University Physics (14th Edition)
14th Edition
ISBN: 9780133969290
Author: Hugh D. Young, Roger A. Freedman
Publisher: PEARSON
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Textbook Question
Chapter 22, Problem 22.41P
A very long, solid cylinder with radius R has positive charge uniformly distributed throughout it, with charge per unit volume ρ. (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 λ in the cylinder? (c) Compare the answers to parts (a) and (b) for r = R. (d) Graph the electric-field magnitude as a function of r from r = 0 to r = 3R.
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Positive charge is distributed in a sphere of radius R that is centered at the origin. Inside the sphere, the electric
field is Ē(r) = kr-1/4 f, where k is a positive constant. There is no charge outside the sphere.
a) How is the charge distributed inside the sphere? In particular, find an equation for the charge density, p.
b) Determine the electric field, E(r), for r > R (outside the sphere).
c) What is the potential difference between the center of the sphere (r = 0) and the surface of the sphere
(r = R)?
d) What is the energy stored in this electric charge configuration?
Find the electric field at the origin of the x,y-plane for charge distributions (a) and (b), see the figures
shown below. The field is produced (a) by a thin half-circle with a radius of 15 cm and the linear charge
density K-10 pc/cm and (b) by a thin quarter-circle with the same radius and the linear charge density
K = -10 pc/cm.
K>0
(a)
For the charge distribution (a):
The x-component of Ea. Ea,x=
The y-component of Ea, Ea,y=
For the charge distribution (b):
The x-component of Eb, Eb,x-
The y-component of Eb, Eb,y =
Units N/C
Units N/C
Units N/C
Units N/C
K<0
(b)
Positive electric charge is uniformly distributed along the y-axis with a linear charge density l.
Consider the case where charge is distributed only between points y = +a and y = -a. For points between the +x-axis, graph the x-component of the electric field as a function of x, Ex (x), for values x = a/2 and x = 4a.
Consider instead the case where charge is distributed along the entire y-axis with the same charge density l. Using the same graph as in part (a), plot the x-component of the electric field, Ex (x), as function of x for values of x between x = a/2 and x = 4a.
Chapter 22 Solutions
University Physics (14th Edition)
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