Explanation Given data: Refer to Figure P20.55 in the textbook for arrangement of point charges. The charges are 1.0 nC , 2.0 nC , and 2.0 nC . The distance between the charges is 1.0 cm . Formula used: Write the expression for electric force ( F ) . F = K | q 1 | | q 2 | r 2 (1) Here, | q 1 | is magnitude of first charge, | q 2 | is magnitude of second charge, r is distance between the charges, and K is electrostatic constant, which is 9 .0 × 10 9 N ⋅ m 2 C 2 . Consider the expression for total force on charge 1.0 nC ( F 1 ) . F 1 = ( F 2 on 1 ) x + ( F 2 on 1 ) y + ( F 3 on 1 ) x + ( F 3 on 1 ) y (2) Here, ( F 2 on 1 ) x is x-component of F 2 on 1 , ( F 2 on 1 ) y is x-component of F 2 on 1 , ( F 3 on 1 ) x is x-component of F 3 on 1 , and ( F 3 on 1 ) y is x-component of F 3 on 1 , Explanation: Consider the charge 1.0 nC as q 1 , charge 2.0 nC as q 2 , and charge 2.0 nC as q 3 . Calculation of force of q 2 on q 1 ( F 2 on 1 ) : Substitute F 2 on 1 for F , 1.0 nC for q 1 , 2.0 nC for q 2 , 9 .0 × 10 9 N ⋅ m 2 C 2 for K , and 1.0 cm for r in equation (1), F 2 on 1 = ( 9 .0 × 10 9 N ⋅ m 2 C 2 ) | 1.0 nC | | 2.0 nC | ( 1.0 cm ) 2 = ( 9 .0 × 10 9 N ⋅ m 2 C 2 ) ( 1.0 × 10 − 9 C ) ( 2.0 × 10 − 9 C ) ( 1.0 × 10 − 2 m ) 2 { ∵ 1 nC = 10 − 9 C , 1 cm = 10 − 2 m } = ( 9 .0 × 10 9 N ⋅ m 2 C 2 ) ( 1.0 × 10 − 9 C ) ( 2.0 × 10 − 9 C ) 1.0 × 10 − 4 m 2 = 1.8 × 10 − 4 N From Figure P20.55, Write the x -component of force F 2 on 1 . ( F 2 on 1 ) x = F 2 on 1 cos 60 ° Substitute 1.8 × 10 − 4 N for F 2 on 1 , ( F 2 on 1 ) x = ( 1.8 × 10 − 4 N ) cos 60 ° = ( 1.8 × 10 − 4 N ) ( 1 2 ) = 0.9 × 10 − 4 N Write the y -component of force F 2 on 1 . ( F 2 on 1 ) y = F 2 on 1 sin 60 ° Substitute 1.8 × 10 − 4 N for F 2 on 1 , ( F 2 on 1 ) y = ( 1

College Physics: A Strategic Approach, Books a la Carte Edition (4th Edition)

4th Edition

ISBN: 9780134700502

Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field

Publisher: PEARSON

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Question

Chapter 20, Problem 55GP

To determine

The magnitude of force on 1.0 nC charge and direction of force.

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Chapter 20, Problem 54GP

Chapter 20, Problem 56GP

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Exercise 1: (a) Using the explicit formulae derived in the lectures for the (2j+1) × (2j + 1) repre- sentation matrices Dm'm, (J/h), derive the 3 × 3 matrices corresponding to the case j = 1. (b) Verify that they satisfy the so(3) Lie algebra commutation relation: [D(Î₁/ħ), D(Î₂/h)]m'm₁ = iƊm'm² (Ĵ3/h). (c) Prove the identity 3 Dm'm,(Î²) = Σ (D(Î¡)D(Î¡))m'¡m; · i=1

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Chapter 20 Solutions

College Physics: A Strategic Approach, Books a la Carte Edition (4th Edition)

Ch. 20 - Four lightweight balls A, B, C, and D are...Ch. 20 - Plastic and glass rods that have been charged by...Ch. 20 - When you take clothes out of the drier right after...Ch. 20 - The positive charge in Figure Q20.5 is +Q. What is...Ch. 20 - As shown in Figure Q20.6, metal sphere A has 4...Ch. 20 - Figure Q20.7 shows a positively charged rod held...Ch. 20 - A plastic balloon that has been rubbed with wool...Ch. 20 - You are given two metal spheres on portable...Ch. 20 - A metal rod A and a metal sphere B, on insulating...Ch. 20 - Prob. 10CQ

Ch. 20 - Prob. 11CQ Ch. 20 - Prob. 12CQ Ch. 20 - Prob. 13CQ Ch. 20 - Prob. 14CQ Ch. 20 - Prob. 15CQ Ch. 20 - Prob. 16CQ Ch. 20 - Iontophoresis is a noninvasive process that...Ch. 20 - A positively charged particle is in the center of...Ch. 20 - Two charged particles are separated by 10 cm....Ch. 20 - A small positive charge q experiences a force of...Ch. 20 - A typical commercial airplane is struck by...Ch. 20 - Microbes such as bacteria have small positive...Ch. 20 - a. Is there a point between a 10 nC charge and a...Ch. 20 - Prob. 24CQ Ch. 20 - Prob. 25CQ Ch. 20 - Prob. 26MCQ Ch. 20 - Prob. 27MCQ Ch. 20 - Prob. 28MCQ Ch. 20 - Prob. 29MCQ Ch. 20 - A glass bead charged to +3.5 nC exerts an 8.0 104...Ch. 20 - A +7.5 nC point charge and a 2.0 nC point charge...Ch. 20 - Prob. 32MCQ Ch. 20 - Prob. 33MCQ Ch. 20 - Prob. 34MCQ Ch. 20 - Prob. 35MCQ Ch. 20 - Prob. 36MCQ Ch. 20 - Prob. 37MCQ Ch. 20 - A glass rod is charged to +5.0 nC by rubbing. a....Ch. 20 - Prob. 2P Ch. 20 - A plastic rod is charged to 20 nC by rubbing. a....Ch. 20 - Prob. 4P Ch. 20 - A plastic rod that has been charged to 15.0 nC...Ch. 20 - A glass rod that has been charged to +12.0 nC...Ch. 20 - Two identical metal spheres A and Bare in contact....Ch. 20 - Two identical metal spheres A and Bare connected...Ch. 20 - Prob. 9P Ch. 20 - Prob. 10P Ch. 20 - Two 1.0 kg masses are 1.0 m apart on a...Ch. 20 - Prob. 12P Ch. 20 - Prob. 13P Ch. 20 - A small plastic sphere with a charge of 5.0 nC is...Ch. 20 - A small metal bead, labeled A, has a charge of 25...Ch. 20 - A small glass bead has been charged to +20 nC. A...Ch. 20 - Prob. 17P Ch. 20 - Prob. 18P Ch. 20 - Object A, which has been charged to +10 nC, is at...Ch. 20 - Prob. 20P Ch. 20 - What magnitude charge creates a 1.0 N/C electric...Ch. 20 - Prob. 22P Ch. 20 - What are the strength and direction of the...Ch. 20 - Prob. 24P Ch. 20 - What are the strength and direction of the...Ch. 20 - A 30 nC charge experiences a 0.035 N electric...Ch. 20 - A 10 nC charge is located at the origin. a. What...Ch. 20 - A +1 0 nC charge is located at the origin. a. What...Ch. 20 - Prob. 29P Ch. 20 - Prob. 30P Ch. 20 - A parallel-plate capacitor is constructed of two...Ch. 20 - Prob. 32P Ch. 20 - A parallel-plate capacitor is formed from two 4.0...Ch. 20 - Two identical closely spaced circular disks form a...Ch. 20 - A parallel-plate capacitor is constructed of two...Ch. 20 - Prob. 36P Ch. 20 - Prob. 37P Ch. 20 - Prob. 38P Ch. 20 - What are the strength and direction of an electric...Ch. 20 - Prob. 40P Ch. 20 - A 0.10 g plastic bead is charged by the addition...Ch. 20 - Prob. 42P Ch. 20 - One kind of e-book display consists of millions of...Ch. 20 - Prob. 44P Ch. 20 - A protein molecule in an electrophoresis gel has a...Ch. 20 - Large electric fields in cell membranes cause ions...Ch. 20 - Molecules of carbon mon-oxide are permanent...Ch. 20 - A 2.0-mmdiameter copper ball is charged to +50 nC....Ch. 20 - Two protons are 2.0 fm apart. (1 fm= 1 femtometer...Ch. 20 - The nucleus of a 12Xe atom (an isotope of the...Ch. 20 - Two equally charged, 1.00 g spheres are placed...Ch. 20 - An electric dipole is formed from 1.0 nC point...Ch. 20 - Prob. 53GP Ch. 20 - Prob. 54GP Ch. 20 - Prob. 55GP Ch. 20 - Prob. 56GP Ch. 20 - Prob. 57GP Ch. 20 - Prob. 58GP Ch. 20 - Prob. 59GP Ch. 20 - As shown in Figure P20.52, a 5.0 nC charge sits at...Ch. 20 - Prob. 61GP Ch. 20 - In a simple model of the hydrogen atom, the...Ch. 20 - A 0.10 g honeybee acquires a charge of +23 pC...Ch. 20 - Two 2.0-cm-diameter disks face each other, 1.0 mm...Ch. 20 - The electron gun in a television tube uses a...Ch. 20 - Prob. 66GP Ch. 20 - A 4.0 mg bead with a charge of 2.5 nC rests on a...Ch. 20 - Prob. 68GP Ch. 20 - A small charged bead has a mass of 1.0 g. It is...Ch. 20 - A bead with a mass of 0.050 g and a charge of 15...Ch. 20 - Prob. 71GP Ch. 20 - Prob. 72GP Ch. 20 - A small bead with a positive charge q is free to...Ch. 20 - A parallel-plate capacitor consists of two plates,...Ch. 20 - Which of the following describes the charges on...Ch. 20 - Because the droplets are conductors, a droplet's...Ch. 20 - Another way to sort the droplets would be to give...

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