The chocolate crumb mystery. Explosions ignited by electrostatic discharges (sparks)

Chapter 23, Problem 60

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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 3.0 106 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 r. (a) Using Gauss law, find an expression for the magnitude of the electric field 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 directed radially inward or outward? (d) For r 1.1 10 3 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? (The story continues with in Chapter 24.)

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