Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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The Chocolate Crumb Mystery Explosions ignited by electrostatic discharges (sparks) constitute a serious danger in facilities handling grain or powder. Such an explosion occurred in chocolate crumb powder at a biscuit factory in the 1970s. Workers usually emptied newly delivered sacks of the powder into a loading bin, from which it was blown through electrically grounded plastic pipes to a silo for storage. Somewhere along this route, two conditions for an explosion were met: 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?
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Transcribed Image Text:The Chocolate Crumb Mystery Explosions ignited by electrostatic discharges (sparks) constitute a serious danger in facilities handling grain or powder. Such an explosion occurred in chocolate crumb powder at a biscuit factory in the 1970s. Workers usually emptied newly delivered sacks of the powder into a loading bin, from which it was blown through electrically grounded plastic pipes to a silo for storage. Somewhere along this route, two conditions for an explosion were met: 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?
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