Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 23, Problem 50P
To determine
The proof that
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A dielectric cylinder with absolute permittivity e, has radius b and height L. The bottom plate of the cylinder is positioned at x-y plane, concentric with the z-axis. The polarization vector in the
dielectric cylinder is given P = 6Por cos(o), where Po is a constant. Find
(a) Bound charge densities
(b) The total charge of the cylinder.
(C) Write the integral expression of the potential at P (0,0,0) explicitly. Define the integral limits and all the components in the integrant expression. Do not take the integral.
Ra1
+9
-9
Rea
Consider two concentric spherical conductors, separated by an isolating material with
(absolute) permittivity e. The two conductors have radius R1 and R2, they are put on a
potential V and V2, which leads to a charge +q and –q sitting on them, respectively.
By the problem's spherical symmetry, we see that the charge on each conductor is
distributed uniformly, and that, in spherical coordinates, the electric field between the
two conductors is of the form
E(r) = -E(r) er.
Determine the capacity C using the following steps:
1. Use Gauss's Law in integral form, with N a ball of radius r (R2 < r < R1), to find
an expression for E(r) in terms of q.
2. Calculate AV = Vị – V2 using the formula
- E•dr
Δν
and with C the black line segment indicated on the drawing (parallel with e,).
3. The capacity now follows from C = q/AV.
A solid conducting sphere of radius ra is placed concentrically inside a conducting spherical shell of inner radius rb1 and outer radius rb2. The inner sphere carries a charge Q while the outer sphere does not carry any net charge. The potential for rb1 < r < rb2 is
Chapter 23 Solutions
Physics for Scientists and Engineers
Ch. 23 - Prob. 1PCh. 23 - Prob. 2PCh. 23 - Prob. 3PCh. 23 - Prob. 4PCh. 23 - Prob. 5PCh. 23 - Prob. 6PCh. 23 - Prob. 7PCh. 23 - Prob. 8PCh. 23 - Prob. 9PCh. 23 - Prob. 10P
Ch. 23 - Prob. 11PCh. 23 - Prob. 12PCh. 23 - Prob. 13PCh. 23 - Prob. 14PCh. 23 - Prob. 15PCh. 23 - Prob. 16PCh. 23 - Prob. 17PCh. 23 - Prob. 18PCh. 23 - Prob. 19PCh. 23 - Prob. 20PCh. 23 - Prob. 21PCh. 23 - Prob. 22PCh. 23 - Prob. 23PCh. 23 - Prob. 24PCh. 23 - Prob. 25PCh. 23 - Prob. 26PCh. 23 - Prob. 27PCh. 23 - Prob. 28PCh. 23 - Prob. 29PCh. 23 - Prob. 30PCh. 23 - Prob. 31PCh. 23 - Prob. 32PCh. 23 - Prob. 33PCh. 23 - Prob. 34PCh. 23 - Prob. 35PCh. 23 - Prob. 36PCh. 23 - Prob. 37PCh. 23 - Prob. 38PCh. 23 - Prob. 39PCh. 23 - Prob. 40PCh. 23 - Prob. 41PCh. 23 - Prob. 42PCh. 23 - Prob. 43PCh. 23 - Prob. 44PCh. 23 - Prob. 45PCh. 23 - Prob. 46PCh. 23 - Prob. 47PCh. 23 - Prob. 48PCh. 23 - Prob. 49PCh. 23 - Prob. 50PCh. 23 - Prob. 51PCh. 23 - Prob. 52PCh. 23 - Prob. 53PCh. 23 - Prob. 54PCh. 23 - Prob. 55PCh. 23 - Prob. 56PCh. 23 - Prob. 57PCh. 23 - Prob. 58PCh. 23 - Prob. 59PCh. 23 - Prob. 60PCh. 23 - Prob. 61PCh. 23 - Prob. 62PCh. 23 - Prob. 63PCh. 23 - Prob. 64PCh. 23 - Prob. 65PCh. 23 - Prob. 66PCh. 23 - Prob. 67PCh. 23 - Prob. 68PCh. 23 - Prob. 69PCh. 23 - Prob. 70PCh. 23 - Prob. 71PCh. 23 - Prob. 72PCh. 23 - Prob. 73PCh. 23 - Prob. 74PCh. 23 - Prob. 75PCh. 23 - Prob. 76PCh. 23 - Prob. 77PCh. 23 - Prob. 78PCh. 23 - Prob. 79PCh. 23 - Prob. 80PCh. 23 - Prob. 81PCh. 23 - Prob. 82PCh. 23 - Prob. 83PCh. 23 - Prob. 84PCh. 23 - Prob. 85PCh. 23 - Prob. 86PCh. 23 - Prob. 87PCh. 23 - Prob. 88PCh. 23 - Prob. 89PCh. 23 - Prob. 90PCh. 23 - Prob. 91PCh. 23 - Prob. 92PCh. 23 - Prob. 93PCh. 23 - Prob. 94P
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
- How many electrons should be removed from an initially uncharged spherical conductor of radius 0.300 m to produce a potential of 7.50 kV at the surface?arrow_forwardA conducting solid sphere of radius R has a total charge Qon it. The electric potential at a point at a distance r from the center varies as (r< R) 1 1arrow_forwardA dielectric cylinder with absolute permittivity ɛ, has radius b and height L. The bottom plate of the cylinder is positioned at x-y plane, concentric with the z-axis. The polarization vector in the dielectric cylinder is given = r Por, where Po is a constant. Find (a) Bound charge densities (b) The total charge of the cylinder. (c) Write the integral expression of the potential at P (0,0,L) explicitly. Define the integral limits and all the components in the integrant expression. Do not take the integral.arrow_forward
- A solid nonconducting cylinder of radius R = 5.00 cm and length L = 15.0 cm has a uniform positive charge distribution of volume charge density p= 20.0 pC/m3 . (a) What is the electric potential at pint P? (b) What are the magnitude and direction of the electric field at point P? (where a = 10 cm, and P is perpendicular to the center of the cylindearrow_forwardCompute for the potential difference, in volts, in moving a charge radially away from the center from a distance of 4 m to a distance of 6 m against the electric field inside a solid insulating sphere of radius 11 m and total charge 6 nC.arrow_forwardA rod of length L = 0.15 m is placed along the x-axis with its center at the origin. The rod has a non-uniform linear charge density of 2 = kịx| C/m, where k = 2.05E-12 C/m? is a у-аxis constant factor. Yob Х-аxis dq Otheexper PA What is the value of the potential at the point (0, yob) in volts if yob= 3.1 m? Grade Summ V(0,yob) = Deductions Potential tan() 7 8 sin() cos() HOME Submissions Attempts rem (5% per atten detailed view cotan() asin() acotan() acos() E 4 atan() sinh() 2 3 cosh() tanh() cotanh() + END Degrees Radians VIBACKSPACE DEL CLEAR Feedback I give up! Submit Hintarrow_forward
- There is a dielectric hollow ball with chemobility Eo, radius R and surface density σ (0) = cos 0. Given a constant E external electric field in the direction of the z axis. Determine the potential magnitude in all places if the vacuum activities are €0 R E €arrow_forwardThe electric field is created by two point charges q1 == 32 nC and q2 = -18 nC, located at a distance of d = 50 mm from each other. Assuming that the charges are located on the x axis, find the components of the field strength vector Ex, Ey, its modulus E and the field potential at a point remote from the first charge by r1 = 40 mm and from the second by r2 = 30 mm.arrow_forwardS-1) Find the potential difference A (2, 1 / 2, 0) and B (4, 11, 5) VAB for a linear charge with density pl = 0.5 nC/m on the z-axisarrow_forward
- Problem 8: A rod of length L = 0.35 m is placed along the x-axis with its center at the origin. The rod has a non-uniform linear charge density of a = k|x| C/m, where k = 1.75E-12 C/m² is a constant factor. У-аxis Yob X-ахis dq What is the value of the potential at the point (0, yob) in volts if yob = 2.85 m? Numeric : A numeric value is expected and not an expression. V(0,yob) =arrow_forwardThe electric field is created by two point charges q1 = 32 nC and q2 = -18 nC, located at a distance of d = 50 mm from each other. Assuming that the charges are located on the x axis, find the components of the field strength vector Ex, Ey, its modulus E and the potential φ of the field at a point remote from the first charge by r1 = 40 mm and from the second by r2 = 30 mm.arrow_forwardA dielectric sphere of radius R and dielec- tric constant e, is hollowed out in the re- gion 0 < R1arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Recommended textbooks for you
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Electric Fields: Crash Course Physics #26; Author: CrashCourse;https://www.youtube.com/watch?v=mdulzEfQXDE;License: Standard YouTube License, CC-BY