Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 20, Problem 61P
A uniform electric field E = 3 000 V/m exists within a certain region. What volume of space contains an energy equal to 1.00 × 10−7 J? Express your answer in cubic meters and in liters.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A uniform electric field E = 3250 V/m exists within a certain region. What volume of space contains an energy equal to 1.15 x 10/ J? Express your answer in cubic meters and in liters.
m3
L
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 () )
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 20 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 20.1 - In Figure 20. 1, two points and are located...Ch. 20.2 - The labeled points in Figure 20.4 are on a series...Ch. 20.3 - A spherical balloon contains a positively charged...Ch. 20.3 - In Active Figure 20.8a, take q1 to be a negative...Ch. 20.4 - In a certain region of space, the electric...Ch. 20.7 - A capacitor stores charge Q at a potential...Ch. 20.8 - Prob. 20.7QQCh. 20.9 - Prob. 20.8QQCh. 20.10 - If you have ever tried to hang a picture or a...Ch. 20 - A parallel-plate capacitor is charged and then is...
Ch. 20 - Prob. 2OQCh. 20 - A proton is released from rest at the origin in a...Ch. 20 - By what factor is the capacitance of a metal...Ch. 20 - Prob. 5OQCh. 20 - Rank the potential energies of the four systems of...Ch. 20 - Prob. 7OQCh. 20 - In a certain region of space, a uniform electric...Ch. 20 - Prob. 9OQCh. 20 - Prob. 10OQCh. 20 - Prob. 11OQCh. 20 - A parallel-plate capacitor is connected to a...Ch. 20 - Rank the electric potential energies of the...Ch. 20 - Four particles are positioned on the rim of a...Ch. 20 - Prob. 15OQCh. 20 - A filament running along the x axis from the...Ch. 20 - An electronics technician wishes to construct a...Ch. 20 - Prob. 18OQCh. 20 - Prob. 19OQCh. 20 - A parallel-plate capacitor filled with air carries...Ch. 20 - Prob. 21OQCh. 20 - Prob. 1CQCh. 20 - Prob. 2CQCh. 20 - Prob. 3CQCh. 20 - Prob. 4CQCh. 20 - Prob. 5CQCh. 20 - Prob. 6CQCh. 20 - Prob. 7CQCh. 20 - Prob. 8CQCh. 20 - Why is it dangerous to touch the terminals of a...Ch. 20 - Prob. 10CQCh. 20 - Prob. 11CQCh. 20 - Prob. 12CQCh. 20 - A uniform electric field of magnitude 325 V/m is...Ch. 20 - Prob. 2PCh. 20 - Calculate the speed of a proton that is...Ch. 20 - Prob. 4PCh. 20 - An electron moving parallel to the x axis has an...Ch. 20 - (a) Find the potential at a distance of 1.00 cm...Ch. 20 - Prob. 8PCh. 20 - Given two particles with 2.00-C charges as shown...Ch. 20 - Three particles with equal positive charges q are...Ch. 20 - The three charged particles in Figure P20.11 are...Ch. 20 - Prob. 12PCh. 20 - Prob. 13PCh. 20 - Review. A light, unstressed spring has length d....Ch. 20 - Review. Two insulating spheres have radii 0.300 cm...Ch. 20 - Review. Two insulating spheres have radii r1 and...Ch. 20 - Two particles each with charge +2.00 C are located...Ch. 20 - Prob. 18PCh. 20 - Two particles, with charges of 20.0 nC and 20.0...Ch. 20 - At a certain distance from a charged particle, the...Ch. 20 - A particle with charge +q is at the origin. A...Ch. 20 - Prob. 22PCh. 20 - Prob. 23PCh. 20 - Prob. 24PCh. 20 - Prob. 25PCh. 20 - A rod of length L (Fig. P20.26) lies along the x...Ch. 20 - For the arrangement described in Problem 26,...Ch. 20 - A wire having a uniform linear charge density is...Ch. 20 - A uniformly charged insulating rod of length 14.0...Ch. 20 - How many electrons should be removed from an...Ch. 20 - Prob. 31PCh. 20 - Prob. 32PCh. 20 - (a) How much charge is on each plate of a 4.00-F...Ch. 20 - Two conductors having net charges of +10.0 C and...Ch. 20 - Prob. 35PCh. 20 - A spherical capacitor consists of a spherical...Ch. 20 - Prob. 37PCh. 20 - A variable air capacitor used in a radio tuning...Ch. 20 - Prob. 39PCh. 20 - Prob. 40PCh. 20 - (a) Regarding the Earth and a cloud layer 800 m...Ch. 20 - Prob. 42PCh. 20 - Prob. 43PCh. 20 - (a) Find the equivalent capacitance between points...Ch. 20 - Four capacitors are connected as shown in Figure...Ch. 20 - Prob. 46PCh. 20 - According to its design specification, the timer...Ch. 20 - Prob. 48PCh. 20 - Prob. 49PCh. 20 - Three capacitors are connected to a battery as...Ch. 20 - Find the equivalent capacitance between points a...Ch. 20 - Consider the circuit shown in Figure P20.52, where...Ch. 20 - Prob. 53PCh. 20 - A parallel-plate capacitor has a charge Q and...Ch. 20 - Prob. 55PCh. 20 - Prob. 56PCh. 20 - Prob. 57PCh. 20 - Prob. 58PCh. 20 - Prob. 59PCh. 20 - Prob. 60PCh. 20 - A uniform electric field E = 3 000 V/m exists...Ch. 20 - Prob. 62PCh. 20 - Prob. 63PCh. 20 - Prob. 64PCh. 20 - Prob. 65PCh. 20 - A parallel-plate capacitor in air has a plate...Ch. 20 - Lightning can be studied with a Van de Graaff...Ch. 20 - Prob. 68PCh. 20 - Prob. 69PCh. 20 - Prob. 70PCh. 20 - Prob. 71PCh. 20 - Prob. 72PCh. 20 - Prob. 73PCh. 20 - Prob. 74PCh. 20 - Prob. 75PCh. 20 - Prob. 76PCh. 20 - Prob. 77PCh. 20 - Prob. 78PCh. 20 - Prob. 79PCh. 20 - Prob. 80PCh. 20 - Prob. 81PCh. 20 - Prob. 82PCh. 20 - A 10.0-F capacitor is charged to 15.0 V. It is...Ch. 20 - Two large, parallel metal plates, each of area A,...Ch. 20 - A capacitor is constructed from two square,...Ch. 20 - Two square plates of sides are placed parallel to...Ch. 20 - Determine the equivalent capacitance of the...
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_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 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:arrow_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 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 () )arrow_forward
- 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.arrow_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 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:arrow_forwardThe plates of a parallel-plate capacitor are 3.50 mmmm apart, and each carries a charge of magnitude 75.0 nCnC. The plates are in vacuum. The electric field between the plates has a magnitude of 5.00×106 V/mV/m. What is the area of each plate? Express your answer in meters squared.arrow_forward
- A uniform electric field E = 3500 V/m exists within a certain region. What volume of space contains an energy equal to 3.00 x 109 J? Express your answer i) in cubic meters, and ii) in liters?arrow_forwardThe electric flux density inside a cylinder is given as D = 7.32 ax + 7.11 ay +9.94 az, measured in picocoulombs per square meter. If the total potential energy stored in the cylinder can be written as me, measured in joules, find real number m. The cylinder has radius and height 1.59 meters and 3.69 meters, respectively. Use = 8.854x10-12 F/m.arrow_forwardAn electric field of 6.50×105 V/m is desired between two parallel plates, each of area 45.0 cm2 and separated by 2.45 mm of air. What charge must be on each plate? Express your answer using three significant figures and include the appropriate units.arrow_forward
- The electric field along the y-axis is given by È= ayî where a = -16 N/m.C. Find the electric potential difference between y1=1.7m and y2=2.1m; V(V2) – V(y1) = ? Express your answer in units of Volts and use one decimal place. Hint: de = îdx +ĵdy +kdzarrow_forwardA charge of 81 pC is distributed on an isolated spherical conductor that has a radius of 4 cm . Point A is 0.9 cm from the center of the conductor and point B is 5 cm from the center of the conductor. Determine the electric potential difference VA – VB. The value of Coulomb’s constant is 8.98755 × 10° N · m²/C². Answer in units of V.arrow_forwardWhat is the value of the electric field in the region between the plates in V/m?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher: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