University Physics (14th Edition)
14th Edition
ISBN: 9780133969290
Author: Hugh D. Young, Roger A. Freedman
Publisher: PEARSON
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Chapter 22, Problem 22.51P
Thomson’s Model of the Atom, Continued. Using Thomson’s (outdated) model of (he atom described in Problem 22.50, consider an atom consisting of two electrons, each of charge −e, embedded in a sphere of charge +2e and radius R. In equilibrium, each electron is a distance d from the center of the atom (Fig. P22.51). Find the distanced in terms of the other properties of the atom.
Figure P22.51
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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 = ae-T/ao + B/r + bo
where alpha (a), beta (8), ao and bo are constants. Find an expression for its capacitance.
First, let us derive the potential difference Vah between the two conductors. The potential difference is related to the electric field by:
Vab =
Edr = -
Edr
Calculating the antiderivative or indefinite integral,
Vab = (-aage-r/a0 + 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 (
))
Problem 12: The classic Millikan oil drop experiment was the first to obtain an accurate
measurement of the charge on an electron. In it, oil drops were suspended against the gravitational
force by a vertical electric field.
microscope
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Given that the oil drop is 0.85 µum in radius and has a density of 925 kg/m³, find the weight of the drop in N.
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If the drop has a single excess electron, find the electric field strength needed to balance its weight.
Chapter 22 Solutions
University Physics (14th Edition)
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