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y of a spar 1. he first com m of negati n. Assume with a volu

y of a spar 1. he first com m of negati n. Assume with a volu

College Physics
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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1. The magnitude of an electric field became 3.0 x 106 N/C or greater, so that electrical breakdown and thus sparking could occur. 2. The energy of a spark was 150 mJ or greater so that it could ignite the powder explosively. Let us check for the first condition in the powder flow through the plastic pipes. Suppose a stream of negatively charged powder was blown through a cylindrical pipe of radius R = 5.0 cm. Assume that the powder and its charge were spread uniformly through the pipe with a volume charge density p. a. Using Gauss' law, find an expression for the magnitude of the electric field E in the pipe as a function of radial distance r from the pipe center. b. Does E increase or decrease with increasing r? c. Is E directed radially inward or outward? d. For p = 1.1 x 10³ C/m³ (a typical value at the factory), find the maximum E and determine where that maximum field occurs. e. Could sparking occur, and if so, where? From the answer to part (a) of the problem, f. Find an expression for the electric potential as a function of the radial distance r from the center of the pipe. (The electric potential is zero on the grounded pipe wall.) g. For the typical volume charge density p = -1.1 x 103 C/m³, what is the difference in the electric potential between the pipe's center and its inside wall?
Transcribed Image Text:1. The magnitude of an electric field became 3.0 x 106 N/C or greater, so that electrical breakdown and thus sparking could occur. 2. The energy of a spark was 150 mJ or greater so that it could ignite the powder explosively. Let us check for the first condition in the powder flow through the plastic pipes. Suppose a stream of negatively charged powder was blown through a cylindrical pipe of radius R = 5.0 cm. Assume that the powder and its charge were spread uniformly through the pipe with a volume charge density p. a. Using Gauss' law, find an expression for the magnitude of the electric field E in the pipe as a function of radial distance r from the pipe center. b. Does E increase or decrease with increasing r? c. Is E directed radially inward or outward? d. For p = 1.1 x 10³ C/m³ (a typical value at the factory), find the maximum E and determine where that maximum field occurs. e. Could sparking occur, and if so, where? From the answer to part (a) of the problem, f. Find an expression for the electric potential as a function of the radial distance r from the center of the pipe. (The electric potential is zero on the grounded pipe wall.) g. For the typical volume charge density p = -1.1 x 103 C/m³, what is the difference in the electric potential between the pipe's center and its inside wall?
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