've already defined in previous video what equipotential surfaces are. These are three-dimensional surfaces which have the exact same potential everywhere on top of it. And an example would be for us, you know, a point charge, the equipotential surfaces would be spheres. And one of the amazing properties of these surfaces we've seen is that these surfaces are always perpendicular to the field lines everywhere. And if you're not familiar with this concept or you need a refresher, feel free to go back and check that, you know, check our previous video out. But anyways, now let's bring in another positive charge and our goal is to figure out logically using this property. We're going to use this property, how the equipotential surfaces is going to change. So if I bring in another charge, so let's say here's another charge over here. You know by now that the presence of this charge is going to change the field lines, right? You may have seen earlier that the field lines are going to sort of change. Maybe these field lines are going to push on each other and so the field lines are going to move upwards like this over here. These field lines are going to move downwards like this over here and so on and so forth. And because the field lines change and because the equipotential surface should always be perpendicular to the field lines, that means our equipotential surfaces are also going to change. So the question is, how would it change? We can't draw an exact thing, but we want to get an intuition for, you know, how it may change and what the rough surface would look like. So let me draw the new field line properly over here. Here's what our new field looks like, somewhat like this. Now what I want to do to figure out what the new equipotential surface looks like is, I want to look at one of these field lines and compare it with what it was before and then see how the potential surface would change, the surface would change. So let me get rid of all the field lines and just compare it with one of the field lines over here. So if I zoom in, okay, so this was our earlier equipotential surface when the field line was like this and this was 90 degrees, this was perpendicular. Let me use white, this was perpendicular. But now notice once it has curved, this is no longer perpendicular. So to make this perpendicular, you can kind of imagine this part of the equipotential surface must be somewhat, let me draw that, okay, somewhat like this, somewhat like this. Can you see that? Then it'll be again 90 degrees. And the same thing would happen somewhere downwards. So if I draw one more field line over here, then this equipotential surface, this part of the equipotential surface should also, to make sure it stays 90 degrees, should bend somewhat like this so that this would stay 90 degrees. And immediately from this, you can kind of see that our new equipotential surface would sort of kind of look somewhat like this. So you can kind of see that it'll be bulged out towards that other positive charge. Can you see that? Okay, now let's see what happens somewhere else. So let me show you one more field line over here. Now let's look at what happens over here. Well, again, notice it's no longer 90 degrees. To maintain that 90 degrees over here, this part of the equipotential surface should be somewhat, somewhat like this so that this will be 90 degrees again. And finally, if I draw one more, something very similar at the bottom, at the bottom, you're going to get something very similar over here. It should be like this to maintain that 90 degrees. And now if I attach, if I complete this figure, you can see it's going to be a little bit squashed behind. Oh, so can you see what the picture looks like? It's kind of like, it's kind of like going to be an egg-shaped equipotential surface. Now this doesn't look very nice, so let me zoom back out. This doesn't look very nice, but if I get rid of it, this is what it would look like, somewhat like this. This would be the new equipotential surface. Let me get rid of that. And so if I get rid of our, let me get rid of this. All right, there we go. This is what the new equipotential surface looks like. So it's kind of like bulge, it's kind of like egg-shaped, but it's kind of like bulge towards this one. And the same thing would happen over here. Same thing would happen over here. And so notice what has changed. So let's try and compare what it was before to what it is now. So if I compare earlier, if I only consider individual charges and I don't consider the effects on each other, it would be spheres. But when I do consider the effects on each other, look at what happens. This was before, this is now. So it's kind of like the equipotential surface is trying to merge with each other. Kind of like a drop of water. Can you see that? Okay. And in fact, if I draw more equipotential surfaces, they will indeed merge with each other. You can see they're slowly merging. And if I go very, very far away, it's pretty much going to look circular. I have a simulation over here. Let me show you. In this simulation, we can visualize equipotential surfaces. So let me put a positive charge over here. And we get spherical equipotential surfaces. The brightness represents how strong the field is over here. But what's important is spherical because there's one charge. Let me put another charge over here and you can see another spherical. You can imagine they're very far away. And so they're kind of not interacting with each other. But now let's see what happens when I bring them close to each other. Can you see that X-shape being formed over here? Look at that. Look at that. Look at that. That's the X-shape being formed. That's exactly what we saw. And I can now keep them over here and draw a few equipotential lines. And let's see what happens. Let me go ahead and draw that. And there you go. Close to the charges. It's pretty circular because they're extremely dominant. You go farther away. It's kind of X-shaped. And then they slowly merge. And if you go very far away, it's going to become more and more circular. Because if I go very far away, it feels like these two charges are very close to each other. It feels like a single charge. And so the equipotential surface of a single charge is pretty much spherical. Okay. Here's a question for you. What's going to happen if I made one of these charges much stronger than the other? So let me show you. So here is I'm going to add more charges over here. More charge. This is two, three charges. Say four charges over here. Okay. What's going to happen if I bring them close to each other? Can you kind of visualize what the new equipotential surface is going to look like? All right. Let's see. I can just do that. And again, we can see it's X-shaped and it's merging. But you can kind of imagine this is huge. This is small. And so now if I were to draw the equipotential lines, you can see the difference. Because this is more dominating, it is more circular. And this is becoming very quickly X-shaped. And then finally they merge together and you get circular. A quick question for you. Instead of two positive charges, what if I kept two negative charges? What do you think is going to happen? Do you think things are going to change or things are going to remain the same? Can you pause and think about it? Here's the thing. If I kept two negative charges, the field lines are going to look pretty much the same except that the lines are going to just reverse in its direction. Right? And therefore nothing much would change. So the equipotential surface should look exactly the same. So let me get rid of these charges. So here's one negative charge. Here's another negative charge. You can imagine blue to be that of a negative potential. Again, spherical equipotential surfaces. If I bring them close, notice they merge. And everything you saw for two positive charges would be the same for two negative charges. So it'll be the same for light charges. Now comes the question. What happens if you have one positive, one negative? Ooh, that's interesting. So going back to our drawing board. One of these charges were negative of equal magnitude. So it's a dipole. How will the equipotential surface change? Can you again pause the video and think about how the field lines would change and as a result how the new equipotential surface would look like? It won't be like these. So pause and think about it. All right. Okay. So let me get rid of these surfaces. Now the big change is going to be instead of field lines curving away from each other, they're going to start curving towards each other. Field starts from positive and goes into negative. Let me show you that. Somewhat like this. Which means now on this side we'll get the equipotential surface to be flatter on this side. And on this side it'll be sort of bulged. Not exactly bulged, but so it'll be the other way around. So let me show you what I mean. Somewhat like this. Does that make sense? And if I were to draw more equipotential surfaces, you can see as it comes closer and closer to the center of the dipole, it's going to get flatter and flatter. In fact right at this point you can see the field lines are all parallel to each other and so you'll get a plane sheet over here. So let me show you that. This is what it would look like. And these would never merge with each other ever because one is producing a positive old potential, one is producing a negative potential. In fact I hope you can see right in between the potential is going to be zero. I hope I've drawn a green over there. It's kind of like neutral potential. And again we can go back to our simulation. So this time we'll bring in one positive charge, one negative charge and you can kind of see that extension happening on the other side. You can kind of see flattening over here. Now let me draw the equipotential surfaces. There you go. Not exactly like what we drew in our drawing board, but you can kind of see it's becoming flatter over here. And again, what if I made one of the charges stronger and one of the charges weaker? If I made the positive charge a little stronger in magnitude, you can kind of see it's going to, you know, this positive would start dominating over this negative and again let me show you that. So let me add more positive charge over here. You can kind of see it's, the positive starts dominating and again let me draw the equipotential surfaces. And there you go. This is very interesting. Over here you see a similar trend. It's getting extended on the opposite side like we saw before with the dipole. But you see more effect over here compared to this one because this is dominating. But if you go far away, they eventually merge. Why is that happening? Why is it merging? One's positive and one negative. That's because if you go far enough, the positive charge dominates and then you start having positive potential. And so that's why eventually if you go far enough, then these two charges merge together. Together they sort of look like a single positive charge and eventually you start getting spherical positive equipotentials.