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(II) A very long solid nonconducting cylinder of radius $R_{0}$ and length $\ell\left(R_{0} \ll \ell\right)$ possesses a uniform volume charge density $\rho_{\mathrm{E}}\left(\mathrm{C} / \mathrm{m}^{3}\right)$ , Fig. $34 .$ Determine the electric field at points $(a)$ outside the cylinder $\left(R>R_{0}\right)$ and $(b)$ inside the cylinder $\left(R<R_{0}\right) .$ Do only for points far from the ends and for which $R<\ell$

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(a)$\frac{\rho_{\mathrm{E}} R_{0}^{2}}{2 \varepsilon_{0} R},$ radially outward(b)$\frac{\rho_{\mathrm{E}} R}{2 \varepsilon_{0}},$ radially outward

Physics 102 Electricity and Magnetism

Chapter 22

Gauss's Law

Electric Charge and Electric Field

Electric Potential

Hope College

University of Sheffield

University of Winnipeg

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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(II) A very long solid non…

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(III) An extremely long, s…

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(II) A long cylindrical sh…

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A very long, solid cylinde…

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A very long, uniformly cha…

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(III) A very long conducti…

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(11) A very long solid non…

So we have a cylindrical rod off land Elf are not. We want to find a field, so let's go in the field for an hour. That is greater than our Not that is any point outside this cylinder. So for that we'll use a costume service that looks something like this. It's another cylinder in closing our cylinder. Why do you use this? The reason is because our system is cylindrical is symmetry. We expect the electric field Toby a radial e outwards on, depend only on the distance from the cylinder it is. We don't expect it to depend on who were these out on the cylinder. So sit on, such as Gaussian surface on these two services, the two circular surface onto ends. The electric field would be worth a call to the coast interfaces, and there will be no contribution to the flux, whereas the center circle the center surface, the electric field will be perpendicular to the area on. Hence, our we could find the electric field body easily. No, let's say that this really is off the cylinder is our as we've seen already. The flex on the two side service's will be zero so the total flux will be only do tow center surface. Let's say this Gaussian surface has excellent on you know that the radius is our the really is off this circular surface off the cynical surface would be x times the rate, the circumference of a circle. This would be to buy our This will be the area we need to multiply with electric field and we expect the electric field with seem all over the cylinder because of our political symmetry. We know that this is going to charge in closed be weighted by That's it. I'm not so if he extend this so if we extend this cylindrical surface all over the our cause in service all over the cylinder on we ignore the changing effect and we put X is equal to hell. We will see there e in tow to bite our and is equal to queuing. Yes, it or not. Now the charge enclosed is simply the charged density times the volume enclosed and you know that the volume in close will be the volume wealthy broad that is enclosed. That would be the area off the road that is fire north square times the distance so that would be road times. I are not square. Not so canceling you Common terms. We see that the electric field Israel are not scared by tow, vessel or not are And it's a directive Really upwards for Barbie be considered Art is less than are out Then we use the same gods and surface and we have The flux is equal. Do in tow Ellen to two pi r But this is a call to charge. Enclosed, derided by accident I'm in this case the charge in close will be. Let's say this is our cylinder with radius are not Let's say we're considering the distance. Distance are so we considered another surrender in this radius. So they were charged in clothes will be rolled times I ask Weird s it on? I'm sorry. And so that is rope. I ask where l by SL or not? No canceling. The comment comes. You can see that our is out until get scattered giving us He's a weirdo. Hello. I'm sorry. This is an r squared So through our by a salon Not again. This field is also director really over words

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