Physics for Scientists and Engineers With Modern Physics
9th Edition
ISBN: 9781133953982
Author: SERWAY, Raymond A./
Publisher: Cengage Learning
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Textbook Question
Chapter 23, Problem 40P
The electric field along the axis of a uniformly charged disk of radius R and total charge Q was calculated in Example 23.3. Show that the electric field at distances x that are large compared with R approaches that of a particle with charge Q = σπR2. Suggestion: First show that x/(x2 + R2)1/2 = (1 + R2/x2)−1/2 and use the binomial expansion (1 + δ)n = 1 + nδ, when δ << 1.
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Two conductors with concentric radii r1=5 m and r2=22 m are placed in such a way that their center is the
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the electric field at point A(19, 32°, 45°) is given below. Find the amplitude of the electric field.
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The electric field along the axis of a uniformly charged disk of radius R and total charge Q was calculated the given example. Show that the electric field at distances x that are large compared with R approaches that of a particle with charge Q = σπR2. Suggestion: First show that x/(x2 + R2)1/2 = (1 +R2/x2)-1/2 and use the binomial expansion (1 + δ)n ≈ 1 + nδ, when δ << 1.
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 = 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 (
))
Chapter 23 Solutions
Physics for Scientists and Engineers With Modern Physics
Ch. 23.1 - Three objects are brought close to each other, two...Ch. 23.2 - Three objects are brought close to one another,...Ch. 23.3 - Object A has a charge of +2 C, and object B has a...Ch. 23.4 - A test charge of +3 C is at a point P where an...Ch. 23.6 - Rank the magnitudes of the electric field at...Ch. 23 - Prob. 1OQCh. 23 - Prob. 2OQCh. 23 - Prob. 3OQCh. 23 - Prob. 4OQCh. 23 - Prob. 5OQ
Ch. 23 - Prob. 6OQCh. 23 - Prob. 7OQCh. 23 - Prob. 8OQCh. 23 - Prob. 9OQCh. 23 - Prob. 10OQCh. 23 - Prob. 11OQCh. 23 - Prob. 12OQCh. 23 - Prob. 13OQCh. 23 - Prob. 14OQCh. 23 - Prob. 15OQCh. 23 - Prob. 1CQCh. 23 - A charged comb often attracts small bits of dry...Ch. 23 - Prob. 3CQCh. 23 - Prob. 4CQCh. 23 - Prob. 5CQCh. 23 - Prob. 6CQCh. 23 - Prob. 7CQCh. 23 - Prob. 8CQCh. 23 - Prob. 9CQCh. 23 - Prob. 10CQCh. 23 - Prob. 11CQCh. 23 - Find to three significant digits the charge and...Ch. 23 - Prob. 2PCh. 23 - Prob. 3PCh. 23 - Prob. 4PCh. 23 - In a thundercloud, there may be electric charges...Ch. 23 - (a) Find the magnitude of the electric force...Ch. 23 - Prob. 7PCh. 23 - Nobel laureate Richard Feynman (19181088) once...Ch. 23 - A 7.50-nC point charge is located 1.80 m from a...Ch. 23 - Prob. 10PCh. 23 - Prob. 11PCh. 23 - Prob. 12PCh. 23 - Prob. 13PCh. 23 - Prob. 14PCh. 23 - Prob. 15PCh. 23 - Prob. 16PCh. 23 - Review. In the Bohr theory of the hydrogen atom,...Ch. 23 - Prob. 18PCh. 23 - Prob. 19PCh. 23 - Prob. 20PCh. 23 - Prob. 21PCh. 23 - Why is the following situation impossible? Two...Ch. 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 - Two charged particles are located on the x axis....Ch. 23 - Prob. 33PCh. 23 - Two 2.00-C point charges are located on the x...Ch. 23 - Prob. 35PCh. 23 - Consider the electric dipole shown in Figure...Ch. 23 - A rod 14.0 cm long is uniformly charged and has a...Ch. 23 - Prob. 38PCh. 23 - A uniformly charged ring of radius 10.0 cm has a...Ch. 23 - The electric field along the axis of a uniformly...Ch. 23 - Prob. 41PCh. 23 - Prob. 42PCh. 23 - A continuous line of charge lies along the x axis,...Ch. 23 - Prob. 44PCh. 23 - Prob. 45PCh. 23 - Prob. 46PCh. 23 - A negatively charged rod of finite length carries...Ch. 23 - Prob. 48PCh. 23 - Prob. 49PCh. 23 - Prob. 50PCh. 23 - A proton accelerates from rest in a uniform...Ch. 23 - Prob. 52PCh. 23 - Prob. 53PCh. 23 - Protons are projected with an initial speed vi =...Ch. 23 - Prob. 55PCh. 23 - Prob. 56PCh. 23 - A proton moves at 4.50 105 m/s in the horizontal...Ch. 23 - Prob. 58APCh. 23 - Consider an infinite number of identical...Ch. 23 - A particle with charge 3.00 nC is at the origin,...Ch. 23 - Prob. 61APCh. 23 - Prob. 62APCh. 23 - Prob. 63APCh. 23 - Prob. 64APCh. 23 - Prob. 65APCh. 23 - Prob. 66APCh. 23 - Prob. 67APCh. 23 - Prob. 68APCh. 23 - Prob. 69APCh. 23 - Two point charges qA = 12.0 C and qB = 45.0 C and...Ch. 23 - Prob. 71APCh. 23 - Prob. 72APCh. 23 - Two small spheres hang in equilibrium at the...Ch. 23 - Prob. 74APCh. 23 - Prob. 75APCh. 23 - Prob. 76APCh. 23 - Prob. 77APCh. 23 - Prob. 78APCh. 23 - Prob. 79APCh. 23 - Prob. 80APCh. 23 - Prob. 81APCh. 23 - Prob. 82APCh. 23 - Prob. 83APCh. 23 - Identical thin rods of length 2a carry equal...Ch. 23 - Prob. 85CPCh. 23 - Prob. 86CPCh. 23 - Prob. 87CPCh. 23 - Prob. 88CPCh. 23 - Prob. 89CPCh. 23 - Prob. 90CPCh. 23 - Two particles, each with charge 52.0 nC, are...
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