Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 22, Problem 55P
(a)
To determine
To Verify:The linear charge density of the cylinder is
(b)
To determine
The expressions of the electric field for the region
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Students have asked these similar questions
An infinite cylinder of radius R has a charge density given by
p(r) = ar³,
where r is the perpendicular distance from the axis of the cylinder, and a is a constant.
Show that the electric field for r > R given by
aRT
E(r) :
7€or
is the same as that obtained if all the charge is concentrated in an infinitely thin wire.
Q.4:
Charge is distributed uniformly throughout the volume of an infinitely ltong solid eylinder of radius R.
a) Show that, at a distance rR.
Note; Some Physical constants
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 =
Chapter 22 Solutions
Physics for Scientists and Engineers
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