{"id":3015,"date":"2022-05-03T20:34:15","date_gmt":"2022-05-03T20:34:15","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=3015"},"modified":"2022-05-03T20:34:15","modified_gmt":"2022-05-03T20:34:15","slug":"coulombs-law","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/05\/03\/coulombs-law\/","title":{"rendered":"Coulomb`s Law"},"content":{"rendered":"\n<h4 class=\"wp-block-heading\">What is&nbsp;Coulomb\u2019s Law?<\/h4>\n\n\n\n<p>According to Coulomb\u2019s law, the force of attraction or repulsion between two charged bodies is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. It acts along the line joining the two charges considered to be point charges.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>coulomb\u2019s Law Formula<\/strong><\/h4>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/11\/Coulombs-Law-1.png\" alt=\"Coulombs law 1\" class=\"wp-image-1443445\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<p>In Short:&nbsp;<\/p>\n\n\n\n<p><strong>F&nbsp;\u221d q<sub>1<\/sub>q<sub>2<\/sub>\/d<sup>2<\/sup><\/strong><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><strong>where,<\/strong><\/p>\n\n\n\n<ul><li><strong>\u03b5 is absolute permittivity<\/strong>,<\/li><li><strong>K<\/strong>\u00a0or\u00a0<strong>\u03b5<sub>r<\/sub><\/strong>\u00a0is the\u00a0<strong>relative permittivity<\/strong>\u00a0or\u00a0<strong>specific inductive capacity\u00a0<\/strong><\/li><li><strong>\u03b5<sub>0<\/sub><\/strong>\u00a0is the\u00a0<strong>permittivity of free space<\/strong>.<\/li><li>K or\u00a0<strong>\u03b5<sub>r<\/sub><\/strong>\u00a0is also called a\u00a0dielectric constant of the medium\u00a0in which the two charges are placed.<\/li><\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">History of Coulomb\u2019s Law<\/h3>\n\n\n\n<p>A French physicist Charles Augustin de Coulomb in 1785 coined a tangible relationship in mathematical form between two bodies that have been electrically charged. He published an equation for the force causing the bodies to attract or repel each other which is known as Coulomb\u2019s law or&nbsp;<strong>Coulomb\u2019s inverse-square law<\/strong>.<br><a><\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Coulomb\u2019s Law in Vector Form<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/mdr.foobrdigital.com\/wp-content\/uploads\/2022\/05\/coulombs-law.png\" alt=\"\" class=\"wp-image-3019\"\/><\/figure>\n\n\n\n<p>F <sub>\u2192 12 <\/sub>= 1 \/ 4 \u03c0 \u2208 <sub>0      <\/sub>q 1 q 2 \/r <sub>12 <\/sub>2   r ^ 12 ; <\/p>\n\n\n\n<p>F \u2192 12 = \u2212 F \u2192 21<\/p>\n\n\n\n<p>Here F<sub>12<\/sub>&nbsp;is the force exerted by q<sub>1<\/sub>&nbsp;on q<sub>2<\/sub>&nbsp;and F<sub>21<\/sub>&nbsp;is the force exerted by q<sub>2<\/sub>&nbsp;on q<sub>1<\/sub>.<\/p>\n\n\n\n<p>Coulomb\u2019s law holds for stationary charges only which are point sized. This law obeys&nbsp;Newton\u2019s third law.<\/p>\n\n\n\n<p>( i e F <sub>\u2192 12<\/sub> = \u2212 F <sub>\u2192 21<\/sub> )<\/p>\n\n\n\n<p>Force on a charged particle due to a number of point charges is the resultant of forces due to individual point charges i.e.<\/p>\n\n\n\n<p>F \u2192 = F \u2192 1 + F \u2192 2 + F \u2192 3 + \u2026 \u2026<\/p>\n\n\n\n<p><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">What is 1 Coulomb of Charge?<\/h2>\n\n\n\n<p>A coulomb is that charge which repels an equal charge of the same sign with a force of 9\u00d710<sup>9<\/sup>&nbsp;N, when the charges are one meter apart in a vacuum.&nbsp;Coulomb force is the conservative mutual and internal force.<\/p>\n\n\n\n<p>The value of&nbsp;\u03b5<sub>o<\/sub>&nbsp;is 8.86 \u00d7 10<sup>-12<\/sup>&nbsp;C<sup>2<\/sup>\/Nm<sup>2<\/sup>&nbsp;(or) 8.86 \u00d7 10<sup>-12<\/sup>&nbsp;Fm<sup>\u20131<\/sup><\/p>\n\n\n\n<p><strong>Note:<\/strong>\u00a0Coulomb force is true only for\u00a0static charges.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Coulomb\u2019s Law \u2013 Conditions for Stability<\/h2>\n\n\n\n<p>If q is slightly displaced towards A, F<sub>A<\/sub>&nbsp;increases in magnitude while F<sub>B<\/sub>&nbsp;decreases in magnitude. Now the net force on q is toward A so it will not return to its original position. So for axial displacement, the equilibrium is unstable.<\/p>\n\n\n\n<p>If q is displaced perpendicular to AB, the force F<sub>A<\/sub>&nbsp;and F<sub>B<\/sub>&nbsp;bring the charge to its original position. So for perpendicular displacement, the equilibrium is stable.<br><a><\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Key Points on Coulomb\u2019s Law<\/h2>\n\n\n\n<p><strong>1.<\/strong>&nbsp;If the force between two charges in two different media is the same for different separations,<\/p>\n\n\n\n<p>F = 1\/ K  * 1\/ 4 \u03c0 \u2208 <sub>0<\/sub>  * q <sub>1<\/sub> q <sub>2<\/sub><sup> <\/sup>r <sup>2<\/sup><\/p>\n\n\n\n<p>= constant .<\/p>\n\n\n\n<p><strong>2.&nbsp;<\/strong>&nbsp;Kr<sup>2<\/sup>&nbsp;= constant or K<sub>1<\/sub>r<sub>1<\/sub><sup>2<\/sup>&nbsp;= K<sub>2<\/sub>r<sub>2<\/sub><sup>2&nbsp;<\/sup><\/p>\n\n\n\n<p><strong>3.<\/strong>&nbsp;If the force between two charges separated by a distance \u2018r<sub>0<\/sub>\u2019 in a vacuum is the same as the force between the same charges separated by a distance \u2018r\u2019 in a medium, then from Coulomb\u2019s Law; Kr<sup>2<\/sup>&nbsp;= r<sub>0<\/sub><sup>2<\/sup><\/p>\n\n\n\n<p><strong>4.<\/strong>&nbsp;Two identical&nbsp;conductors&nbsp;having charges q<sub>1<\/sub>&nbsp;and q<sub>2<\/sub>&nbsp;are put to contact and then separated after which each will have a charge equal to<\/p>\n\n\n\n<p>q <sub>1<\/sub> + q <sub>2<\/sub> \/2<\/p>\n\n\n\n<p><strong>5.<\/strong>&nbsp;Two spherical conductors having charges q<sub>1<\/sub>&nbsp;and q<sub>2<\/sub>&nbsp;and radii r<sub>1<\/sub>&nbsp;and r<sub>2<\/sub>&nbsp;are put to contact and then separated the charges of the conductors after contact is;<\/p>\n\n\n\n<p>q<sub>1<\/sub>&nbsp;= [r<sub>1<\/sub>\/(r<sub>1<\/sub>&nbsp;+ r<sub>2<\/sub>)] (q<sub>1<\/sub>&nbsp;+ q<sub>2<\/sub>) and q<sub>2<\/sub>&nbsp;= [r<sub>2<\/sub>\/(r<sub>1<\/sub>&nbsp;+ r<sub>2<\/sub>)] (q<sub>1<\/sub>&nbsp;+ q<sub>2<\/sub>)<\/p>\n\n\n\n<p><strong>6.<\/strong>&nbsp;If the force of attraction or repulsion between two identical conductors having charges q<sub>1<\/sub>&nbsp;and q<sub>2<\/sub>&nbsp;when separated by a distance d is F. Also if they are put to contact and then separated by the same distance the new force between them is<\/p>\n\n\n\n<p>F = F ( q <sub>1<\/sub> + q <sub>2<\/sub> ) <sup>2<\/sup> \/<\/p>\n\n\n\n<p>4 q <sub>1<\/sub> q <sub>2<\/sub><\/p>\n\n\n\n<p><strong>7.&nbsp;<\/strong>If charges are q<sub>1<\/sub>&nbsp;and -q<sub>2<\/sub>&nbsp;then, F = F(q<sub>1<\/sub>&nbsp;+ q<sub>2<\/sub>)<sup>2<\/sup>&nbsp;\/ 4q<sub>1<\/sub>q<sub>2<\/sub><\/p>\n\n\n\n<p><strong>8.<\/strong>&nbsp;Between two-electrons separated by a certain distance: Electrical force\/Gravitational force =&nbsp;10<sup>42<\/sup><\/p>\n\n\n\n<p><strong>9.<\/strong>&nbsp;Between two protons separated by a certain distance: Electrical force\/Gravitational force = 10<sup>36<\/sup><\/p>\n\n\n\n<p><strong>10.<\/strong>&nbsp;Between a&nbsp;proton and an electron&nbsp;separated by a certain distance: Electrical force\/Gravitational force = 10<sup>39<\/sup><\/p>\n\n\n\n<p><strong>11.<\/strong>&nbsp;The relationship between the velocity of light, the permeability of free space and permittivity of free space is given by the expression c = 1 \/&nbsp;\u221a (\u03bc<sub>o<\/sub>\u03b5<sub>o<\/sub>&nbsp;)<\/p>\n\n\n\n<p><strong>12.<\/strong>&nbsp;If Coulomb\u2019s law is applied to two identical balls of mass m are hung by silk thread of length \u2018l\u2019 from the same hook and carry similar charges q then;<\/p>\n\n\n\n<ul><li>The distance between balls =&nbsp; [ q <sub>2<\/sub> 2 l \/4 \u03c0 \u03f5 <sub>o<\/sub> m g ] <sup>1 3<\/sup><\/li><\/ul>\n\n\n\n<ul><li>The tension in the thread =\\(\\begin{array}{l}\\sqrt{f^2&nbsp;+ (mg)^2}\\end{array} \\)<\/li><li>If the total system is kept in space then the angle between threads is 180\u00b0 and tension in a thread is given by<\/li><\/ul>\n\n\n\n<p>T =<\/p>\n\n\n\n<p>1 4 \u03c0 \u2208<sub> 0 <\/sub>q 2 4 \u2113 2<\/p>\n\n\n\n<ul><li>A charge Q is divided into q and (Q \u2013 q). Then electrostatic force between them is maximum when<\/li><\/ul>\n\n\n\n<p>q \/Q = 1\/ 2 &nbsp; ( o r ) q ( Q \u2212 q ) = 1<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Limitations of Coulomb\u2019s Law<\/h2>\n\n\n\n<ul><li>The law is applicable only for the point charges at rest.<\/li><li>Coulomb\u2019s Law can be only applied in those cases where the&nbsp;inverse square law&nbsp;is obeyed.<\/li><li>It is difficult to implement Coulomb\u2019s law where charges are in arbitrary shape because in such cases we cannot determine the distance\u2019 between the charges.<\/li><li>The law can\u2019t be used directly to calculate the charge on the big planets.<\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>What is&nbsp;Coulomb\u2019s Law? According to Coulomb\u2019s law, the force of attraction or repulsion between two charged bodies is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. It acts along the line joining the two charges considered to be point charges. coulomb\u2019s Law Formula In [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[181],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/3015"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=3015"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/3015\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=3015"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=3015"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=3015"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}