Physics for Scientists and Engineers: Foundations and Connections
15th Edition
ISBN: 9781305289963
Author: Debora M. Katz
Publisher: Cengage Custom Learning
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Textbook Question
Chapter 24, Problem 28PQ
The electric field at a point on the perpendicular bisector of a charged rod was calculated as the first example of a continuous charge distribution, resulting in Equation 24.15:
a. Find an expression for the electric field when the rod is infinitely long.
b. An infinitely long rod with uniform linear charge density λ also contains an infinite amount of charge. Explain why this still produces an electric field near the rod that is finite.
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Chapter 24 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 24.2 - In a few sentences, explain how you know that...Ch. 24.2 - What is the magnitude of the electric field due to...Ch. 24.3 - Which lines in Figure 24.7 cannot represent an...Ch. 24.4 - Figure 24.10 shows a source that consists of two...Ch. 24.4 - A water molecule is made up of two hydrogen atoms...Ch. 24.5 - a. Figure 24.22A shows a rod of length L and...Ch. 24 - The terms electrostatic force and electrostatic...Ch. 24 - Prob. 2PQCh. 24 - A sphere has a charge of 89.5 nC and a radius of...Ch. 24 - Prob. 4PQ
Ch. 24 - A sphere with a charge of 3.50 nC and a radius of...Ch. 24 - Is it possible for a conducting sphere of radius...Ch. 24 - Prob. 7PQCh. 24 - For each sketch of electric field lines in Figure...Ch. 24 - Prob. 9PQCh. 24 - Two large neutral metal plates, fitted tightly...Ch. 24 - Given the two charged particles shown in Figure...Ch. 24 - Prob. 12PQCh. 24 - Prob. 13PQCh. 24 - A particle with charge q on the negative x axis...Ch. 24 - Prob. 15PQCh. 24 - Figure P24.16 shows three charged particles...Ch. 24 - Figure P24.17 shows a dipole. If the positive...Ch. 24 - Find an expression for the electric field at point...Ch. 24 - Figure P24.17 shows a dipole (not drawn to scale)....Ch. 24 - Figure P24.20 shows three charged spheres arranged...Ch. 24 - Often we have distributions of charge for which...Ch. 24 - Prob. 22PQCh. 24 - A positively charged rod with linear charge...Ch. 24 - A positively charged rod of length L = 0.250 m...Ch. 24 - Prob. 25PQCh. 24 - Prob. 26PQCh. 24 - A Find an expression for the position y (along the...Ch. 24 - The electric field at a point on the perpendicular...Ch. 24 - Prob. 29PQCh. 24 - Find an expression for the magnitude of the...Ch. 24 - What is the electric field at point A in Figure...Ch. 24 - A charged rod is curved so that it is part of a...Ch. 24 - If the curved rod in Figure P24.32 has a uniformly...Ch. 24 - aA plastic rod of length = 24.0 cm is uniformly...Ch. 24 - A positively charged disk of radius R = 0.0366 m...Ch. 24 - A positively charged disk of radius R and total...Ch. 24 - A uniformly charged conducting rod of length =...Ch. 24 - Prob. 38PQCh. 24 - Prob. 39PQCh. 24 - Prob. 40PQCh. 24 - Prob. 41PQCh. 24 - Prob. 42PQCh. 24 - What are the magnitude and direction of a uniform...Ch. 24 - An electron is in a uniform upward-pointing...Ch. 24 - Prob. 45PQCh. 24 - Prob. 46PQCh. 24 - A very large disk lies horizontally and has...Ch. 24 - An electron is released from rest in a uniform...Ch. 24 - In Figure P24.49, a charged particle of mass m =...Ch. 24 - Three charged spheres are suspended by...Ch. 24 - Figure P24.51 shows four small charged spheres...Ch. 24 - Prob. 52PQCh. 24 - A uniform electric field given by...Ch. 24 - A uniformly charged ring of radius R = 25.0 cm...Ch. 24 - Prob. 55PQCh. 24 - Prob. 56PQCh. 24 - A potassium chloride molecule (KCl) has a dipole...Ch. 24 - Prob. 58PQCh. 24 - Prob. 59PQCh. 24 - Prob. 60PQCh. 24 - A total charge Q is distributed uniformly on a...Ch. 24 - A simple pendulum has a small sphere at its end...Ch. 24 - A thin, semicircular wire of radius R is uniformly...Ch. 24 - Prob. 64PQCh. 24 - Prob. 65PQCh. 24 - Prob. 66PQCh. 24 - Prob. 67PQCh. 24 - Prob. 68PQCh. 24 - A thin wire with linear charge density =0y0(14+1y)...Ch. 24 - Prob. 70PQCh. 24 - Two positively charged spheres are shown in Figure...Ch. 24 - Prob. 72PQCh. 24 - Prob. 73PQCh. 24 - Prob. 74PQCh. 24 - A conducting rod carrying a total charge of +9.00...Ch. 24 - Prob. 76PQCh. 24 - A When we find the electric field due to a...Ch. 24 - Prob. 78PQCh. 24 - Prob. 79PQCh. 24 - Prob. 80PQCh. 24 - Prob. 81PQCh. 24 - Prob. 82PQ
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- A simple pendulum has a small sphere at its end with mass m and charge q. The pendulums rod has length L and its weight is negligible. The pendulum is placed in a uniform electric field of strength E directed vertically upward. What is the period of oscillation of the sphere if the electric force is less than the gravitational force on the sphere? Assume the oscillations are small. FIGURE P24.63arrow_forwardA charged rod is curved so that it is part of a circle of radius R (Fig. P24.32). The excess positive charge Q is uniformly distributed on the rod. Find an expression for the electric field at point A in the plane of the curved rod in terms of the parameters given in the figure.arrow_forwardA When we find the electric field due to a continuous charge distribution, we imagine slicing that source up into small pieces, finding the electric field produced by the pieces, and then integrating to find the electric field. Lets see what happens if we break a finite rod up into a small number of finite particles. Figure P24.77 shows a rod of length 2 carrying a uniform charge Q modeled as two particles of charge Q/2. The particles are at the ends of the rod. Find an expression for the electric field at point A located a distance above the midpoint of the rod using each of two methods: a. modeling the rod with just two particles and b. using the exact expression E=kQy12+y2 c. Compare your results to the exact expression for the rod by finding the ratio of the approximate expression to the exact expression. FIGURE P24.77 Problems 77 and 78.arrow_forward
- A uniformly charged rod of length L and total charge Q lies along the x axis as shown in Figure P23.6. (a) Find the components of the electric field at the point P on the y axis a distance d from the origin. (b) What are the approximate values of the field components when d L? Explain why you would expect these results. Figure P23.6arrow_forwardIn which of the following contexts can Gausss law not be readily applied to find the electric field? (a) near a long, uniformly charged wire (b) above a large, uniformly charged plane (c) inside a uniformly charged ball (d) outside a uniformly charged sphere (e) Gausss law can be readily applied to find the electric field in all these contexts.arrow_forward(a) Find the electric field at x = 5.00 cm in Figure 18.52 (a), given that q = 1.00 C. (b) at what position between 3.00 and 8.00 cm is the total electric field the same as that for ? 2q alone? (c) Can the electric field be zero anywhere between 0.00 and 8.00 cm? (d) At very large positive or negative values of x, the electric field approaches zero in both (a) and (b). In which does it most rapidly approach zero and why? (e) At what position to the light of 11.0 cm is the total electric field zero, other than at infinity? (Hint: A graphing calculator can yield considerable insight in this problem.)arrow_forward
- Figure P24.20 shows three charged spheres arranged along the y axis. a. What is the electric field at x = 0, y = 3.00 m? b. What is the electric field at x = 3.00 m, y = 0? FIGURE P24.20arrow_forwardA solid, insulating sphere of radius a has a uniform charge density throughout its volume and a total charge Q. Concentric with this sphere is an uncharged, conducting, hollow sphere whose inner and outer radii are b and e as shown in Figure P24.45. We wish to understand completely the charges and electric fields at all locations. (a) Find the charge contained within a sphere of radius r a. (b) From this value, find the magnitude of the electric field for r a. (c) What charge is contained within a sphere of radius r when a r b? (d) From this value, find the magnitude of the electric field for r when a r b. (e) Now consider r when b r c. What is the magnitude of the electric field for this range of values of r? (f) From this value, what must be the charge on the inner surface of the hollow sphere? (g) From part (f), what must be the charge on the outer surface of the hollow sphere? (h) Consider the three spherical surfaces of radii a, b, and c. Which of these surfaces has the largest magnitude of surface charge density? Figure P24.45 Problems 43 and 47.arrow_forwardA very long, thin wire fixed along the x axis has a linear charge density of 3.2 C/m. a. Determine the electric field at point P a distance of 0.50 m from the wire. b. If there is a test charge q0 = 12.0 C at point P, what is the magnitude of the net force on this charge? In which direction will the test charge accelerate?arrow_forward
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