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A metal sphere carrying an evenly distributed charge will have spherical equipotential surfaces surrounding it. Suppose the sphere's radius is 50.0 $\mathrm{cm}$ and it carries a total charge of $+1.50 \mu \mathrm{C}$ (a) Calculate the potential of the sphere's surface.(b) You want to draw equipotential surfaces at intervals of 500 $\mathrm{V}$ outside the sphere's surface. Calculate the distance between the first and the second equipotential surfaces, and between the 20 $\mathrm{th}$ and 21 $\mathrm{st}$ equipotential surfaces. (c) What does the changing spacing of the surfaces tell you about the electric field?

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Physics 101 Mechanics

Physics 102 Electricity and Magnetism

Chapter 18

Electric Potential and Capacitanc

Kinetic Energy

Potential Energy

Energy Conservation

Electric Charge and Electric Field

Gauss's Law

Electric Potential

Capacitance and Dielectrics

Cornell University

Hope College

University of Sheffield

McMaster University

Lectures

13:02

In physics, potential energy is the energy possessed by a body or a system due to its position relative to others, stresses within itself, electric charge, and other factors. The unit for energy in the International System of Units (SI) is the joule (J). One joule is the energy expended (or work done) in applying a force of one newton through a distance of one metre (1 newton metre). The term potential energy was introduced by the 19th century Scottish engineer and physicist William Rankine, although it has links to Greek philosopher Aristotle's concepts of potentiality. Potential energy is associated with forces that act on a body in a way that the work done by these forces on the body depends only on the initial and final positions of the body, and not on the specific path between them. These forces, that are called potential forces, can be represented at every point in space by vectors expressed as gradients of a scalar function called potential. Potential energy is the energy of an object. It is the energy by virtue of a position relative to other objects. Potential energy is associated with restoring forces such as a spring or the force of gravity. The action of stretching the spring or lifting the mass is performed by a force that works against the force field of the potential. This work is stored in the field, which is said to be stored as potential energy.

18:38

In physics, electric flux is a measure of the quantity of electric charge passing through a surface. It is used in the study of electromagnetic radiation. The SI unit of electric flux is the weber (symbol: Wb). The electric flux through a surface is calculated by dividing the electric charge passing through the surface by the area of the surface, and multiplying by the permittivity of free space (the permittivity of vacuum is used in the case of a vacuum). The electric flux through a closed surface is zero, by Gauss's law.

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07:22

Okay, so this is a nice problem. It's, uh I think it's really instructive for relating electric fields toe potential. No. So I'm kind of excited to share it. So, uh, we're given that this fear has a total charge Q of 1.5 times 10 to the minus six cool homes. And that's radius is pretty big 60.5 meters. And first we want to get the potential at the surface. So that's just gonna be cake you over our plugging them into a calculator. I got 27,000 volts per meter. And then the second question asks us, Thio, calculate the distance between the first and second AC with potential surface. And so the the potential surfaces air like rings around this fear because by symmetry, they're gonna all have the same potential. So, um, they were going to space the lines out. Oh, I wish I had a drum. Actually, I'm gonna redo this drawing so I can actually fully do this drawing here with the like, a quick potential lines. So I'm gonna put this in the middle. Okay, so here it is, and then our equity potential lions all draw on red, so as we'll see in the problem, the Lions will start off close, and then they'll sort of taper off with increasing distance. So hey, I mean, I should have been my circle smaller. So if if I, this distance should probably be a bit bigger, let me go ahead in redraw that, um yeah, I know. I should've made this smaller. I'm not going to do it now, though, Uh, I'll just try to clean it up of it, So this Yeah, should be, like a kind of a bigger distance. Yeah, OK. And so, for part A, they want to get the distance between the first and second lines. And so, um, at the second line, V is equal to 27,000 minus 500 which is 26 groups. Okay. Uh oh. Oh, I just made a nice discovery. Um, okay, maybe I'll have a better time using the pen now. Um, no, because there's always, like, this lag with the pen that I kind of have to contend with. Um, and it makes my writing either slow or sloppy. So I try to optimize in between slow and stop sloppy. Um, so Okay, but holding this down. Um, where what was I doing? Why don't have a two? Okay, so it shouldn't be too. Oh, yeah, right. I was gonna write out the actual number, so Oh, whoops. Okay, Sorry. I'm gonna play with this later, and I'll just kind of use my old method of writing. So that's 26 500 bullets. And in that cake you over are So then our is equal to K Q over 26 500. So if I played that into a calculator, I get 0.51 meters. And, um so that's the distance between the first track potential lines and then between the 20th and 21st. So, um, for the 20th line, we need to subtract. Given that the first liquid potential line is at the surface for the the 20th we need to subtract. I was gonna sing 19 times, 500 so V is equal to 27,000 minus, um, should be 19 or 20 times 500. So the first line is you want to subtract minus 500 times one, or that would be the second lines. And then the third line is subtracted 1000 so yeah, um, by the 20th line. You want to subtract 19 times 500 race this. It's not super relevant or clear. So, um, doing that I obtained that this was equal to Did I get Oh, yeah. 17,500. And then again, all just start the sequel that cake you over our So, for our by just rearranging in the same way. And then I obtained that are is equal two 0.771 And then for the next line that would just be via 17,000. So obvious 17,000 and then therefore are is equal to que que over 17,000 And then putting that into a calculator, I obtained 0.794 And so you got that The the spacing between those two accurate potentials. It's the difference between these two, which is 0.0 to to so too 27 Well, I was pretty sloppy. Let me just go ahead and rewrite this

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