Physics for Scientists and Engineers
10th Edition
ISBN: 9781337553278
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 24, Problem 10P
Your roommate is having trouble understanding why solids form. He asks, “Why would atoms bond into solids rather than just floating freely with respect to each other?” To help him understand at least one type of bonding in solids, you decide to embark on an energy explanation. You show him a drawing of a primitive cell of a sodium chloride crystal, NaCl, or simple table salt. The drawing is shown in Figure P24.10, where the orange spheres are Na+ ions and the blue spheres are Cl− ions. Each ion has a charge of magnitude equal to the elementary charge e. The ions lie on the comers of a cube of side d. You explain to your roommate that the electrical potential energy is defined as zero when all eight charges are infinitely far apart from each other. Then you bring them together to form the crystal structure shown. (a) Evaluate the electric potential energy of the crystal as shown and (b) show that it is energetically favorable for such crystals to form.
Figure P24.10
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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 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.
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 () )
Chapter 24 Solutions
Physics for Scientists and Engineers
Ch. 24.1 - In Figure 24.1, two points and are located...Ch. 24.2 - The labeled points in Figure 24.4 are on a series...Ch. 24.3 - In Figure 24.8b, take q2, to be a negative source...Ch. 24.4 - In a certain region of space, the electric...Ch. 24 - How much work is done (by a battery, generator, or...Ch. 24 - (a) Find the electric potential difference Ve...Ch. 24 - Oppositely charged parallel plates are separated...Ch. 24 - Starting with the definition of work, prove that...Ch. 24 - An insulating rod having linear charge density =...Ch. 24 - Review. A block having mass m and charge + Q is...
Ch. 24 - Three positive charges are located at the corners...Ch. 24 - Two point charges Q1 = +5.00 nC and Q2 = 3.00 nC...Ch. 24 - You are working on a laboratory device that...Ch. 24 - Your roommate is having trouble understanding why...Ch. 24 - Four point charges each having charge Q are...Ch. 24 - The two charges in Figure P24.12 are separated by...Ch. 24 - Show that the amount of work required to assemble...Ch. 24 - Two charged particles of equal magnitude are...Ch. 24 - Three particles with equal positive charges q are...Ch. 24 - Review. A light, unstressed spring has length d....Ch. 24 - Review. Two insulating spheres have radii 0.300 cm...Ch. 24 - Review. Two insulating spheres have radii r1 and...Ch. 24 - How much work is required to assemble eight...Ch. 24 - Four identical particles, each having charge q and...Ch. 24 - It is shown in Example 24.7 that the potential at...Ch. 24 - Figure P24.22 represents a graph of the electric...Ch. 24 - Figure P24.23 shows several equipotential lines,...Ch. 24 - An electric field in a region of space is parallel...Ch. 24 - A rod of length L (Fig. P24.25) lies along the x...Ch. 24 - For the arrangement described in Problem 25,...Ch. 24 - A wire having a uniform linear charge density is...Ch. 24 - You are a coach for the Physics Olympics team...Ch. 24 - The electric field magnitude on the surface of an...Ch. 24 - Why is the following situation impossible? A solid...Ch. 24 - A solid metallic sphere of radius a carries total...Ch. 24 - A positively charged panicle is at a distance R/2...Ch. 24 - A very large, thin, flat plate of aluminum of area...Ch. 24 - A solid conducting sphere of radius 2.00 cm has a...Ch. 24 - A spherical conductor has a radius of 14.0 cm and...Ch. 24 - A long, straight wire is surrounded by a hollow...Ch. 24 - Why is the following situation impossible? In the...Ch. 24 - On a dry winter day, you scuff your leather-soled...Ch. 24 - (a) Use the exact result from Example 24.4 to find...Ch. 24 - Why is the following situation impossible? You set...Ch. 24 - The thin, uniformly charged rod shown in Figure...Ch. 24 - A GeigerMueller tube is a radiation detector that...Ch. 24 - Review. Two parallel plates having charges of...Ch. 24 - When an uncharged conducting sphere of radius a is...Ch. 24 - A solid, insulating sphere of radius a has a...Ch. 24 - A hollow, metallic, spherical shell has exterior...Ch. 24 - For the configuration shown in Figure P24.45,...Ch. 24 - An electric dipole is located along the y axis as...Ch. 24 - A disk of radius R (Fig. P24.49) has a nonuniform...Ch. 24 - A particle with charge q is located at x = R, and...Ch. 24 - (a) A uniformly charged cylindrical shell with no...
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