Chapter 24, Problem 070
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 $3.0 \times 10^6$ 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 $R = 5.2$ cm. Assume that the powder and its charge were spread uniformly
through the pipe with a volume charge density $\rho$. (a) 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.) (b) For the typical volume charge density $\rho = -1.9 \times 10^{-3}$ C/m$^3$, what is the difference in the electric potential between
the pipe's center and its inside wall?
(a)V=
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2
(b)V=
