The chocolate crush mystery. Explosions ignited electrostatics 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. At the factor workers usually emptied newly delivered sacks of the powder into a loading bin, from which it was blown th ‘ugh grounded PYC pipes to a silo for storage. Somewhere along this route, two conditions for an explosion were met: (I) The magnitude of an electric field became 3.0 X 106 N/C or greater so that electric breakdown and thus sparking could occur. (2) The energy of a spark was 150 ml or greater so that it could ignite the powder explosively Let us check for the first condition in the powder flow through the PYC pipes. Suppose a stream of negatively charged chocolate crumb powder is blown through a cylindrical PYC pipe with radius R = 5.0 cm. Assume that the powder and its charge are 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 the radial distance r from the center of the pipe. (b) Does the magnitude increase or decrease with (c) Is the electric field E directed radially inward or outward? (d) Assuming a volume charge density p of magnitude 1.1 X 10·’ C/m’.(which was typical at the biscuit factory), find the maximum magnitude of the electric field and determine where hat maximum field occurs. (e) Could sparking occur and if so where The story continues with Problem.