Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN: 9781305116399
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 24, Problem 24.65CP
A spherically symmetric charge distribution has a charge density given by p = a/r; where a is constant. Find the electric field within the charge distribution as a function of r. Note:The volume element dV for a spherical shell of radius r and thickness dr is equal to 4 πr2dr.
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A cylinder of length L=5m has a radius R=2 cm and linear charge density 2=300 µC/m. Although the
linear charge density is a constant through the cylinder, the charge density within the cylinder changes
with r. Within the cylinder, the charge density of the cylinder varies with radius as a function p( r) =p.r/R.
Here R is the radius of the cylinder and R=2 cm and p, is just a constant that you need to determine.
b. Find the constant po in terms of R and 2. Then plug in values of R and 1. to find the value for
the constant p.
c. Assuming that L>>R, use Gauss's law to find out the electric field E inside the cylinder (rR) in terms of 1. and R.
d. Based on your result from problem c, find the electric field E at r=1cm and r=4cm.
Consider any charge distribution with a charge density e(7), let v be a
spherical region of radius Y.. Centered at 0, the average electric field E
within v has the formula:
1
E:
Iar / E(F)dv = Ent + Eot
%3D
where Ent is the average field due to all internal charges v and Eetis the
average field due to all external charges v Prove that
Eint
1
4T€0 r3
Eext
p(T) du'
Jv
4T€0
p13
where p is the electric dipole moment (cycle O) of the internal charge.
and V is the region in space. that includes v and P(F)# 0
3
a) Find the surface charge density σ2 of the cylindrical shell of radius R2. (Note the unit in the input box and the sign of charges.)
Surface charge density σ2Give your answer up to at least three significance digits.
b) Find an expression of electric field at rmm from the center where R1<r<R2. Assume the cylinder has a length L and L is very long so that electric field is uniform. Consider that the insulating material between the cylinders is air. (Hint : use Gauss's law and cylindrical Gaussian surface with radius r.)
Magnitude of the electric field at r=0.76mm
Give your answer up to at least three significance digits.
c) Calculate absolute value of the potential difference between the wire and the cylinder.
Absolute value of the potential difference
Give your answer up to at least three significance digits.
d) Calculate the capacitance C for this cylindrical system. Assume that the length of the cylinder is L=17cm.
Capacitance C for this cylindrical system
Give your…
Chapter 24 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
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