22.41 A very long, solid cylinder with radius R has positive charge uniformly distributed throughout it, with charge per unit volume p. (a) Derive the expression for the electric field inside the volume at a distance r from the axis of the cylinder in terms of the charge density p. (b) What is the electric field at a point outside the volume in terms of the charge per unit length A in the cylinder? (c) Compare the answers to parts (a) and (b) forr = R. (d) Graph the electric-field magnitude as a function of r from 3R. r= 0 to r =
22.41 A very long, solid cylinder with radius R has positive charge uniformly distributed throughout it, with charge per unit volume p. (a) Derive the expression for the electric field inside the volume at a distance r from the axis of the cylinder in terms of the charge density p. (b) What is the electric field at a point outside the volume in terms of the charge per unit length A in the cylinder? (c) Compare the answers to parts (a) and (b) forr = R. (d) Graph the electric-field magnitude as a function of r from 3R. r= 0 to r =
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter25: Gauss’s Law
Section: Chapter Questions
Problem 48PQ
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Hint:To check your answers to parts (a) and (b), a correct answer to part (c) should allow you to further write ρ = Q /LπR2, where Q is the total charge on the cylinder and L is the length of the cylinder.
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