Physics for Scientists and Engineers, Vol. 1
6th Edition
ISBN: 9781429201322
Author: Paul A. Tipler, Gene Mosca
Publisher: Macmillan Higher Education
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
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
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
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, Vol. 1
Ch. 22 - Prob. 1PCh. 22 - Prob. 2PCh. 22 - Prob. 3PCh. 22 - Prob. 4PCh. 22 - Prob. 5PCh. 22 - Prob. 6PCh. 22 - Prob. 7PCh. 22 - Prob. 8PCh. 22 - Prob. 9PCh. 22 - Prob. 10P
Ch. 22 - Prob. 11PCh. 22 - Prob. 12PCh. 22 - Prob. 13PCh. 22 - Prob. 14PCh. 22 - Prob. 15PCh. 22 - Prob. 16PCh. 22 - Prob. 17PCh. 22 - Prob. 18PCh. 22 - Prob. 20PCh. 22 - Prob. 21PCh. 22 - Prob. 22PCh. 22 - Prob. 23PCh. 22 - Prob. 24PCh. 22 - Prob. 25PCh. 22 - Prob. 26PCh. 22 - Prob. 27PCh. 22 - Prob. 28PCh. 22 - Prob. 29PCh. 22 - Prob. 30PCh. 22 - Prob. 31PCh. 22 - Prob. 32PCh. 22 - Prob. 33PCh. 22 - Prob. 34PCh. 22 - Prob. 35PCh. 22 - Prob. 36PCh. 22 - Prob. 37PCh. 22 - Prob. 38PCh. 22 - Prob. 39PCh. 22 - Prob. 40PCh. 22 - Prob. 41PCh. 22 - Prob. 42PCh. 22 - Prob. 43PCh. 22 - Prob. 44PCh. 22 - Prob. 45PCh. 22 - Prob. 46PCh. 22 - Prob. 47PCh. 22 - Prob. 48PCh. 22 - Prob. 49PCh. 22 - Prob. 50PCh. 22 - Prob. 51PCh. 22 - Prob. 52PCh. 22 - Prob. 53PCh. 22 - Prob. 54PCh. 22 - Prob. 55PCh. 22 - Prob. 56PCh. 22 - Prob. 57PCh. 22 - Prob. 58PCh. 22 - Prob. 59PCh. 22 - Prob. 60PCh. 22 - Prob. 61PCh. 22 - Prob. 62PCh. 22 - Prob. 63PCh. 22 - Prob. 64PCh. 22 - Prob. 65PCh. 22 - Prob. 66PCh. 22 - Prob. 67PCh. 22 - Prob. 68PCh. 22 - Prob. 69PCh. 22 - Prob. 70PCh. 22 - Prob. 71PCh. 22 - Prob. 72PCh. 22 - Prob. 73PCh. 22 - Prob. 74PCh. 22 - Prob. 75PCh. 22 - Prob. 76PCh. 22 - Prob. 77PCh. 22 - Prob. 78PCh. 22 - Prob. 79PCh. 22 - Prob. 80PCh. 22 - Prob. 81PCh. 22 - Prob. 82PCh. 22 - Prob. 83PCh. 22 - Prob. 84PCh. 22 - Prob. 85PCh. 22 - Prob. 86PCh. 22 - Prob. 87PCh. 22 - Prob. 88P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- A non-uniformly 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 where in is the infinitesimal charge and is the infinitesimal volume. so, we have p = dq/ - BA So we can write this as dq = 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 =arrow_forwardPlease solve asap and explain how you reached that solution properly. Thank you in advance!arrow_forwardThe axis of a long dielectric tube with an inner radius r = 2m and an outer radius r = 5m coincides with the z-axis. Inside the dielectric body, there is a polarization vector in the form of P = P.(3yâx + 4xây). Find the equivalent volume charge density Ppv at point (2,0,4). Ppv = 0 O A) O, Ppv 7Por sin ø cos Ø %3D B) Ppv Por sin ø cos Øarrow_forward
- 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 3arrow_forwardE(r) = Bzi - ax'y'j+ (6@yxy + Bóz³) k %3D where a, B, y and & are constants and r = xi+yj+zk. Find the corresponding charge density p(r).arrow_forwardIf the electric flux density is given by C D = x²a, + y²z a, determine the volume charge density at the point P(1,2,3).arrow_forward
- A solid cylindrical conductor of radius a is surrounded by a concentric cylindrical shell of inner radius b. The solid cylinder and the shell carry charges +Q and Q , respectively. Assuming that the length L of both conductors is much greater than a or b, determine the electric field as a function of r, the distance from the common central axis of the cylinders, for (a) ra; (b) arb; and (c) rb.arrow_forwardProblem: An infinitely long cylindrical conductor has radius R and uniform surface charge density O. In terms of Rand O, what is the charge per unit length A for the cylinder? Answer: A = 2arrow_forwardanswer is not 1.62*10^-6 and is not 4011.86 and is not 20131.55 and i will dislike of you put any of these answers and u need to give a numerical answer (not an equation with variables) otherwise i will dislikearrow_forward
- at x=1mm and V=0 at x=0 and volume charge density p, is – 10°E, C/m³ constant throughout the region between x=0 to x=1 mm. Calculate V at x=0.5mm and Ex at x=1 mm in free space.arrow_forwardIf D = (2y + z)a, + 4xya, + xa, C/m², find %3D (a) The volume charge density at (-1, 0, 3) (b) The flux through the cube defined by 0 s xs 1,0 sys1,0szs1 (c) The total charge enclosed by the cubearrow_forwardAnswer the following:arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Electric Fields: Crash Course Physics #26; Author: CrashCourse;https://www.youtube.com/watch?v=mdulzEfQXDE;License: Standard YouTube License, CC-BY