A long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire. The wire has a charge per unit length of 2, and the cylinder has a net charge per unit length of 21. From this information, use Gauss's law to find the following. (Use any variable or symbol stat above along with the following as necessary: o and m.) (a) the charge per unit length on the inner surface of the cylinder Ainner - (b) the charge per unit length on the outer surface of the cylinder Aouter- (c) the electric field outside the cylinder a distance r from the axis magnitude E- direction --Select-- V

A long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire. The wire has a charge per unit length of 2, and the cylinder has a net charge per unit length of 21. From this information, use Gauss's law to find the following. (Use any variable or symbol stat above along with the following as necessary: o and m.) (a) the charge per unit length on the inner surface of the cylinder Ainner - (b) the charge per unit length on the outer surface of the cylinder Aouter- (c) the electric field outside the cylinder a distance r from the axis magnitude E- direction --Select-- V

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

**Title: Application of Gauss's Law to a Cylindrical System**

**Problem Statement:**
A long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire. The wire has a charge per unit length of λ, and the cylinder has a net charge per unit length of 2λ.

Using this information, apply Gauss's law to find the following:

(a) **Charge per Unit Length on the Inner Surface of the Cylinder:**
- \(\lambda_{\text{inner}} = \) [ ]

(b) **Charge per Unit Length on the Outer Surface of the Cylinder:**
- \(\lambda_{\text{outer}} = \) [ ]

(c) **Electric Field Outside the Cylinder a Distance \( r \) from the Axis:**
- Magnitude \( E = \) [ ]
- Direction: [Select]

**Instructions:** Use any necessary variable or symbol stated above. Utilize constants such as \( \varepsilon_0 \) and \(\pi\) for calculation purposes.

**Diagram Explanation:**
Though not illustrated here, imagine a cross-section showing:
- A central wire with a uniform linear charge density \(\lambda\).
- An encompassing cylindrical shell with a net charge per unit length of 2λ.
- Indicating surfaces for charges and regions for evaluating the electric field.

**Topics Covered:**
- Gauss's Law
- Electric Fields
- Cylindrical Symmetry
- Charge Distribution

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