In A Vacuum, Two Particles Have Charges Of Q1 And Q2, Where Q1 = +5.1C. They Are Separated By A Distance Of 0.38 M, And Particle 1 Experiences An Attractive Force Of 2.7 N. What Is The Value Of Q2, With Its Sign?<\/p>\n\n\n\n
The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n We are given:<\/p>\n\n\n\n The force between two charges in a vacuum is given by Coulomb\u2019s Law<\/strong>:<\/p>\n\n\n\n [ where ( k = 8.99 \\times 10^9 \\, \\text{N} \\cdot \\text{m}^2 \/ \\text{C}^2 ) (Coulomb’s constant).<\/p>\n\n\n\n First, solve for ( |Q_2| ):<\/p>\n\n\n\n [ Substitute the known values:<\/p>\n\n\n\n [ First, calculate ( r^2 ):<\/p>\n\n\n\n [ Now, multiply ( F ) and ( r^2 ):<\/p>\n\n\n\n [ Now, multiply ( k ) and ( Q_1 ):<\/p>\n\n\n\n [ Now, calculate:<\/p>\n\n\n\n [ [ Since the force is attractive<\/strong>, and ( Q_1 ) is positive<\/strong>, ( Q_2 ) must be negative<\/strong> (because opposite charges attract).<\/p>\n\n\n\n Thus, the final answer is:<\/p>\n\n\n\n [ This problem is a direct application of Coulomb\u2019s Law<\/strong>, which describes the force between two point charges. Coulomb\u2019s Law states that the magnitude of the electric force between two charges is proportional to the product of their charges and inversely proportional to the square of the distance between them. Mathematically, it is expressed as:<\/p>\n\n\n\n [ where ( F ) is the force, ( Q_1 ) and ( Q_2 ) are the charges, ( r ) is the distance between them, and ( k ) is Coulomb\u2019s constant.<\/p>\n\n\n\n In this problem, you are given the force, one of the charges, and the distance between them, and you are asked to find the other charge, ( Q_2 ). Importantly, the problem states that the force is attractive<\/strong>, which provides critical information about the sign of ( Q_2 ). In physics, like charges repel and unlike charges attract. Since ( Q_1 ) is positive and the force is attractive, ( Q_2 ) must be negative.<\/p>\n\n\n\n Using the formula, rearranging for ( Q_2 ), and plugging in the given numbers, we found that the magnitude of ( Q_2 ) is ( 8.5 \\times 10^{-12} \\, \\text{C} ). Considering the sign, the final answer is ( -8.5 \\times 10^{-12} \\, \\text{C} ).<\/p>\n\n\n\n Thus, the key steps were identifying the correct formula, solving algebraically for the unknown, substituting values carefully, and finally, considering the direction (attractive force implies opposite charges) to assign the correct sign.<\/p>\n","protected":false},"excerpt":{"rendered":" In A Vacuum, Two Particles Have Charges Of Q1 And Q2, Where Q1 = +5.1C. They Are Separated By A Distance Of 0.38 M, And Particle 1 Experiences An Attractive Force Of 2.7 N. What Is The Value Of Q2, With Its Sign? The correct answer and explanation is : We are given: The force […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-208744","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/208744","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=208744"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/208744\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=208744"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=208744"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=208744"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
F = k \\frac{|Q_1 Q_2|}{r^2}
]<\/p>\n\n\n\n
|Q_2| = \\frac{F r^2}{k |Q_1|}
]<\/p>\n\n\n\n
|Q_2| = \\frac{(2.7 \\, \\text{N}) (0.38 \\, \\text{m})^2}{(8.99 \\times 10^9 \\, \\text{N} \\cdot \\text{m}^2 \/ \\text{C}^2)(5.1 \\, \\text{C})}
]<\/p>\n\n\n\n
0.38^2 = 0.1444 \\, \\text{m}^2
]<\/p>\n\n\n\n
2.7 \\times 0.1444 = 0.38988
]<\/p>\n\n\n\n
8.99 \\times 10^9 \\times 5.1 = 4.5849 \\times 10^{10}
]<\/p>\n\n\n\n
|Q_2| = \\frac{0.38988}{4.5849 \\times 10^{10}}
]<\/p>\n\n\n\n
|Q_2| \\approx 8.5 \\times 10^{-12} \\, \\text{C}
]<\/p>\n\n\n\n
\\boxed{Q_2 = -8.5 \\times 10^{-12} \\, \\text{C}}
]<\/p>\n\n\n\n
\n\n\n\nDetailed Explanation (around 300 words):<\/h3>\n\n\n\n
F = k \\frac{|Q_1 Q_2|}{r^2}
]<\/p>\n\n\n\n