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render = function render(){var _vm=this,_c=_vm._self._c;return _c('div',[_c('h3',[_vm._v(\"Observational backing\")]),_c('p',[_vm._v(\"\\n    Michael Faraday during his experiments noticed something very\\n    very unusual. He had a ring on whose one half was wound a wire\\n    that carried current while the other half had a wire wound around it too\\n    but it wasn't attached to any source of current. But still, whenever the current\\n    was passed through the wire in the first half, some current also passed through\\n    the wire in the second half. This wireless \\\"transfer\\\" of current would arouse curiosity\\n    in anyone. After some playing around, Faraday discovered more properties of this\\n    \\\"transfer\\\" which is now called induction and published his working. Another contemporary\\n    of Faraday, Joseph Henry also discovered this same phenomenon and worked on this independently,\\n    but Faraday gets the credit because his work was published earlier than that of Henry's.\\n  \")]),_c('h3',[_vm._v(\"Faraday's Law\")]),_vm._m(0),_c('h3',[_vm._v(\"Lenz's Law\")]),_vm._m(1),_c('h3',[_vm._v(\"Is Faraday's law incomplete?\")]),_vm._m(2),_c('h3',[_vm._v(\"Some more analysis\")]),_vm._m(3),_c('v-responsive',[_c('v-layout',{attrs:{\"align-center\":\"\",\"justify-center\":\"\"}},[_c('div',{staticClass:\"edliy-box-about\",attrs:{\"id\":\"jxgbox1\"}})])],1)],1)\n}\nvar staticRenderFns = [function (){var _vm=this,_c=_vm._self._c;return _c('p',[_vm._v(\"\\n    The law states that \"),_c('i',[_vm._v(\"\\\"E.M.F induced in a coil is directly propotional to the negative of the rate of change of\\n      magnetic flux through the coil\\\" \")]),_c('br'),_vm._v(\" Mathematically, if a coil has \\\\(N\\\\) turns,\\n    $$\\\\epsilon =-N\\\\frac{d\\\\phi}{dt}$$\\n    This animation from \"),_c('a',{attrs:{\"href\":\"https://upload.wikimedia.org/wikipedia/commons/7/72/Electromagnetic_induction_-_solenoid_to_loop_-_animation.gif\"}},[_vm._v(\"Wikipedia\")]),_vm._v(\"\\n    explains the concept\\n    \"),_c('br'),_c('img',{staticStyle:{\"width\":\"25%\",\"height\":\"25%\"},attrs:{\"src\":\"https://upload.wikimedia.org/wikipedia/commons/7/72/Electromagnetic_induction_-_solenoid_to_loop_-_animation.gif\"}})])\n},function (){var _vm=this,_c=_vm._self._c;return _c('p',[_vm._v(\"\\n    Lenz's law states that, \"),_c('i',[_vm._v(\"\\\"The emf induced in a coil is such that the current produced by it would\\n      produce a magnetic field such that it would oppose the change in flux that caused the induction.\\\" \")]),_c('br'),_c('br'),_vm._v(\"\\n    As an example, consider a coil in the x-y plane with a magnetic field in the -z direction(into the plane-which is denoted by a cross) that is increasing with time.\\n    This magnetic field would now produce a counterclockwise current in the coil because the magnetic field due\\n    to the new induced current would be opposite to the initial magnetic field.\\n    \"),_c('br'),_c('img',{staticStyle:{\"width\":\"50%\",\"height\":\"50%\"},attrs:{\"src\":\"Lenz's Law.png\"}})])\n},function (){var _vm=this,_c=_vm._self._c;return _c('p',[_vm._v(\"\\n    After looking at Lenz's law and what most teachers teach is that we use Faraday's law to find the\\n    \"),_c('i',[_vm._v(\"magnitude\")]),_vm._v(\" of the induced emf and we use Lenz's law to find the \"),_c('i',[_vm._v(\"direction\")]),_vm._v(\" of the induced current.\\n    This would lead you to think that Faraday's law is incomplete as it does not provide you the direction of the induced\\n    current. This isn't true. Notice the minus sign in the mathematical statement of Faraday's law. That negative\\n    sign takes care of the direction and indicates that the induced emf will produce a current that will oppose the\\n    original change in magnetic flux through the coil.\\n  \")])\n},function (){var _vm=this,_c=_vm._self._c;return _c('p',[_vm._v(\"\\n    Magnetic flux is defined as:\\n    $$\\\\Phi=\\\\textbf{B}\\\\cdot \\\\textbf{A}= BAcos\\\\theta$$\\n    Where, \\\\(\\\\textbf{A}\\\\) is the area vector which has direction perpendicular to the coil surface and\\n    \\\\(\\\\theta\\\\) is the angle between the area vector and the magnetic field vector.\\n    \"),_c('br'),_vm._v(\" Using this in Faraday's law gives us four key points to keep in mind:\\n    \"),_c('br'),_vm._v(\"The induced emf is non zero if:\\n    \"),_c('ol',[_c('li',[_vm._v(\"Either the magnetic field changes with time\")]),_c('li',[_vm._v(\"or the Area changes with time\")]),_c('li',[_vm._v(\"or if \\\\(\\\\theta\\\\) changes with time\")]),_c('li',[_vm._v(\"or if any two or more of these change with time\")])])])\n}]\n\nexport { render, staticRenderFns }","import {\r\n  makeResponsive,\r\n  //makeResponsive(brd1);\r\n  placeTitle,\r\n  //placeTitle(brd1,'title', 'subtitle');\r\n  placeImage,\r\n  placeInput,\r\n  placeSlider,\r\n  hoverMe,\r\n  placeRec,\r\n  hiddenPt,\r\n  fixedPt,\r\n  clearInputFields,\r\n  dragMe,\r\n  placeArrow,\r\n  //placeArrow(board, pt1, pt2, width, cols)\r\n  placeGravity,\r\n  placeText,\r\n  //placeText(board, positionX, positionY, message)\r\n  placeLine,\r\n  placePoint,\r\n  placeGlider,\r\n  placeRuler,\r\n  placeLeftText,\r\n  placeSliderSwitch,\r\n  placeBoldText,\r\n  //placeBoldText(brd6, -9, 1, 'Liquid');\r\n  placeDash,\r\n  // placeDash(board, [x1, y1], [x2, y2], width, cols)\r\n  placeRightText,\r\n  placeLabel\r\n} from '../../../common/edliy_utils-energy';\r\nconst Boxes = {\r\n    box1: function () {\r\n    //Create the Board\r\n    var brd1 = JXG.JSXGraph.initBoard('jxgbox1',{boundingbox: [-2, 11, 12, -3],\r\n    keepaspectratio: true, axis:false, ticks:{visible:false},\r\n    grid:true, showCopyright:false, showNavigation:false,\r\n    pan:{enabled:false}, zoom:{enabled:false}});\r\n   //suspend updates\r\n    brd1.suspendUpdate();\r\n    // Layering\r\n    brd1.options.board.minimizeReflow = 'none';\r\n    brd1.options.point.showInfobox =false;\r\n    //Set CSS\r\n    brd1.options.text.cssDefaultStyle = 'fontFamily:Oswald;'\r\n    brd1.options.text.highlightCssDefaultStyle = 'fontFamily:Oswald';\r\n    //Set Highlight\r\n    brd1.options.text.highlight = false;\r\n    brd1.options.line.highlight=false;\r\n    brd1.options.arrow.highlight=false;\r\n    brd1.options.point.highlight=false;\r\n    brd1.options.arc.highlight=false;\r\n//   Fixing\r\n    brd1.options.text.fixed=true;\r\n//    JXG.Options.point.fixed=true;\r\n    brd1.options.layer['image']=17;\r\n    brd1.options.layer['text']=16;\r\n    //brd1.options.layer['line']=14;\r\n    brd1.options.layer['point']=15;\r\n    brd1.options.layer['glider']=15;\r\n    //Make the board responsive\r\n    makeResponsive(brd1);\r\n    // Creat titleStyle\r\n    placeTitle(brd1, 'Electric Flux', 'Magnetic Flux and Electromotive Force');\r\n    //dragMe(brd1, 5, 5);\r\n    //var xaxis = brd1.create('line',[[0,0], [0.5, 0]],{visible:false});\r\n    //Title and tetxs\r\n    //var title1 = brd1.create('text', [5, 8.5, \"<b> Faraday's Law of Induction <b>\"],{fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(26*brd1.canvasWidth/500.)}},);\r\n    //Title and tetxs\r\n    var title1 = brd1.create('text', [5, 10, '<b> Electric Flux <b>'],{fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(28*brd1.canvasWidth/500.)}},);\r\n    var title2 = brd1.create('text', [5, 9, 'Drag the charges into the field'],{fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(18*brd1.canvasWidth/500.)}},);\r\n\r\n    var txt1 = brd1.create('text', [3.2, 7.5, 'q > 0'],{fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(14*brd1.canvasWidth/500.)}},);\r\n    var txt2 = brd1.create('text', [7.2, 7.5, 'q < 0'],{fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(14*brd1.canvasWidth/500.)}},);\r\n\r\n    var ymax = 5;\r\n    var xmax = 10;\r\n    var sizeImg = 0.2; //Put the half of the size of the image\r\n\r\n    //Polygon\r\n    var polygon = brd1.create('polygon', [[-1, -1], [xmax+1, -1], [xmax+1, ymax+1], [-1, ymax+1]], {visible: true, vertices:{visible:false, fixed:true}, borders:{visible:true, strokeColor: '#949494', strokeWidth: 3}, fillColor: '#D9D9D9', fillOpacity:1});\r\n\r\n    //Charges\r\n    var ChargesQ=[]\r\n    var ChargesP=[]\r\n\r\n    for(let i=0; i <= 100; i++){\r\n\r\n        var p_val = brd1.create('image', ['assets/positiveCharge.svg', [2.3, 7.3], [0.4, 0.4]], {visible: true, fixed: false});\r\n        //var p_val = brd1.create('point', [2.5, 7.5],{face:'o' , name:'', size:5, color: '#FC3C3C', withLabel:true, fixed:false, visible:true, label:{fontSize:function(){return 18*brd1.canvasHeight/800}, cssStyle:'fontFamily:Oswald'}});\r\n        var q_val = 10;\r\n        ChargesP.push(p_val);\r\n        ChargesQ.push(q_val);\r\n\r\n    }\r\n\r\n    for(let i=0; i <= 100; i++){\r\n\r\n        var p_val = brd1.create('image', ['assets/negativeCharge.svg', [6.3, 7.3], [0.4, 0.4]], {visible: true, fixed: false});\r\n        //var p_val = brd1.create('point', [6.5, 7.5],{face:'o' , name:'', size:5, color: '#323BB3', withLabel:true, fixed:false, visible:true, label:{fontSize:function(){return 18*brd1.canvasHeight/800}, cssStyle:'fontFamily:Oswald'}});\r\n        var q_val = -10;\r\n        ChargesP.push(p_val);\r\n        ChargesQ.push(q_val);\r\n    }\r\n\r\n    //Points in plane where to show the electric field\r\n    var points1 = [];\r\n\r\n    for(let y=0; y <= ymax; y++){\r\n\r\n        var pVector1 = [];\r\n\r\n        for(let x=0; x<= xmax; x++){\r\n\r\n            var pt1 = brd1.create('point', [x, y],{face: 'o', name: '', size:0.1, color: 'red', fixed:true, visible:false, label:{offset: [10, 15], fontSize:function(){return 18*brd1.canvasHeight/800}, cssStyle:'fontFamily:Oswald'}});\r\n            var pt2 = brd1.create('point', [function(){return electricField(x,y)[0];}, function(){return electricField(x,y)[1];}] ,{face: 'o', name: '', size:0.1, color: 'black', fixed:true, visible:false, label:{offset: [10, 15], fontSize:function(){return 18*brd1.canvasHeight/800}, cssStyle:'fontFamily:Oswald'}});\r\n\r\n            var arrows = brd1.create('segment', [pt1, pt2], {fixed: true, strokeColor: '#464B6E', visible:true, strokeWidth: 1.5,\r\n                                                    highlightStrokeWidth: 2,\r\n                                                    lastArrow: {type: 2, size: 8, highlightSize: 6},\r\n                                                    touchLastPoint: false,\r\n                                                    firstArrow: {type: 2, size: 0}\r\n            });\r\n\r\n            pVector1.push(pt1);\r\n        }\r\n\r\n        points1.push(pVector1);\r\n    }\r\n\r\n    function electricField(x,y){\r\n\r\n        var EFx=0; //Intensity of the electric field in y\r\n        var EFy=0; //Intensity of the electric field on x\r\n        var EFi=0; //Intensity of the electric field\r\n\r\n        for (let i=0; i<ChargesP.length; i++){\r\n\r\n            if(ChargesP[i].Y() <= 6 && ChargesP[i].Y() >= -1 ){\r\n\r\n                k= 2*1/(4*Math.PI*8.854);\r\n                r = Math.sqrt(Math.pow((x-(ChargesP[i].X() + sizeImg)),2) + Math.pow((y-(ChargesP[i].Y() + sizeImg)),2))\r\n                EFi = k*ChargesQ[i]/(r*r);\r\n\r\n                var alpha = Math.atan((y-(ChargesP[i].Y() + sizeImg))/(x-(ChargesP[i].X() + sizeImg)));\r\n                if((x - (ChargesP[i].X() + sizeImg) < 0)){\r\n                    alpha = Math.PI + alpha;\r\n                }\r\n                var ex = EFi * Math.cos(alpha) ;\r\n                var ey = EFi * Math.sin(alpha) ;\r\n\r\n                EFx = EFx + ex;\r\n                EFy = EFy + ey;\r\n            }\r\n        }\r\n        return [EFx +x,EFy +y];\r\n    }\r\n\r\n        brd1.unsuspendUpdate();\r\n\r\n                      },\r\n              }\r\nexport default Boxes;\r\n","<template>\r\n  <div>\r\n    <h3>Observational backing</h3>\r\n    <p>\n      Michael Faraday during his experiments noticed something very\r\n      very unusual. He had a ring on whose one half was wound a wire\r\n      that carried current while the other half had a wire wound around it too\r\n      but it wasn't attached to any source of current. But still, whenever the current\r\n      was passed through the wire in the first half, some current also passed through\r\n      the wire in the second half. This wireless \"transfer\" of current would arouse curiosity\r\n      in anyone. After some playing around, Faraday discovered more properties of this\r\n      \"transfer\" which is now called induction and published his working. Another contemporary\r\n      of Faraday, Joseph Henry also discovered this same phenomenon and worked on this independently,\r\n      but Faraday gets the credit because his work was published earlier than that of Henry's.\r\n    </p>\r\n    <h3>Faraday's Law</h3>\r\n    <p>\n      The law states that <i>\"E.M.F induced in a coil is directly propotional to the negative of the rate of change of\r\n        magnetic flux through the coil\" </i>\r\n      <br> Mathematically, if a coil has \\(N\\) turns,\r\n      $$\\epsilon =-N\\frac{d\\phi}{dt}$$\r\n      This animation from <a href=\"https://upload.wikimedia.org/wikipedia/commons/7/72/Electromagnetic_induction_-_solenoid_to_loop_-_animation.gif\">Wikipedia</a>\r\n      explains the concept\r\n      <br>\r\n      <img src=\"https://upload.wikimedia.org/wikipedia/commons/7/72/Electromagnetic_induction_-_solenoid_to_loop_-_animation.gif\" style=\"width: 25%; height: 25%;\">\n    </p>\r\n    <h3>Lenz's Law</h3>\r\n    <p>\n      Lenz's law states that, <i>\"The emf induced in a coil is such that the current produced by it would\r\n        produce a magnetic field such that it would oppose the change in flux that caused the induction.\" </i>\r\n      <br>\r\n      <br>\r\n      As an example, consider a coil in the x-y plane with a magnetic field in the -z direction(into the plane-which is denoted by a cross) that is increasing with time.\r\n      This magnetic field would now produce a counterclockwise current in the coil because the magnetic field due\r\n      to the new induced current would be opposite to the initial magnetic field.\r\n      <br>\r\n      <img src=\"Lenz's Law.png\" style=\"width: 50%; height: 50%;\">\r\n    </p>\r\n    <h3>Is Faraday's law incomplete?</h3>\r\n    <p>\n      After looking at Lenz's law and what most teachers teach is that we use Faraday's law to find the\r\n      <i>magnitude</i> of the induced emf and we use Lenz's law to find the <i>direction</i> of the induced current.\r\n      This would lead you to think that Faraday's law is incomplete as it does not provide you the direction of the induced\r\n      current. This isn't true. Notice the minus sign in the mathematical statement of Faraday's law. That negative\r\n      sign takes care of the direction and indicates that the induced emf will produce a current that will oppose the\r\n      original change in magnetic flux through the coil.\r\n    </p>\r\n    <h3>Some more analysis</h3>\r\n    <p>\n      Magnetic flux is defined as:\r\n      $$\\Phi=\\textbf{B}\\cdot \\textbf{A}= BAcos\\theta$$\r\n      Where, \\(\\textbf{A}\\) is the area vector which has direction perpendicular to the coil surface and\r\n      \\(\\theta\\) is the angle between the area vector and the magnetic field vector.\r\n      <br> Using this in Faraday's law gives us four key points to keep in mind:\r\n      <br>The induced emf is non zero if:\r\n      <ol>\r\n        <li>Either the magnetic field changes with time</li>\r\n        <li>or the Area changes with time</li>\r\n        <li>or if \\(\\theta\\) changes with time</li>\r\n        <li>or if any two or more of these change with time</li>\r\n      </ol>\r\n    </p>\r\n    <v-responsive>\r\n      <v-layout align-center justify-center>\r\n        <div id=\"jxgbox1\" class=\"edliy-box-about\" />\r\n      </v-layout>\r\n    </v-responsive>\r\n  </div>\r\n</template>\r\n<script>\r\nimport Boxes from './Boxes.js'\r\nexport default {\r\n  name: 'Mag',\r\n  created: function () {\r\n    this.$store.commit('navigation/resetState');\r\n    let title = 'Faraday\\'s Law';\r\n    this.$store.commit('navigation/changeTitle', title);\r\n    this.$store.commit('navigation/changeMenu', title);\r\n    let newTopics = [\r\n      {title: 'What is a lens?', img:'/assets/number-1.svg', action: () => this.goto('ia')},\r\n      {title: 'Ray Diagrams', img:'/assets/number-2.svg', action: () => this.goto('ja')},\r\n      {title: 'Lens Formula', img:'/assets/number-3.svg', action: () => this.goto('ka')},\r\n      {title: 'MagicGraph' ,img:'/assets/touch.svg', action: () => this.goto('graphical')},\r\n    ];\r\n    this.$store.commit('navigation/replaceTopics', newTopics);\r\n    let newshowhome = false;\r\n    this.$store.commit('navigation/toggleshowhome', newshowhome);\r\n    let newPhys =true;\r\n    this.$store.commit('navigation/replacePhys', newPhys);\r\n    let newLeftArrow =true;\r\n    this.$store.commit('navigation/replaceLeftArrow', newLeftArrow);\r\n    let newModule =true;\r\n    this.$store.commit('navigation/replaceModule', newModule);\r\n  },\r\n  mounted () {\r\n    MathJax.Hub.Queue([\"Typeset\", MathJax.Hub]);\r\n    Boxes.box1();\r\n  },\r\n  metaInfo() {\r\n  return{ title: 'Magnetism',\r\n          titleTemplate: '%s - Learn interactively',\r\n          meta: [ {name: 'viewport', content: 'width=device-width, initial-scale=1'},\r\n                  {name: 'description', content: 'Learn interactively how to use ray diagram'}\r\n                ]\r\n        }\r\n   },\r\n}\r\n</script>\r\n<style lang=\"scss\">\r\n@import 'src/styles/edliy-box.scss';\r\n@import 'src/styles/subtopic-menu.scss';\r\n@import 'src/styles/edliy-box-about.scss';\r\n@import 'src/styles/screen-sizes.scss';\r\n</style>\r\n","import mod from \"-!../../../../node_modules/cache-loader/dist/cjs.js??ref--12-0!../../../../node_modules/thread-loader/dist/cjs.js!../../../../node_modules/babel-loader/lib/index.js!../../../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../../../node_modules/vue-loader/lib/index.js??vue-loader-options!./Lesson.vue?vue&type=script&lang=js&\"; export default mod; export * from \"-!../../../../node_modules/cache-loader/dist/cjs.js??ref--12-0!../../../../node_modules/thread-loader/dist/cjs.js!../../../../node_modules/babel-loader/lib/index.js!../../../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../../../node_modules/vue-loader/lib/index.js??vue-loader-options!./Lesson.vue?vue&type=script&lang=js&\"","import { render, staticRenderFns } from \"./Lesson.vue?vue&type=template&id=7c884ef0&\"\nimport script from \"./Lesson.vue?vue&type=script&lang=js&\"\nexport * from \"./Lesson.vue?vue&type=script&lang=js&\"\nimport style0 from \"./Lesson.vue?vue&type=style&index=0&id=7c884ef0&prod&lang=scss&\"\n\n\n/* normalize component */\nimport normalizer from \"!../../../../node_modules/vue-loader/lib/runtime/componentNormalizer.js\"\nvar component = normalizer(\n  script,\n  render,\n  staticRenderFns,\n  false,\n  null,\n  null,\n  null\n  \n)\n\nexport default component.exports","export * from \"-!../../../../node_modules/mini-css-extract-plugin/dist/loader.js??ref--8-oneOf-1-0!../../../../node_modules/css-loader/index.js??ref--8-oneOf-1-1!../../../../node_modules/vue-loader/lib/loaders/stylePostLoader.js!../../../../node_modules/postcss-loader/src/index.js??ref--8-oneOf-1-2!../../../../node_modules/sass-loader/dist/cjs.js??ref--8-oneOf-1-3!../../../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../../../node_modules/vue-loader/lib/index.js??vue-loader-options!./Lesson.vue?vue&type=style&index=0&id=7c884ef0&prod&lang=scss&\""],"sourceRoot":""}