{"id":8890,"date":"2018-02-08T10:19:46","date_gmt":"2018-02-08T04:49:46","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/?p=8890"},"modified":"2018-10-06T18:01:39","modified_gmt":"2018-10-06T12:31:39","slug":"electric-charges-fields-class-12-notes-physics","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/electric-charges-fields-class-12-notes-physics\/","title":{"rendered":"Electric Charges and Fields class 12 Notes Physics"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mycbseguide.com\/blog\/electric-charges-fields-class-12-notes-physics\/#CBSE_Guide_Electric_Charges_and_Fields_class_12_Notes\" >CBSE Guide Electric Charges and Fields class 12 Notes<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mycbseguide.com\/blog\/electric-charges-fields-class-12-notes-physics\/#12_Physics_notes_Chapter_1_Electric_Charges_and_Fields\" >12 Physics notes Chapter 1 Electric Charges and Fields<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/electric-charges-fields-class-12-notes-physics\/#CBSE_Class_12_Physics_Revision_Notes_Chapter_1_Electric_Charges_and_Fields\" >CBSE Class 12 Physics Revision Notes Chapter 1 Electric Charges and Fields<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/electric-charges-fields-class-12-notes-physics\/#Electric_Charges_and_Fields_class_12_Notes\" >Electric Charges and Fields class 12 Notes<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/electric-charges-fields-class-12-notes-physics\/#CBSE_Class-12_Revision_Notes_and_Key_Points\" >CBSE Class-12 Revision Notes and Key Points<\/a><\/li><\/ul><\/nav><\/div>\n<p>CBSE class 12 Physics Chapter 1 Electric Charges and Fields notes in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Electric Charges and Fields class 12 Notes latest chapter wise notes for quick preparation of CBSE board exams and school based annual examinations. Class 12 Physics notes on chapter 1 Electric charges and fields are also available for download in CBSE Guide website.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_Guide_Electric_Charges_and_Fields_class_12_Notes\"><\/span>CBSE Guide Electric Charges and Fields class 12 Notes<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>CBSE guide notes are the comprehensive notes which covers the latest syllabus of CBSE and NCERT. It includes all the topics given in NCERT class 12 Physics text book. Users can download CBSE guide quick revision notes from myCBSEguide mobile app and my CBSE guide website.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"12_Physics_notes_Chapter_1_Electric_Charges_and_Fields\"><\/span>12 Physics notes Chapter 1 Electric Charges and Fields<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Download CBSE class 12th revision notes for chapter 1 Electric Charges and Fields in PDF format for free. Download revision notes for Electric Charges and Fields class 12 Notes and score high in exams. These are the Electric Charges and Fields class 12 Notes prepared by team of expert teachers. The revision notes help you revise the whole chapter in minutes. Revising notes in exam days is on of the the best tips recommended by teachers during exam days.<\/p>\n<p style=\"text-align: center;\"><strong>Revision Notes for Class 12 Physics\u00a0<a class=\"button\" href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-12-physics\/1251\/cbse-revision-notes\/7\/\">Download as PDF<\/a><\/strong><\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_Class_12_Physics_Revision_Notes_Chapter_1_Electric_Charges_and_Fields\"><\/span><strong>CBSE Class 12 Physics Revision Notes Chapter 1 Electric Charges and Fields<br \/>\n<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<hr \/>\n<ul>\n<li><strong>Like Charges and Unlike Charges:<\/strong> Like charges repel and unlike charges attract each other.<\/li>\n<li><strong>Conductors and Insulators:<\/strong> Conductors allow movement of electric charge through them, insulators do not.<\/li>\n<li><strong>Quantization of Electric Charge:<\/strong> It means that total charge (q) of a body is always an integral multiple of a basic quantum of charge (e)<br \/>\nq = ne where <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"28\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%7B%5C%5Ctext%7Bn%20%7D%7D%20%3D%20%7B%5C%5Ctext%7B%20%7D%7D0%2C%7B%5C%5Ctext%7B%20%7D%7D%20%5C%5Cpm%20%7B%5C%5Ctext%7B1%7D%7D%2C%7B%5C%5Ctext%7B%20%7D%7D%20%5C%5Cpm%20%7B%5C%5Ctext%7B2%7D%7D%2C%7B%5C%5Ctext%7B%20%7D%7D%20%5C%5Cpm%20%7B%5C%5Ctext%7B3%7D%7D%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{\\text{n }} = {\\text{ }}0,{\\text{ }} \\pm {\\text{1}},{\\text{ }} \\pm {\\text{2}},{\\text{ }} \\pm {\\text{3}}\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span>, \u2026.<\/li>\n<li><strong>Additivity of Electric Charges: <\/strong>Total charge of a system is the algebraic sum of all individual charges in the system.<\/li>\n<li><strong>Conservation of Electric Charges: <\/strong>The total charge of an isolated system remains uncharged with time.<\/li>\n<li><strong>Superposition Principle: <\/strong>It is the properties of forces with which two charges attract or repel each other are not affected by the presence of a third (or more) additional charge(s).<\/li>\n<li><strong>The Electric Field E at a Point due to a Charge Configuration: <\/strong>It is the force on a small positive test charges q placed at the point divided by a magnitude <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"27\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Cfrac%7B%7Cq%7C%7D%7B4%5C%5Cpi%20%7B%7B%5C%5Cvarepsilon%20%7D_%7B0%7D%7D%7B%7Br%7D%5E%7B2%7D%7D%7D%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\frac{|q|}{4\\pi {{\\varepsilon }_{0}}{{r}^{2}}}\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span><br \/>\nIt is radially outwards from q, if q is positive and radially inwards if q is negative.<br \/>\n<em>E <\/em>at a point varies inversely as the square of its distance from <em>Q<\/em>, the plot of <em>E <\/em>versus <em>r <\/em>will look like the figure given below.<br \/>\n<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/physics\/12_physics_revise_ch01_01.png\" data-cke-saved-src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/physics\/12_physics_revise_ch01_01.png\" \/><\/li>\n<li><strong>Coulomb\u2019s Law:<\/strong> The mutual electrostatic force between two point charges <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"26\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7Dq_1%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?q_1\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> and <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"25\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7Dq_2%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?q_2\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> is proportional to the product <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"24\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7Dq_1%20q_2%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?q_1 q_2\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> and inversely proportional to the square of the distance <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"23\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7Dr_21%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?r_21\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> separating them.<\/li>\n<\/ul>\n<p><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"22\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%7B%7B%5C%5Coverrightarrow%7BF%7D%7D_%7B21%7D%7D(force%5C%5Ctext%7B%20on%20%7D%7B%7B%5C%5Ctext%7Bq%7D%7D_%7B2%7D%7D%5C%5Ctext%7B%20due%20to%20%7D%7B%7B%5C%5Ctext%7Bq%7D%7D_%7B1%7D%7D)%3D%5C%5Cfrac%7Bk(%7B%7Bq%7D_%7B1%7D%7D%7B%7Bq%7D_%7B2%7D%7D)%7D%7Br_%7B21%7D%5E%7B2%7D%7D%7B%7B%5C%5Coverset%7B%5C%5Chat%7B%5C%5C%20%7D%7D%7B%5C%5Cmathop%7Br%7D%7D%5C%5C%2C%7D_%7B21%7D%7D%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{\\overrightarrow{F}}_{21}}(force\\text{ on }{{\\text{q}}_{2}}\\text{ due to }{{\\text{q}}_{1}})=\\frac{k({{q}_{1}}{{q}_{2}})}{r_{21}^{2}}{{\\overset{\\hat{\\ }}{\\mathop{r}}\\,}_{21}}\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span><\/p>\n<p>Where <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"21\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%20%7B%7B%5C%5Coverset%7B%5C%5Chat%7B%5C%5C%20%7D%7D%7B%5C%5Cmathop%7Br%7D%7D%5C%5C%2C%7D_%7B21%7D%7D%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi? {{\\overset{\\hat{\\ }}{\\mathop{r}}\\,}_{21}}\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> is a unit vector in the direction from <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"20\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7Dq_1%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?q_1\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> to <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"19\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7Dq_2%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?q_2\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> and <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"18\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7Dk%3D%5C%5Cfrac%7B1%7D%7B4%5C%5Cpi%20%7B%7B%5C%5Cvarepsilon%20%7D_%7B0%7D%7D%7D%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?k=\\frac{1}{4\\pi {{\\varepsilon }_{0}}}\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> is the proportionality constant.<\/p>\n<ul>\n<li><strong>An Electric Field Line: <\/strong>It is a curve drawn in such a way that the tangent at each point on the curve gives the direction of electric field at that point.<\/li>\n<li><strong>Important Properties of Field Lines: <\/strong><\/li>\n<\/ul>\n<ol>\n<li>(i) Field lines are continuous curves without any breaks.<\/li>\n<li>(ii) Two field lines cannot cross each other.<\/li>\n<li>(iii) Electrostatic field lines start at positive charges and end at negative charges<\/li>\n<li>they cannot form closed loops.<\/li>\n<\/ol>\n<ul>\n<li><strong>Electric Field at a Point due to Charge q:<\/strong> <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"17\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Coverrightarrow%7BE%7D%3D%5C%5Cfrac%7B%5C%5Coverrightarrow%7BF%7D%7D%7Bq%7D%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\overrightarrow{E}=\\frac{\\overrightarrow{F}}{q}\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span><\/li>\n<li><strong>Electric Field due to an Electric Dipole in its Equatorial Plane at a Distance r from the Centre:<\/strong><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"16\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7DE%3D%5C%5Cfrac%7B-p%7D%7B4%5C%5Cpi%20%7B%7B%5C%5Cvarepsilon%20%7D_%7B0%7D%7D%7D%5C%5Cfrac%7B1%7D%7B%7B%7B(%7B%7Ba%7D%5E%7B2%7D%7D%2B%7B%7Br%7D%5E%7B2%7D%7D)%7D%5E%7B%5C%5Cfrac%7B3%7D%7B2%7D%7D%7D%7D%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?E=\\frac{-p}{4\\pi {{\\varepsilon }_{0}}}\\frac{1}{{{({{a}^{2}}+{{r}^{2}})}^{\\frac{3}{2}}}}\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"15\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Ccong%20%5C%5Cfrac%7B-p%7D%7B4%5C%5Cpi%20%7B%7B%5C%5Cvarepsilon%20%7D_%7B0%7D%7D%7D%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\cong \\frac{-p}{4\\pi {{\\varepsilon }_{0}}}\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> ,for r&gt;&gt;a<\/li>\n<li><strong>Electric Field due to an Electric Dipole on the Axis at a Distance r from the Centre: <\/strong><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"14\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7DE%3D%5C%5Cfrac%7B2pr%7D%7B4%5C%5Cpi%20%7B%7B%5C%5Cvarepsilon%20%7D_%7B0%7D%7D%7B%7B(%7B%7Br%7D%5E%7B2%7D%7D-%7B%7Ba%7D%5E%7B2%7D%7D)%7D%5E%7B2%7D%7D%7D%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?E=\\frac{2pr}{4\\pi {{\\varepsilon }_{0}}{{({{r}^{2}}-{{a}^{2}})}^{2}}}\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"13\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Ccong%20%5C%5Cfrac%7B2p%7D%7B4%5C%5Cpi%20%7B%7B%5C%5Cvarepsilon%20%7D_%7B0%7D%7D%7B%7Br%7D%5E%7B3%7D%7D%7D%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\cong \\frac{2p}{4\\pi {{\\varepsilon }_{0}}{{r}^{3}}}\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span>, for r&gt;&gt;a<\/li>\n<li><strong>A Dipole Placed in Uniform Electric Field E experiences: <\/strong>Torque <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"12\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Coverrightarrow%20%5C%5Ctau%C2%A0%20%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\overrightarrow \\tau\u00a0 \" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span>,<\/li>\n<li><strong>The Electric Flux: <\/strong><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"10\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Cphi%20%3D%5C%5Cint%7Bd%5C%5Cphi%20%3D%5C%5Cint%7B%5C%5Coverrightarrow%7BE%7D.d%5C%5Coverrightarrow%7Bs%7D%7D%7D%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\phi =\\int{d\\phi =\\int{\\overrightarrow{E}.d\\overrightarrow{s}}}\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> is a \u2018dot\u2019 product, hence it is scalar.<\/li>\n<\/ul>\n<p><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"9\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5CDelta%20%5C%5Cphi%20%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\Delta \\phi \" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> is positive for all values of <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"8\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Ctheta%C2%A0%20%3C%20%5C%5Cfrac%7B%5C%5Cpi%20%7D%7B2%7D%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\theta\u00a0 &amp;lt; \\frac{\\pi }{2}\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span><\/p>\n<p><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"7\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5CDelta%20%5C%5Cphi%20%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\Delta \\phi \" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> is negative for all values of <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"6\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Ctheta%C2%A0%20%3E%20%5C%5Cfrac%7B%5C%5Cpi%20%7D%7B2%7D%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\theta\u00a0 &amp;gt; \\frac{\\pi }{2}\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span><\/p>\n<ul>\n<li><strong>Gauss\u2019s Law: <\/strong>The flux of electric field through any closed surface S is 1\/\u03b50 times the total charge enclosed by S.<\/li>\n<li>Electric field outside the charged shell is as though the total charge is concentrated at the centre. The same result is true for a solid sphere of uniform volume charge density.<\/li>\n<li>The electric field is zero at all points inside a charged shell.<\/li>\n<li><strong>Electric field E, due to an infinitely long straight wire of uniform linear charge density <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"4\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%CE%BB%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\u03bb\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> :<\/strong><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"3\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7DE%20%3D%20%5C%5Cfrac%7B%5C%5Clambda%20%7D%7B%7B2%5C%5Cpi%20%7B%5C%5Cvarepsilon%20_0%7Dr%7D%7D.%5C%5Cmathop%20n%5C%5Climits%5E%20%5C%5Cwedge%C2%A0%20%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?E = \\frac{\\lambda }{{2\\pi {\\varepsilon _0}r}}.\\mathop n\\limits^ \\wedge\u00a0 \" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span><\/li>\n<\/ul>\n<p>where r is the perpendicular distance of the point from the wire and is the radial unit vector in the plane normal to the wire passing through the point.<\/p>\n<ul>\n<li><strong>Electric field E, due to an infinite thin plane sheet of uniform surface charge density \u03c3: <\/strong><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"2\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7DE%20%3D%20%5C%5Cfrac%7B%5C%5Csigma%20%7D%7B%7B2%7B%5C%5Cvarepsilon%20_0%7D%7D%7D.%5C%5Cmathop%20n%5C%5Climits%5E%20%5C%5Cwedge%C2%A0%20%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?E = \\frac{\\sigma }{{2{\\varepsilon _0}}}.\\mathop n\\limits^ \\wedge\u00a0 \" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span><\/li>\n<\/ul>\n<p>Where <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"1\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7D%5C%5Cmathop%20n%5C%5Climits%5E%20%5C%5Cwedge%C2%A0%20%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\mathop n\\limits^ \\wedge\u00a0 \" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span> is a unit vector normal to the plane, outward on either side.<\/p>\n<ul>\n<li><strong>Electric field E, due to thin spherical shell of uniform surface charge density \u03c3: <\/strong><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\" tabindex=\"-1\" contenteditable=\"false\" data-cke-widget-wrapper=\"1\" data-cke-filter=\"off\" data-cke-display-name=\"math\" data-cke-widget-id=\"0\"><span class=\"math-tex cke_widget_element\" data-cke-survive=\"1\" data-cke-widget-data=\"%7B%22math%22%3A%22%7Btex%7DE%20%3D%20%5C%5Cfrac%7Bq%7D%7B%7B4%5C%5Cpi%20%7B%5C%5Cvarepsilon%20_0%7D%7Br%5E2%7D%7D%7D.%5C%5Cmathop%20r%5C%5Climits%5E%20%5C%5Cwedge%C2%A0%20%7B%5C%5Ctext%7B%C2%A0%C2%A0%C2%A0%20(r%7D%7D%20%5C%5Cgeqslant%20%7B%5C%5Ctext%7BR)%7D%7D%7B%2Ftex%7D%22%2C%22classes%22%3A%7B%22math-tex%22%3A1%7D%7D\" data-cke-widget-upcasted=\"1\" data-cke-widget-keep-attr=\"0\" data-widget=\"mathjaxlatex\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?E = \\frac{q}{{4\\pi {\\varepsilon _0}{r^2}}}.\\mathop r\\limits^ \\wedge\u00a0 {\\text{\u00a0\u00a0\u00a0 (r}} \\geqslant {\\text{R)}}\" \/><\/span><img decoding=\"async\" class=\"cke_reset cke_widget_mask\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" \/><span class=\"cke_reset cke_widget_drag_handler_container\"><img loading=\"lazy\" decoding=\"async\" class=\"cke_reset cke_widget_drag_handler\" title=\"Click and drag to move\" draggable=\"true\" src=\"data:image\/gif;base64,R0lGODlhAQABAPABAP\/\/\/wAAACH5BAEKAAAALAAAAAABAAEAAAICRAEAOw==\" width=\"15\" height=\"15\" data-cke-widget-drag-handler=\"1\" \/><\/span><\/span>E=0 (r&lt;R)<\/li>\n<\/ul>\n<p>where r is the distance of the point from the centre of the shell and R the radius of the shell, q is the total charge of the shell &amp; q = 4\u03c0R2\u03c3.<\/p>\n<ul>\n<li>Electric field E along the outward normal to the surface is zero and \u03c3 is the surface charge density. Charges in a conductor can reside only at its surface. Potential is constant within and on the surface of a conductor. In a cavity within a conductor (with no charges), the electric field is zero.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Electric_Charges_and_Fields_class_12_Notes\"><\/span>Electric Charges and Fields class 12 Notes<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>CBSE Revision notes (PDF Download) Free<\/li>\n<li>CBSE Revision notes for Class 12 Physics PDF<\/li>\n<li>CBSE Revision notes Class 12 Physics \u2013 CBSE<\/li>\n<li>CBSE Revisions notes and Key Points Class 12 Physics<\/li>\n<li>Summary of the NCERT books all chapters in Physics class 12<\/li>\n<li>Short notes for CBSE class 12th Physics<\/li>\n<li>Key notes and chapter summary of Physics class 12<\/li>\n<li>Quick revision notes for CBSE board exams<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_Class-12_Revision_Notes_and_Key_Points\"><\/span><strong>CBSE Class-12 Revision Notes and Key Points<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Electric Charges and Fields class 12 Notes. CBSE quick revision note for class-12 Physics, Chemistry, Maths, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.<\/p>\n<ul>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-physics\/1251\/cbse-revision-notes\/7\/\">Physics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-chemistry\/1267\/cbse-revision-notes\/7\/\">Chemistry<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-mathematics\/1284\/cbse-revision-notes\/7\/\">Mathematics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-biology\/1298\/cbse-revision-notes\/7\/\">Biology<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-accountancy\/1315\/cbse-revision-notes\/7\/\">Accountancy<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-economics\/1327\/cbse-revision-notes\/7\/\">Economics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-business-studies\/1727\/cbse-revision-notes\/7\/\">Business Studies<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-computer-science\/1851\/cbse-revision-notes\/7\/\">Computer Science<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-informatics-practices\/1873\/cbse-revision-notes\/7\/\">Informatics Practices<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-english-core\/1855\/cbse-revision-notes\/7\/\">English Core<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-history\/1869\/cbse-revision-notes\/7\/\">History<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-physical-education\/1877\/cbse-revision-notes\/7\/\">Physical Education<\/a><\/li>\n<\/ul>\n<p>To download Electric Charges and Fields class 12 Notes, sample paper for class 12 Physics, Chemistry, Biology, History, Political Science, Economics, Geography, Computer Science, Home Science, Accountancy, Business Studies and Home Science; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\"><strong>the best app for CBSE students<\/strong><\/a>\u00a0and myCBSEguide website.<\/p>\n<ul>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/electrostatic-potential-capacitance-class-12-notes-physics\/\">Electrostatic Potential and Capacitance class 12 Notes Physics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/current-electricity-class-12-notes-physics\/\">Current Electricity class 12 Notes Physics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/moving-charges-magnetism-class-12-notes-physics\/\">Moving Charges and Magnetism class 12 Notes Physics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/magnetism-matter-class-12-notes-physics\/\">Magnetism and Matter class 12 Notes Physics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/electromagnetic-induction-class-12-notes-physics\/\">Electromagnetic Induction class 12 Notes Physics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/alternating-current-class-12-notes-physics\/\">Alternating Current class 12 Notes Physics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/electromagnetic-waves-class-12-notes-physics\/\">Electromagnetic Waves class 12 Notes Physics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/ray-optics-and-optical-class-12-note-physics\/\">Ray Optics and Optical class 12 Notes Physics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/wave-optics-class-12-notes-physics\/\">Wave Optics class 12 Notes Physics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/dual-nature-radiation-matter-class-12-notes-physics\/\">Dual Nature of Radiation and Matter class 12 Notes Physics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/atoms-class-12-notes-physics\/\">Atoms class 12 Notes Physics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/nuclei-class-12-notes-physics\/\">Nuclei class 12 Notes Physics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/electronic-devices-class-12-notes-physics\/\">Electronic Devices class 12 Notes Physics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/communication-systems-class-12-notes-physics\/\">Communication Systems class 12 Notes Physics<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>CBSE class 12 Physics Chapter 1 Electric Charges and Fields notes in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Electric Charges and Fields class 12 Notes latest chapter wise notes for quick preparation of CBSE board exams and school based annual examinations. Class 12 &#8230; <a title=\"Electric Charges and Fields class 12 Notes Physics\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/electric-charges-fields-class-12-notes-physics\/\" aria-label=\"More on Electric Charges and Fields class 12 Notes Physics\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":8891,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[48,456],"tags":[457,150,459,458,426,240],"class_list":["post-8890","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cbse-class-12","category-revision-notes","tag-cbse-notes","tag-cbse-notes-and-key-points","tag-electric-charges-and-fields","tag-physics-notes","tag-quick-revision","tag-quick-revision-notes"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Electric Charges and Fields class 12 Notes Physics | myCBSEguide<\/title>\n<meta name=\"description\" content=\"Electric Charges and Fields class 12 Notes Physics chapter 1 in PDF format for free download. 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