Explanation Formula used: Write the expression for electric field ( E → ) . E → = K | q | r 2 (1) Here, | q | is magnitude of charge, r is distance, and K is electrostatic constant, which is 9 .0 × 10 9 N ⋅ m 2 C 2 . Write the expression for net electric field. E → = E 1 → + E 2 → + E 3 → (2) Here, E 1 → is field due to first charge, E 2 → is field due to second charge, and E 3 → is field due to third charge. Explanation: Consider E → as a basic charge and is equal to 1 unit and charge is q . E → = 1 unit Re-draw the Figure Q20.29 as shown in Figure 1. From Figure 1, case A: The charge is q and the distance between first charge and dot is 2 r . Substitute 2 r for r and E 1 → for E → in equation (1), E 1 → = K | q | ( 2 r ) 2 = K | q | 4 r 2 = 1 4 ( K | q | r 2 ) Substitute E → for ( K | q | r 2 ) , E 1 → = 1 4 E → Substitute 1 unit for E → , E 1 → = 1 4 ( 1 unit ) = 1 4 units The charge is q and the distance between second and third charges and dot is r , and hence the magnitude of field is equal to 1 unit. Therefore, E 1 → = 1 4 units E 2 → = 1 unit E 3 → = − 1 unit Substitute 1 4 units for E 1 → , 1 unit for E 2 → , − 1 unit for E 3 → in equation (2), E → = 1 4 units+ 1 unit − 1 unit = 1 4 units Therefore, the total electric field is 1 4 units due to charge 1. From Figure 1, case B: The charge is q and the distance between first and second charges and dot is r , and hence the magnitude of field is equal to 1 unit. The field direction of both charges is in same direction. The charge is q and the distance between third charge and dot is 2 r . Substitute 2 r for r and E 3 → for E → in equation (1), E 3 → = K | q | ( 2 r ) 2 = K | q | 4 r 2 = 1 4 ( K | q | r 2 ) Substitute E → for ( K | q | r 2 ) , E 3 → = 1 4 E → Substitute 1 unit for E → , E 3 → = 1 4 ( 1 unit ) = 1 4 units Therefore, E 1 → = 1 unit E 2 → = 1 unit E 3 → = − 1 4 units Substitute 1 unit for E 1 → , 1 unit for E 2 → , − 1 4 units for E 3 → in equation (2), E → = 1 unit+ 1 unit − 1 4 unit = 7 4 units Therefore, the total electric field is 7 4 units due to charges 1, 2, and 3

College Physics: A Strategic Approach (4th Edition)

4th Edition

ISBN: 9780134609034

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

Publisher: PEARSON

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Chapter 20, Problem 29MCQ

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To find: Which has the largest magnitude of electric field at the dot.

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Chapter 20, Problem 28MCQ

Chapter 20, Problem 30MCQ

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College Physics: A Strategic Approach (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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