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Field due to Equipotential Surfaces

Patrick Ford
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What's up, folks? Let's work out to this example problem with equal potential surfaces. So we've got these eco potential surfaces and we're told with the potentials of each of those surfaces, are were also given with the spacing between them is and using that information. We're supposed to figure out what the magnitude and the direction of the electric field due to those eco potential surfaces. Remember that there's two rules that we need to remember. The hours are perpendicular to the equal potentials, which means that we know the electric field is gonna point along this direction. But they also point in decreasing potentials. They point along decreasing potentials. So that means that the electric field has two point in this direction, which actually takes care of the second part of our problem. What is the direction of the electric field and in more precise terms, if we know that the electric field is gonna point in this direction, we could say, is that if this angle makes a 60 degree angle with the X axis, that means our electric field is actually gonna be pointing. We're gonna need to know this angle right here. So this is 30 degrees because these two things they're supposed to be perpendicular. So in other words, as for the direction so that's gonna be direction. Wow, I can't spell. So the direction the E field will point degrees below the negative X axis and that is the answer. As for the direction So how do we calculate the magnitude? How do we calculate what the electric field is due to potential surfaces or changing potentials? We use the equation. E is equal to negative. Sorry, Negative Delta V over Delta X. But in this case, we're Onley interested in the magnitude of the electric field because we already took care of the direction down here. So the magnitude of the direction of the electric field all we have to do is figure out what the change and potential differences is or the potential difference. And we have to figure out the spacing. So we already know that the between each successive sector here are each little specific segment who were going. We're changing five volts and we're doing that across the spacing of one centimeter, so it's gonna be 0.1 So these distances are 0.1 meters. So that means that the electric field is gonna have a constant magnitude off 500 volts per meter. By the way, if you're not familiar with this volts per meter unit, this actually, if you work out with the units of revolt is this actually also turns into Newtons per Coolum, just a different way to sort of express that. Okay, so that's how you figure out with the magnitude. And the direction of the electric field is due to eco potentials. So first, figure out what the potential differences are the spacings, and then just figure out your direction by going in towards towards decreasing potentials and perpendicular to those eco potential services. All right, let me know if you guys have any questions.