Explanation Write the integral expression. I = ∫ 0 R R ⋅ d R R 2 + x 2 Here, R is the radius of disc and x is the distance to any point on the axial line from the center of disc. Use the substitution method to solve the integral. Use the substitution given below. R 2 + x 2 = u (I) Differentiate the expression with respect to x . 2 R d R = d u R d R = 1 2 d u (II) On applying the substitution method, limits of integration will also be changed to new integral. Substitute 0 for x in equation (I) to find the new lower limit. R 2 + 0 = u R 2 = u So the lower limit corresponding to x = 0 is u = R 2

Webassign Printed Access Card For Katz's Physics For Scientists And Engineers: Foundations And Connections, 1st Edition, Single-term

1st Edition

ISBN: 9781337684637

Author: Debora M. Katz

Publisher: Cengage Learning

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Chapter 26, Problem 81PQ

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Prove that ∫0RR⋅dRR2+x2=(R2+x2)−x.

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Chapter 26, Problem 80PQ

Chapter 27.1, Problem 27.1CE

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Chapter 26 Solutions

Webassign Printed Access Card For Katz's Physics For Scientists And Engineers: Foundations And Connections, 1st Edition, Single-term

Ch. 26.2 - Complete the analogies by filling in the blanks,...Ch. 26.3 - Prob. 26.2CE Ch. 26.3 - A water molecule is made up of two hydrogen atoms...Ch. 26.4 - Match the topographical maps in Figure 26.15 with...Ch. 26.5 - Which term or phrase is a synonym for electric...Ch. 26.7 - If the contours in Figure 26.26 represent the...Ch. 26.9 - Prob. 26.7CE Ch. 26 - What does it mean when a force is negative? What...Ch. 26 - Review Return to Chapter 8 and the potential...Ch. 26 - Review A system consists of a planet and a star,...

Ch. 26 - Try to complete Table P26.4 from memory. If you...Ch. 26 - Try to complete Table P26.5 from memory. If you...Ch. 26 - Can you associate electric potential energy with...Ch. 26 - Consider the final arrangement of charged...Ch. 26 - Using the usual convention that the electric...Ch. 26 - FIGURE P26.8 A Find an expression for the electric...Ch. 26 - A hydrogen atom consists of an electron and a...Ch. 26 - What is the work that a generator must do to move...Ch. 26 - How far should a +3.0-C charged panicle be from a...Ch. 26 - A proton is fired from very far away directly at a...Ch. 26 - Four charged particles are at rest at the corners...Ch. 26 - FIGURE P26.14 Problems 14, 15, and 16. Four...Ch. 26 - Four charged particles are at rest at the corners...Ch. 26 - Eight identical charged particles with q = 1.00 nC...Ch. 26 - A conducting sphere with a radius of 0.25 m has a...Ch. 26 - The speed of an electron moving along the y axis...Ch. 26 - Figure P26.20 is a topographic map. a. Rank A, B,...Ch. 26 - At a point in space, the electric potential due to...Ch. 26 - Explain the difference between UE(r) = kQq/r and...Ch. 26 - Suppose a single electron moves through an...Ch. 26 - Two point charges, q1 = 2.0 C and q2 = 2.0 C, are...Ch. 26 - Separating the electron from the proton in a...Ch. 26 - Can a contour map help you visualize the electric...Ch. 26 - Prob. 27PQ Ch. 26 - Find the electric potential at the origin given...Ch. 26 - Prob. 29PQ Ch. 26 - Prob. 30PQ Ch. 26 - Prob. 31PQ Ch. 26 - Prob. 32PQ Ch. 26 - A source consists of three charged particles...Ch. 26 - Two identical metal balls of radii 2.50 cm are at...Ch. 26 - Figure P26.35 shows four particles with identical...Ch. 26 - Two charged particles with qA = 9.75 C and qB =...Ch. 26 - Two charged particles with q1 = 5.00 C and q2 =...Ch. 26 - Prob. 38PQ Ch. 26 - Prob. 39PQ Ch. 26 - A uniformly charged ring with total charge q =...Ch. 26 - A line of charge with uniform charge density lies...Ch. 26 - A line of charge with uniform charge density =...Ch. 26 - A Consider a thin rod of total charge Q and length...Ch. 26 - Figure P26.44 shows a rod of length = 1.00 m...Ch. 26 - The charge density on a disk of radius R = 12.0 cm...Ch. 26 - Prob. 46PQ Ch. 26 - In some region of space, the electric field is...Ch. 26 - A particle with charge 1.60 1019 C enters midway...Ch. 26 - Prob. 49PQ Ch. 26 - Prob. 50PQ Ch. 26 - Prob. 51PQ Ch. 26 - Prob. 52PQ Ch. 26 - Prob. 53PQ Ch. 26 - According to Problem 43, the electric potential at...Ch. 26 - The electric potential is given by V = 4x2z + 2xy2...Ch. 26 - The electric potential V(x, y, z) in a region of...Ch. 26 - Prob. 57PQ Ch. 26 - In three regions of space, the electric potential...Ch. 26 - Prob. 59PQ Ch. 26 - Prob. 60PQ Ch. 26 - The distance between two small charged spheres...Ch. 26 - Prob. 62PQ Ch. 26 - A glass sphere with radius 4.00 mm, mass 85.0 g,...Ch. 26 - Prob. 64PQ Ch. 26 - Two 5.00-nC charged particles are in a uniform...Ch. 26 - A 5.00-nC charged particle is at point B in a...Ch. 26 - A charged particle is moved in a uniform electric...Ch. 26 - Figure P26.68 shows three small spheres with...Ch. 26 - What is the work required to charge a spherical...Ch. 26 - For a system consisting of two identical...Ch. 26 - Figure P26.71 shows three charged particles...Ch. 26 - Problems 72, 73, and 74 are grouped. 72. A Figure...Ch. 26 - A Start with V=2k[(R2+x2)x] for the electric...Ch. 26 - A Review Consider the charged disks in Problem 72...Ch. 26 - A long thin wire is used in laser printers to...Ch. 26 - An electric potential exists in a region of space...Ch. 26 - A disk with a nonuniform charge density =ar2 has...Ch. 26 - An infinite number of charges with q = 2.0 C are...Ch. 26 - An infinite number of charges with |q| =2.0 C are...Ch. 26 - Figure P26.80 shows a wire with uniform charge per...Ch. 26 - Prob. 81PQ

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Prove that ∫ 0 R R ⋅ d R R 2 + x 2 = ( R 2 + x 2 ) − x .

Solution Summary: The author analyzes the substitution method to solve the integral. R is the radius of disc and x the distance to any point on the axial line.

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Prove that ∫0RR⋅dRR2+x2=(R2+x2)−x.

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Chapter 26 Solutions