22.53 CALC A nonuniform, but spherically symmetric, dis- tribution of charge has a charge density p(r) given as follows: Ho-(1-2 r p(r)= Po for r R R for r R P(r) 0 where po 30/TR is a positive constant. (a) Show that the total charge contained in the charge distribution is Q. (b) Show that the electric field in the region r 2 R is identical to that produced by a point charge Q at r = 0. (c) Obtain an expression for the electric field in the region r = R. (d) Graph the electric-field magnitude E (e) Find the value of r at which the electric field is maximum, and find the value of that maximum field. as a function of r. slab of insulating nar- 22.5 22.56 CALC A nonuniform, but spherically symmetric, distri- bution of charge has a charge density p(r) given as follows: 4r P(r) = A for r R 3R, P(r)= 0 for r R where po is a positive constant. (a) Find the total charge contained in the charge distribution. Obtain an expression for the electric field in the region (b) r z R; (c) rs R. (d) Graph the electric- field magnitude E as a function of r. (e) Find the value of r at which the electric field is maximum, and find the value of that maximum field.
22.53 CALC A nonuniform, but spherically symmetric, dis- tribution of charge has a charge density p(r) given as follows: Ho-(1-2 r p(r)= Po for r R R for r R P(r) 0 where po 30/TR is a positive constant. (a) Show that the total charge contained in the charge distribution is Q. (b) Show that the electric field in the region r 2 R is identical to that produced by a point charge Q at r = 0. (c) Obtain an expression for the electric field in the region r = R. (d) Graph the electric-field magnitude E (e) Find the value of r at which the electric field is maximum, and find the value of that maximum field. as a function of r. slab of insulating nar- 22.5 22.56 CALC A nonuniform, but spherically symmetric, distri- bution of charge has a charge density p(r) given as follows: 4r P(r) = A for r R 3R, P(r)= 0 for r R where po is a positive constant. (a) Find the total charge contained in the charge distribution. Obtain an expression for the electric field in the region (b) r z R; (c) rs R. (d) Graph the electric- field magnitude E as a function of r. (e) Find the value of r at which the electric field is maximum, and find the value of that maximum field.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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(Problems in images below.)
Both problems require a volume charge integration of the given charge density functions. Technically, a volume integration is a triple integral. However, since the charge density is spherically symmetric, this reduces to a one-dimensional integration.
Transcribed Image Text:22.53 CALC A nonuniform, but spherically symmetric, dis-
tribution of charge has a charge density p(r) given as follows:
Ho-(1-2
r
p(r)= Po
for r R
R
for r R
P(r) 0
where po 30/TR is a positive constant. (a) Show that the total
charge contained in the charge distribution is Q. (b) Show that the
electric field in the region r 2 R is identical to that produced by a
point charge Q at r = 0. (c) Obtain an expression for the electric
field in the region r = R. (d) Graph the electric-field magnitude E
(e) Find the value of r at which the electric field
is maximum, and find the value of that maximum field.
as a function of r.
slab of insulating
nar-
22.5
Transcribed Image Text:22.56 CALC A nonuniform, but spherically symmetric, distri-
bution of charge has a charge density p(r) given as follows:
4r
P(r) = A
for r R
3R,
P(r)= 0
for r R
where po is a positive constant. (a) Find the total charge contained
in the charge distribution. Obtain an expression for the electric
field in the region (b) r z R; (c) rs R. (d) Graph the electric-
field magnitude E as a function of r. (e) Find the value of r at
which the electric field is maximum, and find the value of that
maximum field.
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