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 .
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 = 1.1 x
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?
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 = -1.1 x
10-3 C/m3, what is the difference
in the electric potential between the pipe’s center and its inside
wall?