A charged nonconducting rod has a length L of 2.0 m and a cross-sectional area A of 8.0 cm?; it is placed along the positive side of an x axis with one end at the origin. The volume charge density p is the charge per unit volume, with the units of coulomb per cubic meter. a) How many excess electrons are on the rod if the rod's volume charge density pu is uniform with a value of –10 µC/m³? How does that compare to the total number of electrons you would estimate would be in the rod? (By compare, just a ballpark estimate- to within several orders of magnitude, factors of ten). b) What is an expression for the number of excess electrons on the rod if the rod's volume charge is nonuniform and is given instead by pN=ax³ where a is a constant? c) What value of a is necessary for the rod in part b to have the same number of excess electrons as the rod in part a)?

A charged nonconducting rod has a length L of 2.0 m and a cross-sectional area A of 8.0 cm?; it is placed along the positive side of an x axis with one end at the origin. The volume charge density p is the charge per unit volume, with the units of coulomb per cubic meter. a) How many excess electrons are on the rod if the rod's volume charge density pu is uniform with a value of –10 µC/m³? How does that compare to the total number of electrons you would estimate would be in the rod? (By compare, just a ballpark estimate- to within several orders of magnitude, factors of ten). b) What is an expression for the number of excess electrons on the rod if the rod's volume charge is nonuniform and is given instead by pN=ax³ where a is a constant? c) What value of a is necessary for the rod in part b to have the same number of excess electrons as the rod in part a)?

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter6: Gauss's Law

Section: Chapter Questions

Problem 52P: A long copper cylindrical shell of inner radius 2 cm and outer radius 3 cm surrounds concentrically...

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