**Part 2: Potential of Long Conducting Cylindrical Shell**We will now study the electric field of a system consisting of an infinitely long solid conducting cylinder (1 cm radius) held at a positive potential \( V_0 = 10 \, \text{V} \) that is centered within a uniformly long conducting cylindrical shell (10 cm radius) held at ground (our zero of potential). You can picture the painted conductive paper as being a perpendicular slice of this infinitely long system.**Preliminary calculations:**2a) Using Gauss's Law, \((\oint \vec{E} \cdot d\vec{A} = Q_{\text{enc}} / \epsilon_0)\) show that the electric field outside an infinitely long charged conducting cylinder is given by\[\vec{E} = \frac{\lambda}{2\pi\epsilon_0 r} \hat{r}\](3)where \(\lambda\) is the charge per length, \(r\) is the distance from the axis and \(\hat{r}\) is the radial unit vector. Make sure you draw a Gaussian surface and show all your calculations, even the trivial ones. Note that there should be two different cylinders in your drawing - the real conducting cylinder and the Gaussian surface.

Answered: Image /qna-images/answer/8ce1abb9-1df3-4a3b-8c54-63422e219444.jpg

2a) Using Gauss's Law, (§ Ē·dÃ = Qenc/to) show that the electric field outside an infinitely long charged conducting cylinder is given by X 2πer Ē (3) where is the charge per length, r is the distance from the axis and is the radial unit vector. Make sure you draw a Gaussian surface and show all your calculations, even the trivial ones. Note that there should be two different cylinders in your drawing - the real conducting cylinder and the Gaussian surface. -F

2a) Using Gauss's Law, (§ Ē·dÃ = Qenc/to) show that the electric field outside an infinitely long charged conducting cylinder is given by X 2πer Ē (3) where is the charge per length, r is the distance from the axis and is the radial unit vector. Make sure you draw a Gaussian surface and show all your calculations, even the trivial ones. Note that there should be two different cylinders in your drawing - the real conducting cylinder and the Gaussian surface. -F

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

Question

**Part 2: Potential of Long Conducting Cylindrical Shell**

We will now study the electric field of a system consisting of an infinitely long solid conducting cylinder (1 cm radius) held at a positive potential \( V_0 = 10 \, \text{V} \) that is centered within a uniformly long conducting cylindrical shell (10 cm radius) held at ground (our zero of potential). You can picture the painted conductive paper as being a perpendicular slice of this infinitely long system.

**Preliminary calculations:**

2a) Using Gauss's Law, \((\oint \vec{E} \cdot d\vec{A} = Q_{\text{enc}} / \epsilon_0)\) show that the electric field outside an infinitely long charged conducting cylinder is given by

\[
\vec{E} = \frac{\lambda}{2\pi\epsilon_0 r} \hat{r}
\]

(3)

where \(\lambda\) is the charge per length, \(r\) is the distance from the axis and \(\hat{r}\) is the radial unit vector. Make sure you draw a Gaussian surface and show all your calculations, even the trivial ones. Note that there should be two different cylinders in your drawing - the real conducting cylinder and the Gaussian surface.

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