Fundamentals of Physics, Volume 1, Chapter 1-20
10th Edition
ISBN: 9781118233764
Author: David Halliday
Publisher: WILEY
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Textbook Question
Chapter 23, Problem 76P
Charge is distributed uniformly throughout the volume of an infinitely long solid cylinder of radius R. (a) Show that, at a distance r < R from the cylinder axis,
where ρ is the volume charge density. (b) Write an expression for E when r > R.
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A charged sphere of radius Rohas charge density p=p,. Find the total charge in
the sphere.
A non-uniformiy charged insulating sphere has a volume charge density p that is expressed as
p= Br
where Bis a constant, and ris the radius from the center of the sphere. If the, the total charge of the sphere is Q and its maximum radius is R. What is the value for B?
Sol.
By definition, the volume charge density is expressed infinitesimally as
p=
where in
is the infinitesimal charge and
is the infinitesimal volume.
so, we have
p = dal
- B
So we can write this as
dg
= B
dV
But,
dV =
dr
By substitution, we get the following
dq = 4BT
dr
Using Integration operation and evaluating its limits, the equation, leads to
Q =
Rearranging, we get
B =
A non-uniformly charged insulating sphere has a volume charge density p that is expressed as
p= Br
where B is a constant, andris the radius from the center of the sphere. If the, the total charge of the sphere
is Q and its maximum radius is R. What is the value for B?
Sol.
By definition, the volume charge density is expressed infinitesimally as
p=
where in
is the infinitesimal charge and
is the infinitesimal volume.
So, we have
p = dq/
= B
So we can write this as
dq = B
dv
But,
dV =
TT
dr
By substitution, we get the following
dq = 4BT
dr
Using Integration operation and evaluating its limits, the equation, leads to
Q =
Rearranging, we get
B =
4)
Chapter 23 Solutions
Fundamentals of Physics, Volume 1, Chapter 1-20
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