Hey, everyone. So by now, we should be pretty familiar with the idea of Electropotentials and potential differences. In this video, we're gonna cover an idea called equipotential surfaces which are really just these boundaries where you have the same potential. We're gonna see how that relates back to things like electric fields and I'm gonna show you a quick example. Alright? So let's get started. So the word equipotential, right, equi just means equal, potential means potential, basically just means that these are surfaces in which you have constant potential. Alright? So what this means here is that along these surfaces, ΔV=0. So what does that mean? So remember that for a point charge, the potential equation is kqr. Alright. So we just have a constant. We have the charge and basically what this means here is the potential is related to the distance away from the point charge. So if I took this point charge here and if I went a distance I'm gonna call this R and if I did that for a bunch of other locations like this and I would always go out the same exact distance r, then I would just end up with a circle of points like this. Mean, I could just connect them all. So if I went anywhere along this circle, I would measure the exact same potential. I'm just gonna go ahead and put a number to this just to make that a little bit simpler. I'm gonna say this is 10 volts. Alright? This is what an equipotential surface is. It's basically just this surface here in which you're gonna have constant potential as you go all the way around. Okay? And so the potential the equipotential surface for point charges just looks like circles. And by the way so there's a couple of things you should know. The one is that, you know, this is the equipotential surface for 10 volts, but there's actually an infinite number of them. Right? So there's another equipotential surface here and this is gonna be for, let's say, this is, 20 volts. Right? There's gonna be another one all the way out here and this is gonna be for 5 volts or something like that. Right? So there's an infinite number of them each corresponding to a very specific number for that potential. Alright? So, before we move on and draw the potential for a dipole, there's a couple of important rules that you need to know. They have to do with the relationship between the electric field and the potential. So just to sort of recap the equation for the electric field you may have seen, this is gonna be -ΔVΔx. What this just means here is that anytime you have a potential difference like you do along these equipotential surfaces here, So here you're gonna have a ΔV. Right? Because your potential is dropping from 20 to 10 to 5. Then you're gonna have an electric field and the electric field points outwards like this. Alright. So another way you could also see this equation written is ΔV=-eΔx. This is just taking this equation over here and rewriting it for ΔV. Now the one thing that's really important you need to know is that this electric field is always going to be perpendicular. So it's always perpendicular to the equipotential surfaces. So notice here how the electric field lines point outwards radially away from the point charge and the equipotential surfaces are circles so that anywhere along you could always basically just draw right angles between the electric field and the equipotential surface. Alright, So that's always going to be true. They're always going to be perpendicular. So what that means is that in some in some questions you might be given some sort of weird equipotential surface like this. So let's say this is your equipotential and you can actually figure out where the electric field is gonna point. We know that it's always gonna be perpendicular so in other words they're gonna be at right angles like this. So th
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25. Electric Potential
Equipotential Surfaces
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