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(II) A thin cylindrical shell of radius $R_{1}=6.5 \mathrm{cm}$ is surrounded by a second cylindrical shell of radius $R_{2}=9.0 \mathrm{cm},$ as in Fig. $35 .$ Both cylinders are 5.0 $\mathrm{m}$ long and the inner one carries a total charge $Q_{1}=-0.88 \mu \mathrm{C}$ and the outer one $Q_{2}=+1.56 \mu \mathrm{C} .$ For points far from the ends of the cylinders, determine the electric field at a radial distance $R$ from the central axis of $(a) 3.0 \mathrm{cm},(b) 7.0 \mathrm{cm}$ and $(c) 12.0 \mathrm{cm} .$

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a) $E_{3 \mathrm{cm}}=0$b) $-4.5 \times 10^{4} N / C$c) $2.0 \times 10^{4} N / C$

Physics 102 Electricity and Magnetism

Chapter 22

Gauss's Law

Electric Charge and Electric Field

Electric Potential

Hossein S.

April 23, 2022

A thin nonconductive cylindrical shell of radius R=10 cm

University of Michigan - Ann Arbor

University of Washington

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 thin cylindrical sh…

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Two Concentric Cylinders T…

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A solid cylindrical conduc…

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(II) A very long solid non…

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Solid Cylinder A long, non…

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A long. nonconducting, sol…

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(a) Consider a uniformly c…

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(so $\mathrm{A}$ long, no…

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so we have. Ah, too cynical Shells 6.5 centimeters on nine city readers on the carry charge off minus 0.88 Micro pullem on 1.56 Michael Kula. We want to find the field in the distance is off 3.7 centimeters, which is inside the inner sitting down seven points of the city We does, which is in between the do cylinders on four point serious injury does, which is beyond the two cylinders. So let's start before we go ahead. Uh, remember that if you don't the last few problems that the eloquent feel for a cylinder is that the form your way by accident. Q. Is its charge enclosed? It is. If you consider a cylinder, we simply draw cards and surface that is another cylinder around it off radius are the 80 off. This course in service will be. Why are I'm still? And once he had this be used, Gaza's Tatum. You see that flux is equal. Do electric field time Syria, which is charged enclosed. Do you read it by its it or not? Using this formula, you get here No for Barbie when you are inside the inner cylinder. The charge enclosed is simply zero. So the electric field will also with zero or Bobby. When you're in between the two cylinders, your charge enclosed. It's simply minus zero point. A dating micro cooler. Hence the electric field will be using this form. Look you enclosed by a person or not, Carol. We contracted us. Took you excellent enclosed. You had it before, but it's not. How did so that we know that one by four banks that are not is 8.98 eight in tow in far nine Newton meters square. Put Coolum square toe in tow. The charge enclosed is 0.8 into tend bar minus six. We also have a minus. Same divided by are is someone simply reduces us with that suit of one single seven meters. I'm still is five meters. By turning this into a calculator, we can see that this is equal to minus 455 to 10 for using for cooling. Similarly, for party, I've used the same formula, but this time be charging closed is the some off the two charges. So one by four by external parties again, 8.988 Entertain part ninth. We have two into charging closed, which is 1.56 minus 0.88 micrograms. Do you want a fight where he gets his first? And they were So that's it. 112 meters times our readers. It's chancellor to be 2.0 into 10 part for Newton Occluded. This is the electrical outside the board, he surrenders. Notice that I've used to significant digits because that's what was used in the question.

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