Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 24, Problem 80PQ
(a)
To determine
The electric filed at the point A by modelling the rod with five particles.
(b)
To determine
The electric filed at the point A by modelling the rod with the exact expression.
(c)
To determine
The ratio of approximate result to the exact electric field.
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Five charged particles are equally spaced around a semicircle of radius 100 mm, with one particle at each end of the semicircle and the remaining three spaced equally between the two ends. The semicircle lies in the region x<0 of an xy plane, such that the complete circle is centered on the origin.
If each particle carries a charge of 6.00 nC , what is the electric field at the origin?
Where could you put a single particle carrying a charge of -5.00 nC to make the electric field magnitude zero at the origin?
Two thin rods of length L lie along the x-axis, one between x=a/2 and x=a/2 + L and the other between x=−a/2 and x=−a/2 − L.
Each rod has positive charge Q distributed uniformly along its length.
Calculate the electric field produced by the second rod at points along the positive x-axis. Express your answer in terms of the variables x, a, L, Q and constant k.Find the magnitude of the force that one rod exerts on the other. Express your answer in terms of the variables a, L, Q and constant k.
A uniformly charged rod of length L = 1.2 m lies along the x-axis with its right end at the origin. The rod has a total charge of Q = 6.8 μC. A point P is located on the x-axis a distance a = 2.4 m to the right of the origin.Integrate the electric field contributions from each slice over the length of the rod to write an equation for the net electric field E at point P.
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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- Figure P24.16 shows three charged particles arranged in the xy plane at the coordinates shown, with qA = qB = 3.30 nC and qC = 4.70 nC. What is the electric field due to these particles at the origin? FIGURE P24.16arrow_forwardFind an expression for the magnitude of the electric field at point A mid-way between the two rings of radius R shown in Figure P24.30. The ring on the left has a uniform charge q1 and the ring on the right has a uniform charge q2. The rings are separated by distance d. Assume the positive x axis points to the right, through the center of the rings. FIGURE P24.30 Problems 30 and 31.arrow_forwardIn Figure P24.49, a charged particle of mass m = 4.00 g and charge q = 0.250 C is suspended in static equilibrium at the end of an insulating thread that hangs from a very long, charged, thin rod. The thread is 12.0 cm long and makes an angle of 35.0 with the vertical. Determine the linear charge density of the rod. FIGURE P24.49arrow_forward
- aA plastic rod of length = 24.0 cm is uniformly charged with a total charge of +12.0 C. The rod is formed into a semicircle with its center at the origin of the xy plane (Fig. P24.34). What are the magnitude and direction of the electric field at the origin? Figure P24.34arrow_forwardThe infinite sheets in Figure P25.47 are both positively charged. The sheet on the left has a uniform surface charge density of 48.0 C/m2, and the one on the right has a uniform surface charge density of 24.0 C/m2. a. What are the magnitude and direction of the net electric field at points A, B, and C? b. What is the force exerted on an electron placed at points A, B, and C? FIGURE P25.47arrow_forwardA circular ring of charge with radius b has total charge q uniformly distributed around it. What is the magnitude of the electric field at the center of the ring? (a) 0 (b) keq/b2 (c) keq2/b2 (d) keq2/b (e) none of those answersarrow_forward
- Figure P24.17 shows a dipole. If the positive particle has a charge of 35.7 mC and the particles are 2.56 mm apart, what is the electric field at point A located 2.00 mm above the dipoles midpoint?arrow_forwardA conducting rod carrying a total charge of +9.00 C is bent into a semicircle of radius R = 33.0 cm, with its center of curvature at the origin (Fig.P24.75). The charge density along the rod is given by = 0 sin , where is measured clockwise from the +x axis. What is the magnitude of the electric force on a 1.00-C charged particle placed at the origin?arrow_forwardA positively charged disk of radius R = 0.0366 m and total charge 56.8 C lies in the xz plane, centered on the y axis (Fig. P24.35). Also centered on the y axis is a charged ring with the same radius as the disk and a total charge of 34.1 C. The ring is a distance d = 0.0050 m above the disk. Determine the electric field at the point P on the y axis, where P is y = 0.0100 m above the origin. FIGURE P24.35 Problems 35 and 36.arrow_forward
- Why is the following situation impossible? A solid copper sphere of radius 15.0 cm is in electrostatic equilibrium and carries a charge of 40.0 nC. Figure P24.30 shows the magnitude of the electric field as a function of radial position r measured from the center of the sphere. Figure P24.30arrow_forwardTwo positively charged spheres are shown in Figure P24.70. Sphere 1 has twice as much charge as sphere 2. If q = 6.55 nC, d = 0.250 m, and y = 1.25 m, what is the electric field at point A?arrow_forwardGiven the two charged particles shown in Figure P24.11, find the electric field at the origin.arrow_forward
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