1. The magnitude of an electric field became 3.0 x 106 N/C or greater, so thatelectrical breakdown and thus sparking could occur.2. The energy of a spark was 150 mJ or greater so that it could ignite the powderexplosively.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 ofradius R = 5.0 cm. Assume that the powder and its charge were spread uniformlythrough the pipe with a volume charge density p.a. Using Gauss' law, find an expression for the magnitude of the electric field E inthe 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 anddetermine 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 rfrom the center of the pipe. (The electric potential is zero on the grounded pipewall.)g. For the typical volume charge density p = -1.1 x 103 C/m³, what is the differencein the electric potential between the pipe's center and its inside wall?

a) b) Hence, magnitude of E increases with increase in r.

Answered: y of a spar 1. he first com m of negati…

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y of a spar 1. he first com m of negati n. Assume with a volu

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Proper Length

The theory of special relativity explains the connection between space and time to objects that move in a straight line at a constant speed. The objects move at the speed of light. When an object approaches light speed, its mass is endless and cannot move faster than light. The most crucial postulate of Einstein's special relativity is that the laws of nature do not change in each frame of reference.

Question

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?
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 p = -1.1 x 103 C/m³, what is the difference
in the electric potential between the pipe's center and its inside wall?

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