{"id":1425,"date":"2019-01-14T03:05:51","date_gmt":"2019-01-14T03:05:51","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/ivytech-sci111\/chapter\/coulombs-law-2\/"},"modified":"2019-01-28T16:36:07","modified_gmt":"2019-01-28T16:36:07","slug":"coulombs-law-2","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-sci111\/chapter\/coulombs-law-2\/","title":{"raw":"Module 4 Coulomb's Law","rendered":"Module 4 Coulomb&#8217;s Law"},"content":{"raw":"<div class=\"boundless-concept\">\r\n<h2>Superposition of Forces<\/h2>\r\nThe superposition principle (superposition property) states that for all linear forces the total force is a vector sum of individual forces.\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\nApply the superposition principle to determine the net response caused by two or more stimuli\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Key Takeaways<\/h3>\r\n<h4>Key Points<\/h4>\r\n<ul>\r\n \t<li>The superposition principle suggests that the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually.<\/li>\r\n \t<li>Total Coulomb force on a test charge due to a group of charges is equal to the vector sum of all the Coulomb forces between the test charge and other individual charges.<\/li>\r\n \t<li>The superposition of forces is not limited to Coulomb forces. It applies to any types (or combinations) of forces.<\/li>\r\n<\/ul>\r\n<h4>Key Terms<\/h4>\r\n<ul>\r\n \t<li><strong>Lorentz force<\/strong>: The force exerted on a charged particle in an electromagnetic field.<\/li>\r\n \t<li><strong>unit vector<\/strong>: A vector with length 1.<\/li>\r\n \t<li><strong>electrostatic force<\/strong>: The electrostatic interaction between electrically charged particles; the amount and direction of attraction or repulsion between two charged bodies.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<em>The superposition principle<\/em> (also known as superposition property) states that: <em>for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually<\/em>. For Coulomb's law, the stimuli are forces. Therefore, the principle suggests that total force is a vector sum of individual forces.\r\n<h3>Coulomb Force<\/h3>\r\nThe scalar form of Coulomb's Law relates the magnitude and sign of the electrostatic force F, acting simultaneously on two point charges q<sub>1<\/sub> and q2:\r\n\r\n[latex]|\\boldsymbol{\\text{F}}|= \\frac{1}{4\\pi ar\\epsilon_0}\\frac{|\\text{q}_1\\text{q}_2|}{\\text{r}^2}[\/latex],\r\n<div class=\"wp-caption alignright\" style=\"width: 329px\">\r\n<div class=\"figure-cont\">\r\n\r\n<img class=\"\" src=\"https:\/\/textimgs.s3.amazonaws.com\/boundless-physics\/lorentz-force-particle.svg#fixme#fixme\" alt=\"image\" width=\"329\" height=\"349\" \/>\r\n<p class=\"wp-caption-text\"><strong>Lorentz Force on a Moving Particle<\/strong>: Lorentz force f on a charged particle (of charge q) in motion (instantaneous velocity v). The E field and B field vary in space and time.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"boundless-concept\">\r\n\r\nwhere r is the separation distance and \u03b5<sub>0<\/sub> is electric permittivity. If the product q<sub>1<\/sub>q<sub>2<\/sub> is positive, the force between them is repulsive; if q<sub>1<\/sub>q<sub>2<\/sub> is negative, the force between them is attractive. The principle of linear superposition allows the extension of Coulomb's law to include any number of point charges\u2014in order to derive the force on any one point charge by a vector addition of these individual forces acting alone on that point charge. The resulting force vector happens to be parallel to the electric field vector at that point, with that point charge removed.\r\n\r\n<\/div>\r\n<div class=\"boundless-concept\">\r\n<div class=\"embed-wrap\">\r\n<div class=\"figure-cont\">\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"<div class=\"boundless-concept\">\n<h2>Superposition of Forces<\/h2>\n<p>The superposition principle (superposition property) states that for all linear forces the total force is a vector sum of individual forces.<\/p>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<p>Apply the superposition principle to determine the net response caused by two or more stimuli<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Key Takeaways<\/h3>\n<h4>Key Points<\/h4>\n<ul>\n<li>The superposition principle suggests that the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually.<\/li>\n<li>Total Coulomb force on a test charge due to a group of charges is equal to the vector sum of all the Coulomb forces between the test charge and other individual charges.<\/li>\n<li>The superposition of forces is not limited to Coulomb forces. It applies to any types (or combinations) of forces.<\/li>\n<\/ul>\n<h4>Key Terms<\/h4>\n<ul>\n<li><strong>Lorentz force<\/strong>: The force exerted on a charged particle in an electromagnetic field.<\/li>\n<li><strong>unit vector<\/strong>: A vector with length 1.<\/li>\n<li><strong>electrostatic force<\/strong>: The electrostatic interaction between electrically charged particles; the amount and direction of attraction or repulsion between two charged bodies.<\/li>\n<\/ul>\n<\/div>\n<p><em>The superposition principle<\/em> (also known as superposition property) states that: <em>for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually<\/em>. For Coulomb&#8217;s law, the stimuli are forces. Therefore, the principle suggests that total force is a vector sum of individual forces.<\/p>\n<h3>Coulomb Force<\/h3>\n<p>The scalar form of Coulomb&#8217;s Law relates the magnitude and sign of the electrostatic force F, acting simultaneously on two point charges q<sub>1<\/sub> and q2:<\/p>\n<p>[latex]|\\boldsymbol{\\text{F}}|= \\frac{1}{4\\pi ar\\epsilon_0}\\frac{|\\text{q}_1\\text{q}_2|}{\\text{r}^2}[\/latex],<\/p>\n<div class=\"wp-caption alignright\" style=\"width: 329px\">\n<div class=\"figure-cont\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/textimgs.s3.amazonaws.com\/boundless-physics\/lorentz-force-particle.svg#fixme#fixme\" alt=\"image\" width=\"329\" height=\"349\" \/><\/p>\n<p class=\"wp-caption-text\"><strong>Lorentz Force on a Moving Particle<\/strong>: Lorentz force f on a charged particle (of charge q) in motion (instantaneous velocity v). The E field and B field vary in space and time.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"boundless-concept\">\n<p>where r is the separation distance and \u03b5<sub>0<\/sub> is electric permittivity. If the product q<sub>1<\/sub>q<sub>2<\/sub> is positive, the force between them is repulsive; if q<sub>1<\/sub>q<sub>2<\/sub> is negative, the force between them is attractive. The principle of linear superposition allows the extension of Coulomb&#8217;s law to include any number of point charges\u2014in order to derive the force on any one point charge by a vector addition of these individual forces acting alone on that point charge. The resulting force vector happens to be parallel to the electric field vector at that point, with that point charge removed.<\/p>\n<\/div>\n<div class=\"boundless-concept\">\n<div class=\"embed-wrap\">\n<div class=\"figure-cont\">\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-1425\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Curation and Revision. <strong>Provided by<\/strong>: Boundless.com. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Coulomb&#039;s law. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/Coulomb&#039;s_law\">http:\/\/en.wikipedia.org\/wiki\/Coulomb&#039;s_law<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>electrostatic force. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/electrostatic%20force\">http:\/\/en.wikipedia.org\/wiki\/electrostatic%20force<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Lorentz force. <strong>Provided by<\/strong>: Wiktionary. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wiktionary.org\/wiki\/Lorentz_force\">http:\/\/en.wiktionary.org\/wiki\/Lorentz_force<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>unit vector. <strong>Provided by<\/strong>: Wiktionary. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wiktionary.org\/wiki\/unit_vector\">http:\/\/en.wiktionary.org\/wiki\/unit_vector<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Lorentz force. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/Lorentz_force\">http:\/\/en.wikipedia.org\/wiki\/Lorentz_force<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>OpenStax College, Coulombu2019s Law. September 17, 2013. <strong>Provided by<\/strong>: OpenStax CNX. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/content\/m42308\/latest\/\">http:\/\/cnx.org\/content\/m42308\/latest\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Coulomb&#039;s law. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/Coulomb&#039;s_law\">http:\/\/en.wikipedia.org\/wiki\/Coulomb&#039;s_law<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>electrostatic force. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/electrostatic%20force\">http:\/\/en.wikipedia.org\/wiki\/electrostatic%20force<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Lorentz force. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/Lorentz_force\">http:\/\/en.wikipedia.org\/wiki\/Lorentz_force<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>OpenStax College, Coulombu2019s Law. October 25, 2012. <strong>Provided by<\/strong>: OpenStax CNX. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/content\/m42308\/latest\/\">http:\/\/cnx.org\/content\/m42308\/latest\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>George Brown, Coulomb Law Forces. September 17, 2013. <strong>Provided by<\/strong>: OpenStax CNX. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/content\/m12742\/latest\/\">http:\/\/cnx.org\/content\/m12742\/latest\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>George Brown, CLF Multiple Point Sources. September 17, 2013. <strong>Provided by<\/strong>: OpenStax CNX. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/content\/m12747\/latest\/\">http:\/\/cnx.org\/content\/m12747\/latest\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Coulomb&#039;s law. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/Coulomb&#039;s_law\">http:\/\/en.wikipedia.org\/wiki\/Coulomb&#039;s_law<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>electrostatic force. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/electrostatic%20force\">http:\/\/en.wikipedia.org\/wiki\/electrostatic%20force<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Lorentz force. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/Lorentz_force\">http:\/\/en.wikipedia.org\/wiki\/Lorentz_force<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>OpenStax College, Coulombu2019s Law. October 25, 2012. <strong>Provided by<\/strong>: OpenStax CNX. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/content\/m42308\/latest\/\">http:\/\/cnx.org\/content\/m42308\/latest\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>George Brown, CLF Multiple Point Sources. October 25, 2012. <strong>Provided by<\/strong>: OpenStax CNX. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/content\/m12747\/latest\/\">http:\/\/cnx.org\/content\/m12747\/latest\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>George Brown, Coulomb Law Forces. October 25, 2012. <strong>Provided by<\/strong>: OpenStax CNX. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/content\/m12742\/latest\/\">http:\/\/cnx.org\/content\/m12742\/latest\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>George Brown, CLF Multiple Point Sources. October 26, 2012. <strong>Provided by<\/strong>: OpenStax CNX. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/content\/m12747\/latest\/\">http:\/\/cnx.org\/content\/m12747\/latest\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Coulomb&#039;s Law. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.youtube.com\/watch?v=Fbyew6sBiOA\">http:\/\/www.youtube.com\/watch?v=Fbyew6sBiOA<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/a><\/em>. <strong>License Terms<\/strong>: Standard YouTube license<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":18,"menu_order":10,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Coulomb\\'s law\",\"author\":\"\",\"organization\":\"Wikipedia\",\"url\":\"http:\/\/en.wikipedia.org\/wiki\/Coulomb\\'s_law\",\"project\":\"\",\"license\":\"cc-by-sa\",\"license_terms\":\"\"},{\"type\":\"cc-attribution\",\"description\":\"electrostatic force\",\"author\":\"\",\"organization\":\"Wikipedia\",\"url\":\"http:\/\/en.wikipedia.org\/wiki\/electrostatic%20force\",\"project\":\"\",\"license\":\"cc-by-sa\",\"license_terms\":\"\"},{\"type\":\"cc-attribution\",\"description\":\"Lorentz force\",\"author\":\"\",\"organization\":\"Wiktionary\",\"url\":\"http:\/\/en.wiktionary.org\/wiki\/Lorentz_force\",\"project\":\"\",\"license\":\"cc-by-sa\",\"license_terms\":\"\"},{\"type\":\"cc-attribution\",\"description\":\"unit vector\",\"author\":\"\",\"organization\":\"Wiktionary\",\"url\":\"http:\/\/en.wiktionary.org\/wiki\/unit_vector\",\"project\":\"\",\"license\":\"cc-by-sa\",\"license_terms\":\"\"},{\"type\":\"cc-attribution\",\"description\":\"Lorentz force\",\"author\":\"\",\"organization\":\"Wikipedia\",\"url\":\"http:\/\/en.wikipedia.org\/wiki\/Lorentz_force\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc-attribution\",\"description\":\"OpenStax College, Coulombu2019s Law. 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