FUND PHYS 10TH EXT WILEY PLUS
10th Edition
ISBN: 9781119500100
Author: Halliday
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Question
Chapter 40, Problem 79P
To determine
(a) the magnitude of electric field for 0 ≤ R ≤ r
(b) the electric field for r ≥ R
(c) the potential for r ≥ R
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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 rp has charge -Q. The electric field
E at a radial distance r from the central axis is given by the function:
E = aer/ao + B/r + bo
%3D
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 = |
S"Edr= - [ *Edr
Calculating the antiderivative or indefinite integral,
Vab = (-aage-r/ao + 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/(
(e-rb/ao - eralao) + B In(
) + bo (
))
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 rp has
charge -Q. The electric field E at a radial distance r from the central axis is given by the function:
E = aer/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:
Va
Edr=
Edr
Calculating the antiderivative or indefinite integral,
Vab = (-aaoe-r/ao + 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/(
(e-"b/ao - era/ao) + B In(
) + bo (
))
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 rh has charge -Q. The electric field E at a radial distancer 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 = (-aaoe-r/ao + B
+ bo
By definition, the capacitance C is related to the charge and potential difference by:
C= Q
I Vab
Chapter 40 Solutions
FUND PHYS 10TH EXT WILEY PLUS
Ch. 40 - Prob. 1QCh. 40 - Prob. 2QCh. 40 - Prob. 3QCh. 40 - Prob. 4QCh. 40 - Prob. 5QCh. 40 - Prob. 6QCh. 40 - Prob. 7QCh. 40 - Figure 40-22 shows three points at which a spin-up...Ch. 40 - Prob. 9QCh. 40 - Prob. 10Q
Ch. 40 - Prob. 11QCh. 40 - Prob. 12QCh. 40 - Prob. 13QCh. 40 - Prob. 14QCh. 40 - Prob. 1PCh. 40 - Prob. 2PCh. 40 - Prob. 3PCh. 40 - Prob. 4PCh. 40 - Prob. 5PCh. 40 - Prob. 6PCh. 40 - Prob. 7PCh. 40 - Prob. 8PCh. 40 - Prob. 9PCh. 40 - Prob. 10PCh. 40 - Prob. 11PCh. 40 - Prob. 12PCh. 40 - SSM What is the acceleration of a silver atom as...Ch. 40 - Prob. 14PCh. 40 - Prob. 15PCh. 40 - Assume that in the SternGerlach experiment as...Ch. 40 - Prob. 17PCh. 40 - Prob. 18PCh. 40 - Prob. 19PCh. 40 - Prob. 20PCh. 40 - Prob. 21PCh. 40 - Prob. 22PCh. 40 - Prob. 23PCh. 40 - Prob. 24PCh. 40 - Prob. 25PCh. 40 - Prob. 26PCh. 40 - Prob. 27PCh. 40 - Show that the number of states with the same...Ch. 40 - Prob. 29PCh. 40 - For a helium atom in its ground state, what are...Ch. 40 - Prob. 31PCh. 40 - Prob. 32PCh. 40 - Prob. 33PCh. 40 - Prob. 34PCh. 40 - Prob. 35PCh. 40 - Prob. 36PCh. 40 - Prob. 37PCh. 40 - Prob. 38PCh. 40 - Prob. 39PCh. 40 - Prob. 40PCh. 40 - Prob. 41PCh. 40 - Prob. 42PCh. 40 - Prob. 43PCh. 40 - Prob. 44PCh. 40 - Prob. 45PCh. 40 - Prob. 46PCh. 40 - Prob. 47PCh. 40 - Prob. 48PCh. 40 - Prob. 49PCh. 40 - Prob. 50PCh. 40 - Prob. 51PCh. 40 - Prob. 52PCh. 40 - Prob. 53PCh. 40 - Prob. 54PCh. 40 - Prob. 55PCh. 40 - Prob. 56PCh. 40 - Prob. 57PCh. 40 - Prob. 58PCh. 40 - Prob. 59PCh. 40 - Prob. 60PCh. 40 - Prob. 61PCh. 40 - Prob. 62PCh. 40 - Prob. 63PCh. 40 - Prob. 64PCh. 40 - Prob. 65PCh. 40 - Prob. 66PCh. 40 - Prob. 67PCh. 40 - Prob. 68PCh. 40 - Prob. 69PCh. 40 - Prob. 70PCh. 40 - Prob. 71PCh. 40 - Prob. 72PCh. 40 - Prob. 73PCh. 40 - Prob. 74PCh. 40 - Prob. 75PCh. 40 - Prob. 76PCh. 40 - Prob. 77PCh. 40 - Prob. 78PCh. 40 - Prob. 79P
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