Physics for Scientists and Engineers With Modern Physics
9th Edition
ISBN: 9781133953982
Author: SERWAY, Raymond A./
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 25, Problem 68AP
(a)
To determine
The proof for
(b)
To determine
The proof for
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Suppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius rb has charge -Q. The electric field E at a radial distance r from the central axis is given by the function:
E = αe-r/a0 + β/r + b0
where alpha (α), beta (β), a0 and b0 are constants. Find an expression for its capacitance.
First, let us derive the potential difference Vab between the two conductors. The potential difference is related to the electric field by:
First, let us derive the potential difference Vab between the two conductors. The potential difference is related to the electric field by:
Calculating the antiderivative or indefinite integral ,
Vab = (-αa0e-r/a0 + β + b0 )
By definition, the capacitance C is related to the charge and potential difference by:
C = /
Evaluating with the upper and lower limits of integration for Vab, then simplifying:
C = Q / ( (e-rb/a0 - e-ra/a0) + β ln() + b0 () )
Suppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius rb has charge -Q. The electric field E at a radial distance r from the central axis is given by the function:
E = αe-r/a0 + β/r + b0
where alpha (α), beta (β), a0 and b0 are constants. Find an expression for its capacitance.
First, let us derive the potential difference Vab between the two conductors. The potential difference is related to the electric field by:
Suppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius rb has charge -Q. The electric field E at a radial distance r from the central axis is given by the function:
E = αe-r/a0 + β/r + b0
where alpha (α), beta (β), a0 and b0 are constants. Find an expression for its capacitance.
Chapter 25 Solutions
Physics for Scientists and Engineers With Modern Physics
Ch. 25.1 - two points and are located within a region in...Ch. 25.2 - QUICK QUIZ 24.2 The labeled points in Figure 24.4...Ch. 25.3 - In Figure 24.8b, take q2, to be a negative source...Ch. 25.4 - In a certain region of space, the electric...Ch. 25 - Prob. 1OQCh. 25 - Prob. 2OQCh. 25 - Prob. 3OQCh. 25 - Prob. 4OQCh. 25 - Prob. 5OQCh. 25 - Prob. 6OQ
Ch. 25 - Prob. 7OQCh. 25 - Prob. 8OQCh. 25 - Prob. 9OQCh. 25 - Prob. 10OQCh. 25 - Prob. 11OQCh. 25 - Prob. 12OQCh. 25 - Prob. 13OQCh. 25 - Prob. 14OQCh. 25 - Prob. 15OQCh. 25 - Prob. 1CQCh. 25 - Prob. 2CQCh. 25 - When charged particles are separated by an...Ch. 25 - Prob. 4CQCh. 25 - Prob. 5CQCh. 25 - Prob. 6CQCh. 25 - Oppositely charged parallel plates are separated...Ch. 25 - Prob. 2PCh. 25 - Prob. 3PCh. 25 - How much work is done (by a battery, generator, or...Ch. 25 - Prob. 5PCh. 25 - Starting with the definition of work, prove that...Ch. 25 - Prob. 7PCh. 25 - (a) Find the electric potential difference Ve...Ch. 25 - Prob. 9PCh. 25 - Prob. 10PCh. 25 - Prob. 11PCh. 25 - Prob. 12PCh. 25 - Prob. 13PCh. 25 - Prob. 14PCh. 25 - Prob. 15PCh. 25 - Two point charges Q1 = +5.00 nC and Q2 = 3.00 nC...Ch. 25 - Prob. 17PCh. 25 - Prob. 18PCh. 25 - Given two particles with 2.00-C charges as shown...Ch. 25 - Prob. 20PCh. 25 - Four point charges each having charge Q are...Ch. 25 - Prob. 22PCh. 25 - Prob. 23PCh. 25 - Show that the amount of work required to assemble...Ch. 25 - Prob. 25PCh. 25 - Prob. 26PCh. 25 - Prob. 27PCh. 25 - Prob. 28PCh. 25 - Prob. 29PCh. 25 - Prob. 30PCh. 25 - Prob. 31PCh. 25 - Prob. 32PCh. 25 - How much work is required to assemble eight...Ch. 25 - Four identical particles, each having charge q and...Ch. 25 - Prob. 35PCh. 25 - Prob. 36PCh. 25 - Prob. 37PCh. 25 - Prob. 38PCh. 25 - Prob. 39PCh. 25 - Prob. 40PCh. 25 - Prob. 41PCh. 25 - Prob. 42PCh. 25 - Prob. 43PCh. 25 - Prob. 44PCh. 25 - Prob. 45PCh. 25 - Prob. 46PCh. 25 - Prob. 47PCh. 25 - The electric field magnitude on the surface of an...Ch. 25 - Prob. 49PCh. 25 - Prob. 50PCh. 25 - Prob. 51PCh. 25 - Prob. 52PCh. 25 - Prob. 53APCh. 25 - Prob. 54APCh. 25 - Prob. 55APCh. 25 - Prob. 56APCh. 25 - Prob. 57APCh. 25 - Prob. 58APCh. 25 - Prob. 59APCh. 25 - Prob. 60APCh. 25 - Prob. 61APCh. 25 - Prob. 62APCh. 25 - Prob. 63APCh. 25 - Prob. 64APCh. 25 - Prob. 65APCh. 25 - Prob. 66APCh. 25 - Prob. 67APCh. 25 - Prob. 68APCh. 25 - Review. Two parallel plates having charges of...Ch. 25 - When an uncharged conducting sphere of radius a is...Ch. 25 - Prob. 71CPCh. 25 - Prob. 72CPCh. 25 - Prob. 73CPCh. 25 - Prob. 74CPCh. 25 - Prob. 75CPCh. 25 - Prob. 76CPCh. 25 - Prob. 77CP
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
- Suppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius rb has charge -Q. The electric field E at a radial distance r from the central axis is given by the function: E = αe-r/a0 + β/r + b0 where alpha (α), beta (β), a0 and b0 are constants. Find an expression for its capacitance. First, let us derive the potential difference Vab between the two conductors. The potential difference is related to the electric field by: Calculating the antiderivative or indefinite integral , Vab = (-αa0e-r/a0 + β + b0 ) By definition, the capacitance C is related to the charge and potential difference by: C = / Evaluating with the upper and lower limits of integration for Vab, then simplifying: C = Q / ( (e-rb/a0 - e-ra/a0) + β ln() + b0 () )arrow_forwardHow many electrons are in a 1.00-g electrically neutral steel paper clip? The molar mass of steel is approximately that of iron, or 55.845 g/mol, and a neutral iron atom has 26 electrons.arrow_forwardE = E1 E = 0 E= E1 E= E1 The electric field is measured all over a cubical surface, and the pattern of field detected is shown in the figure above. On the right side of the cube, the electric field has magnitude Ej = 426 V/m, and the angle between the electric field and the surface of the cube is 0 = 15 degrees. On the bottom of the cube, the electric field has the same magnitude Ej, and the angle between the electric field and the surface of the cube is also 0 = 15 degrees. On the top of the cube and the left side of the cube, the electric field is zero. On half of the front and back faces, the electric field has magnitude Ej and is parallel to the face; on the other half of the front and back faces, the electric field is zero. One edge of the cube is 41 cm long. Part 1 What is the net electric flux on this cubical surface? Net electric flux = i V•m Save for Later Attempts: 0 of 4 used Submit Answerarrow_forward
- Ex. 51 The temperature of interstellar space has an average value of about 5 K. Find the rms speed of a proton in the Imp space. [m, = 1.673 x 10 27 kg, kg = 1.38 x 10 23 J/K] %3D %3Darrow_forwardThe following are electron carriers in a hypothetical biological system: Electron Carriers (E° , V) A (0.17 V), B (0.04 V), C (0.31 V), D (-0.65 V), E (-0.25 V). a. Which electron carrier will be the best electron donor? b. Which electron carrier will be the final electron acceptor?arrow_forwardElectrons flow through a 1.5-mm-diameter aluminum wire at 1.0x10-4 m/s. Part A How many electrons move through a cross section of the wire each day? 5 ΑΣΦ xa Xb Ĵ a + √x vx x N= 9.16.1023 x Submit Previous Answers Request Answer X Incorrect; Try Again; 9 attempts remaining |xx| ? X. 10m B electronsarrow_forward
- What is the number density of free electron carries in the metallic element nickel if the electrons available for electrical conduction is 1 e- per nickel atom? The atomic mass of nickel is 58.6934 g/mole and the density of nickel is 8.902 g/cm3. a. 3.32 x 1028 e- ' s /m3 b. 1.56 x 1029 e- ' s /m3 c. 5.64 x 1028 e- ' s /m3 d. 9.13 x 1028 e- ' s /m3 e. 7.63 x 1028 e- ' s /m3arrow_forwardSuppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius rp has charge -Q. The electric field E at a radial distance r from the central axis is given by the function: E = ae-r/ao + B/r + bo where alpha (a), beta (B), ao and bo are constants. Find an expression for its capacitance. First, let us derive the potential difference Vab between the two conductors. The potential difference is related to the electric field by: ['´e Vob = Edr= - Edr Calculating the antiderivative or indefinite integral, Vab = (-aaoe¯r7ao + B + bo By definition, the capacitance C is related to the charge and potential difference by: C = Evaluating with the upper and lower limits of integration for Vab, then simplifying: C = Q / ( (erb/ao - eralao) + B In( ) + bo ( ))arrow_forwardB A hair dryer is basically a duct of constant diameter in which a few layers of electric resistors are placed. A small fan pulls the air in and forces it through the resistors where it is heated. If the density of air is 1.15 kg/m3 at the inlet and 1.05 kg/m3 at the exit, determine the percent increase in the velocity of air as it flows through the hair dryer 1.05 kg/m³ The increase in velocity is Pin kg/m³ Check my work %6arrow_forward
- Q. The ends of the cylinder are made of conducting discs and the space between these discs are filled with an inhomogeneous ohmic medium whose conductivity o = L/(z+1). Where L is the separation distance of the discs. A d-c voltage Vo is applied across the discs as shown on the right. Determine V. a) The total resistance between the discs b) The surface charge densities on the discs c) The volume charge density and the total amount of charge between the discsarrow_forwardSuppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius rh has charge -Q. The electric field E at a radial distance r from the central axis is given by the function: E = ae-r/ao + B/r + bo where alpha (a), beta (B), ao and bo are constants. Find an expression for its capacitance. First, let us derive the potential difference Vab between the two conductors. The potential difference is related to the electric field by: Vab = Edr = - Edr Calculating the antiderivative or indefinite integral, Vab = (-aager/ao + B + bo By definition, the capacitance Cis related to the charge and potential difference by: C = Evaluating with the upper and lower limits of integration for Vab, then simplifying: C = Q/( (e rb/ao - eTalao) + B In( ) + bo ( ))arrow_forwardAn electron is fired at a speed vi = 4.3 × 106 m/s and at an angle θi = 39.7° between two parallel conducting plates as shown in the figure. If s = 1.7 mm and the voltage difference between the plates is ΔV = 99.8 V, determine how close, w, the electron will get to the bottom plate. Put your answer in meters and include at 6 decimal places in your answer. Do not include units. The x-axis of the coordinate system is in the middle of the parallel plate capacitor. Round your answer to 6 decimal places.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher: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
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
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