{"id":206,"date":"2023-03-02T12:55:11","date_gmt":"2023-03-02T12:55:11","guid":{"rendered":"https:\/\/www.vartmaaninstitutesirsa.com\/?page_id=206"},"modified":"2024-02-09T11:45:17","modified_gmt":"2024-02-09T11:45:17","slug":"unit-i-electrostatics","status":"publish","type":"page","link":"https:\/\/vartmaaninstitutesirsa.com\/index.php\/unit-i-electrostatics\/","title":{"rendered":"Unit\u2013I Electrostatics"},"content":{"rendered":"\n<p>vartmaan institute sirsa<\/p>\n\n\n\n<p><strong>Unit I: Electrostatics<\/strong><br>Chapter\u20131: Electric Charges and Fields<br>Electric charges, Conservation of charge, Coulomb&#8217;s law-force between two point charges, forces between multiple charges; superposition principle and<br>continuous charge distribution.<br>Electric field, electric field due to a point charge, electric field lines, electric<br>dipole, electric field due to a dipole, torque on a dipole in uniform electric field.<br>Electric flux, statement of Gauss&#8217;s theorem and its applications to find field<br>due to infinitely long straight wire, uniformly charged infinite plane sheet and<br>uniformly charged thin spherical shell (field inside and outside).<\/p>\n\n\n\n<p><strong>To download notes click on the link given at just end of the topics<\/strong><\/p>\n\n\n\n<p><a href=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/1.-electrostatic-force-and-field.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Chapter\u20131: Electric Charges and Fields<\/a><\/p>\n\n\n\n<p>\u00a0<\/p>\n\n\n\n<p>&nbsp;<\/p>\n\n\n\n<p><strong>Chapter\u20132: Electrostatic Potential and Capacitance<\/strong><br>Electric potential, potential difference, electric potential due to a point charge,<br>a dipole and system of charges; equipotential surfaces, electrical potential<br>energy of a system of two-point charges and of electric dipole in an<br>electrostatic field.<br>Conductors and insulators, free charges and bound charges inside a<br>conductor. Dielectrics and electric polarization, capacitors and capacitance,<br>combination of capacitors in series and in parallel, capacitance of a parallel<br>plate capacitor with and without dielectric medium between the plates, energy<br>stored in a capacitor. loss of energy in sharing of capacitor<\/p>\n\n\n\n<p><strong>To download notes click on the link given at just end of the topics<\/strong><\/p>\n\n\n\n<p><a href=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/2.electrostatic-potential-and-capacitance.pdf\" target=\"_blank\" rel=\"noopener\">Chapter\u20132: Electrostatic Potential and Capacitance<\/a><\/p>\n\n\n\n<p>\u00a0<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<strong><u>Unit \u2013 I Electrostatics<\/u><\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\" type=\"1\">\n<li><strong><u>Electrostatics:-<\/u><\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong><em>The branch of physics which deals with the study of charges at rest &amp; the forces &amp; fields, potential of charges is called electrostatics<\/em><\/strong><strong>.<\/strong><\/p>\n\n\n\n<p>* Electrostatics was discovered around 600Bc by a Greek philosopher Thales of Miletus. He showed that when amber was rubbed with a cloth, then cloths starts attracting small piece of paper. In Greek amber is called electron so phenomenon was called electricity. (<em>Amber is a yellow gum like substance obtained from old plants).<\/em><\/p>\n\n\n\n<p>* In 1544 \u2013 1603 Sir William Gilbert found that a force was present after rubbing of amber or any other substance called electrostatic force.<\/p>\n\n\n\n<p>* In 1731 Stephen gray found that charge can be moved through a metal for a long distance but not through a thread. This leads to two types of materials<\/p>\n\n\n\n<p>(i) Conductor (ii) Insulator.<\/p>\n\n\n\n<p>* In 1733 Du Fay discovered that charges are of two types + ve charge \u2013 ve charge.<\/p>\n\n\n\n<p>* In 1750 Benjamin Franklin proposed one fluid theory. He believed that charge occurs due to transfer of electrons. The excess electrons means -vely charged body &amp; deficiency of electrons means + vely charged body.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong><em><u>What is electric charge:-<\/u><\/em><\/strong><\/li>\n<\/ul>\n\n\n\n<p>The property of electrons due to which they experience force of interactions is called electric charge.<\/p>\n\n\n\n<p>The gravitational force of attraction between two electrons<img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image.png\" alt=\"\"> separated by 1 cm distance is<\/p>\n\n\n\n\n\n<p>&nbsp;<\/p>\n\n\n\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-1.png\" alt=\"\" width=\"442\" \/><\/figure>\n\n\n\n<p>But it is found that two electrons separated by 1 cm distance repel each other with a force of 2.3 &nbsp;10<sup>-24<\/sup><sub>N<\/sub>. This force is called electric force.<\/p>\n\n\n\n<p>The charge on an electron is -1.6 10<sup>-19<\/sup>C &amp; charge on an proton is+ 1.6 10<sup>-19<\/sup>C.<\/p>\n\n\n\n<p>Neutrons have no charge though they have mass.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong><em><u>Two kinds of charge:-<\/u><\/em><\/strong><\/li>\n<\/ul>\n\n\n\n<p>In 1733 Du Fay discovered that charges are of two types.<\/p>\n\n\n\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-4.png\" alt=\"\" width=\"220\" \/><\/figure>\n\n\n\n<p>(i) Positive charge (ii) negative charge<\/p>\n\n\n\n<p>This can be shown by the flowing simple experiments.<\/p>\n\n\n\n<p><strong><em><u>Exp-1.<\/u><\/em><\/strong> When two glass rods rubbed with silk are brought near each other then they started repel each other.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-5.png\" alt=\"\" \/><\/figure>\n\n\n\n<p>&nbsp;<\/p>\n\n\n\n<p><strong><em><u>Exp.2<\/u><\/em><\/strong> When two ebonite rods rubbed with cat\u2019s fur are also broughtnear each other, then they also repeal each other.&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;<strong><em><u>Exp. 3:-<\/u><\/em><\/strong> But when a glass rod &amp; ebonite rod are brought near each other then they started attracting each other.<\/p>\n\n\n\n<p>Thus charges are of two types. Here we can see that like charges repel each other &amp; unlike charges attract each other.<\/p>\n\n\n\n<p><em><u>Here the property which differentiates the two kinds of charges is called polarity of charges.<\/u><\/em><\/p>\n\n\n\n<p>* The charge on glass rod is called <strong>vitreous charge <\/strong>(Latin vitrum = glass) &amp; the charge on amber when rubbed with wool is called <strong>resinous charge<\/strong> (Amber is resin)<\/p>\n\n\n\n<p>Now according to Benjamin frankly, charges may define as.<\/p>\n\n\n\n<ol class=\"wp-block-list\" type=\"1\">\n<li>Positive charge:-The charge developed on glass rod when rubbed with silk is called + ve charge. Or if numbers of p are greater than number of e<sup>&#8211; <\/sup>in a body, then body is called +vely charged.<\/li>\n\n\n\n<li>Negative charge:-The charge developed on plastic rod when rubbed with wool is called negative charge. Or If number of e<sup>&#8211;<\/sup> is more than number of p<sup>+<\/sup> in a body, and then body is called negative charged.<\/li>\n<\/ol>\n\n\n\n<p>E, g:-Two kind of charge developed on rubbing<\/p>\n\n\n\n<figure>\n<table>\n<tbody>\n<tr>\n<td><strong>Column \u2013 I (+ ve)<\/strong><\/td>\n<td><strong>\u00a0\u00a0\u00a0 Column \u2013 II (- ve charge)<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>Glass rod, fur or cat skin, woolen cloth\u00a0\u00a0\u00a0 <\/strong><\/td>\n<td>Silk cloth ebonite rod Amber rod plastic, rubber<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n\n\n\n<p><strong>4. <u>Conductor, insulator &amp; dielectrics<\/u>:-<\/strong><\/p>\n\n\n\n<p><strong>Conductor:- <\/strong>A substance which can be used to conduct electric charge from one place to another place is called conductor. Silver is the best conductor. Other examples are copper, aluminum, iron mercury, earth, human body etc.<\/p>\n\n\n\n<p><strong>Insulator:-&nbsp; <\/strong>A substance which cannot be used to conduct electric charge is called insulator<\/p>\n\n\n\n<p>e, g :- glass, rubber, plastic, ebonite, mica, wax etc.<\/p>\n\n\n\n<p><strong><u>Dielectric:- &nbsp;<\/u><\/strong>Dielectric are those insulators which does not conduct electricity but on Appling external electric field charge induces on it e, g:- glass rod &amp; paper acquire charge on rubbing.<\/p>\n\n\n\n<p><strong><em><u>5. Gold leaf electroscope ( G L E )<\/u><\/em><\/strong><\/p>\n\n\n\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-6.png\" alt=\"\" \/><\/figure>\n\n\n\n<p>It is a device which is used for detecting an electric Charge &amp;identifying its polarity. It is consist of a vertical conducting rod passing through a rubber stopper fitted in the mouth of glass vessel. Two thin gold leafs are attached to the lower end of the rod. When a charged object touches the metal knob at the outer end of the rod, the charge flow down throw the leaves. The leaves diverge (moves away) due to repulsion of the like charge. The degree of divergence of the leaves gives measure of the amount of charge.<\/p>\n\n\n\n<p>6.<strong><u>Method of charge<\/u><\/strong><\/p>\n\n\n\n<p>&nbsp;&nbsp; (i)&nbsp; <strong><em><u>Charging by friction:-<\/u><\/em><\/strong><\/p>\n\n\n\n<p>When a body having loosely bounded electrons, is rubbed with a body having strongly bounded electrons, then both the bodies becomes charged by transfer of e<sup>&#8211;<\/sup>.<\/p>\n\n\n\n<p>E,g:- when glass rod is rubbed with fur then glass rod become +vely charged by transferring electron &amp; fur become&nbsp; -vely charged by acquiring electron.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em><u>By loosing electron mass of the body decreases &amp; by gaining e<sup>&#8211;<\/sup> mass of body increases. As electron have mass 9.1<\/u><\/em> <em><u>10<sup>-32<\/sup>kg.<\/u><\/em><\/li>\n<\/ul>\n\n\n\n<p>&nbsp; (ii) <strong><em><u>Charging by electrostatic induction:-<\/u><\/em><\/strong><\/p>\n\n\n\n<p><em>The phenomenon of charging a neutral body by placing it in the neighboring of a charge body is called electrostatic<\/em> induction.<\/p>\n\n\n\n\n\n<p>When a positively charge body is bring toward a neutral body then charge separation takes place in neutral body which remains till the + vely charged body remains near to the neutral body. These induced charges may be explained in following ways.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Charging by induction ( by earthing a conductor);-<\/strong><img fetchpriority=\"high\" decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-11.png\" alt=\"\" width=\"321\" height=\"156\"><\/li>\n<\/ul>\n\n\n\n<p>Suppose a neutral ball on an insulating stand &amp; a positively charged glass rod is bringing toward it. Due to + ve charge on glass rod, the \u2013ve char<\/p>\n\n\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>&nbsp;Charging by induction ( By separating conductors)<\/strong><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-9.png\" alt=\"\" width=\"198\" height=\"311\"><\/li>\n<\/ul>\n\n\n\n<p>&nbsp;<\/p>\n\n\n\n<p><strong>Q.1\u00a0 \u00a0how can you charge a metal sphere positively without touching it?<\/strong><\/p>\n<p>\n\n\n\n<\/p>\n<p>Ans: By bringing a negatively charged body towared metal sphere.<\/p>\n<p>\n\n\n\n<\/p>\n<p><strong>(iii)\u00a0 <u>Charging by conduction (contact):-<\/u><\/strong><\/p>\n<p>\n\n\n\n<\/p>\n<p>Charging by conduction requires the actual contact between the two bodies.<\/p>\n<p>\n\n\n\n<\/p>\n<p>In case of gold leaf electroscope when glass rod rubbed with silk is touched to the knob of leaf, than leaf diverse from their ac<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-12.png\" alt=\"\" \/><\/p>\n<p>tu<\/p>\n<p>al position, which remains separated even after removal of glass rod. Thus charging may be done by conduction.<\/p>\n<p>\n\n\n\n\n\n<\/p>\n<p><strong>7.\u00a0 <u>Polar &amp; Non Polar Bodies:-<\/u><\/strong><\/p>\n<p>\n\n\n\n<\/p>\n<p>Polar body:- A body having different center of +ve&amp; -ve charge is called polar body. E, g: &#8211; HCl , H<sub>2<\/sub>O etc.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n<p>\n\n\n\n<\/p>\n<p>Non polar body:-A body having same center of +ve&amp; -ve charge is called non polar body. \u00a0E, g: &#8211; H<sub>2<\/sub>, O<sub>2<\/sub>, N<sub>2<\/sub>, etc<\/p>\n<p>\n\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-13.png\" alt=\"\" width=\"198\" height=\"327\" \/><\/figure>\n<p>\n\n\n\n<\/p>\n<p><strong>Q.2. (a) A comb run through one\u2019s dry hair attracts small bits of paper. Why? What happens if the hair is wet or if it is a rainy day? (Remember, a paper does not conduct electricity.)<\/strong><\/p>\n<p>\n\n\n\n<\/p>\n<p><strong>(b) Ordinary rubber is an insulator. But special rubber tyres of aircraft are made slightly conducting. Why is this necessary?<\/strong><\/p>\n<p>\n\n\n\n<\/p>\n<p><strong>(c) Vehicles carrying inflammable materials usually have metallic ropes touching the ground during motion. Why?<\/strong><\/p>\n<p>\n\n\n\n<\/p>\n<p><strong>\u00a0(d) A bird perches on a bare high power line, and nothing happens to the bird. A man standing on the ground touches the same line and gets a fatal shock. Why?<\/strong><\/p>\n<p>\n\n\n\n<\/p>\n<p>Solution (a) this is because the comb gets charged by friction. The molecules in the paper gets polarized by the charged comb, resulting in a net force of attraction. If the hair is wet, or if it is rainy day, friction between hair and the comb reduces. The comb does not get charged and thus it will not attract small bits of paper.<\/p>\n<p>\n\n\n\n<\/p>\n<p>(b) To enable them to conduct charge (produced by friction) to the ground; as too much of static electricity accumulated may result in spark and result in fire.<\/p>\n<p>\n\n\n\n<\/p>\n<p>\u00a0(c) Reason similar to (b).<\/p>\n<p>\n\n\n\n<\/p>\n<p>(d) Current passes only when there is difference in potential.<\/p>\n<p>\n\n\n\n<\/p>\n<p><strong>8.\u00a0 <u>Some Basic Properties &amp; electric charge:-<\/u><\/strong><\/p>\n<p>\n\n\n\n<\/p>\n<p>Same as mass, charge is also a fundamental &amp; intrinsic property of matter. As like charges repel each other &amp; unlike charge attract each other. There are three basic properties of charge.<\/p>\n<p>\n\n\n\n<\/p>\n<p>(i) Quantization of charge (ii) conservative nature of charge (iii) Additive Nature of charge<\/p>\n<p>\n\n\n\n<\/p>\n<ul class=\"wp-block-list\">\n\n<li><strong>Quantization Of Charge:- (Discrete Nature of charge )<\/strong><\/li>\n\n<\/ul>\n<p>\n\n\n\n<\/p>\n<p>According to quantization nature of charge, the charge on a body is always whole number multiple of charge on an electron.<\/p>\n<p>\n\n\n\n<\/p>\n<p>I,e charge on a body q = \u00a0ne\u00a0 \u00a0\u00a0n= 1, 2, 3, 4, \u2026\u2026\u2026 n\u2260 \u00bd, 3\/2, 1.5 etc.<\/p>\n<p>\n\n\n\n<\/p>\n<p>Where e = 1.6 10<sup>\u201319<\/sup>C (charge on an electron) &amp; n is a whole number<\/p>\n<p>\n\n\n\n<\/p>\n<ul class=\"wp-block-list\">\n\n<li><em>During rubbing, electron can transfer from one body to another body in a whole number. So charge is quantized as half electron cannot be transferred.<\/em><\/li>\n\n\n<li><em>A elementary particle quart of very small life time have fraction of charge.<\/em><\/li>\n\n<\/ul>\n<p>\n\n\n\n<\/p>\n<p><em>\u00b1<\/em> <em>e &amp; \u00b1<\/em> <em>\u00a0e. (it is exception of quantization of charge)<\/em><\/p>\n<p>\n\n\n\n<\/p>\n<p><strong>Q.3. \u00a0If 10<sup>9<\/sup> electrons move out of a body to another body every second, how much time is required to get a total charge of 1 C on the other body?<\/strong><\/p>\n<p>\n\n\n\n<\/p>\n<p>Solution:\u00a0 Therefore the charge given out in one second is= 1.6 \u00d7 10<sup>\u201319<\/sup> \u00d7 10<sup>9<\/sup> C\u00a0\u00a0\u00a0\u00a0\u00a0 = 1.6 \u00d7 10<sup>\u201310<\/sup> C.<\/p>\n<p>\n\n\n\n<\/p>\n<p>The time required to accumulate a charge of 1 C is<\/p>\n<p>\n\n\n\n<\/p>\n<figure><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-14.png\" alt=\"\" width=\"568\" height=\"47\" \/><\/figure>\n<p>\n\n\n\n<\/p>\n<p>Thus to collect a charge of one coulomb, from a body from which 10<sup>9<\/sup> electrons move out every second, we will need approximately 200 years.<\/p>\n<p>\n\n\n\n<\/p>\n<ul class=\"wp-block-list\">\n\n<li>One coulomb is, therefore, a very large unit for many practical purposes.<\/li>\n\n<\/ul>\n<p>\n\n\n\n<\/p>\n<p>\u00a0 <strong>Q.4. \u00a0how much positive and negative charge is there in a cup of water?<\/strong><\/p>\n<p>\n\n\n\n<\/p>\n<p>Solution: \u00a0Let us assume that the mass of one cup of water is 250 g.<\/p>\n<p>\n\n\n\n<\/p>\n<p>The molecular mass of water is 18g. so we can say 18g of water contain 6.022&#215;10<sup>23<\/sup> molecules \u00a0<\/p>\n<p>\n\n\n\n<\/p>\n<p>\u00a0 \u00a0 \u00a0 1g of water contain<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-15.png\" alt=\"\" width=\"100\" height=\"36\" \/> molecules<\/p>\n<p>\n\n\n\n\n\n<\/p>\n<p>\u00a0<\/p>\n<p>\n\n\n\n<\/p>\n<p>Therefore the number of molecules in one cup of water is\u00a0 <img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-16.png\" alt=\"\" \/><\/p>\n<p>\n\n\n\n\n\n<\/p>\n<p>Each molecule of water contains two hydrogen atoms and one oxygen atom, i.e., 10 electrons and 10 protons.<\/p>\n<p>\n\n\n\n<\/p>\n<p>\u00a0Hence the total positive or total negative charge =<\/p>\n<p>\n\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-17.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n\n<\/p>\n<p><strong>Q.5. A polythene piece rubbed with wool is found to have a negative charge of 3 \u00d7 10<sup>\u22127<\/sup> C. (a) Estimate the number of electrons transferred (from which to which?) (b) Is there a transfer of mass from wool to polythene?<\/strong><\/p>\n<p>\n\n\n\n<\/p>\n<ul class=\"wp-block-list\">\n\n<li>When polythene is rubbed against wool, electrons get transferred from wool to polythene. Hence, wool becomes positively charged and polythene becomes negatively charged. Amount of charge on the polythene piece, q = \u22123 \u00d7 10<sup>\u22127<\/sup> C<\/li>\n\n<\/ul>\n<p>\n\n\n\n<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Amount of charge on an electron, e = \u22121.6 \u00d7 10<sup>\u221219<\/sup> C<\/p>\n<p>\n\n\n\n<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Number of electrons transferred from wool to polythene = n<\/p>\n<p>\n\n\n\n<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 as q = ne\u00a0 Therefore, the number of electrons transferred from wool to polythene is 1.87 \u00d7 10<sup>12<\/sup> .<\/p>\n<p>\n\n\n\n<\/p>\n<p>(b) Yes. There is a transfer of mass taking place. This is because an electron has mass, me = 9.1 \u00d7 10<sup>\u22123<\/sup> kg Total mass transferred to polythene from wool, m = m<sub>e<\/sub> \u00d7 n = 9.1 \u00d7 10<sup>\u221231<\/sup> \u00d7 1.85 \u00d7 10<sup>12<\/sup> = 1.706 \u00d7 10<sup>\u221218<\/sup> kg Hence, a negligible amount of mass is transferred from wool to polythene.<\/p>\n<p>\n\n\n\n<\/p>\n<ul class=\"wp-block-list\">\n\n<li><strong><em><u>Conservative nature of electric charge:-<\/u><\/em><\/strong><\/li>\n\n<\/ul>\n<p>\n\n\n\n<\/p>\n<p>According to low of conservation of electric charge, the total charge on an isolated system remains constant, it can neither be created nor be destroyed&amp; can only be transferred from one body to another body.E,g:- (i)<\/p>\n<p>\n\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-18.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n\n<\/p>\n<p>Here charge on reactant is zero &amp; charge on product = +1-1=0<\/p>\n<p>\n\n\n\n<\/p>\n<p>So law of conservation of charge hold good.,<\/p>\n<p>\n\n\n\n<\/p>\n<p><strong>(iii) <em><u>Addition nature of electric charge:-<\/u><\/em><\/strong><\/p>\n<p>\n\n\n\n<\/p>\n<p>According to additive nature of charge, the net charge on an isolated system can be simply obtained by adding all the charges scalarly.<\/p>\n<p>\n\n\n\n<\/p>\n<p>If a system having charge q<sub>1<\/sub>, q<sub>2<\/sub>, q<sub>3 <\/sub>\u2026q<sub>n <\/sub>then total charge on the system q = \u00a0q<sub>1<\/sub>+ q<sub>2<\/sub>+ q<sub>3 <\/sub>\u2026\u2026\u2026\u2026 q<sub>n<\/sub><\/p>\n<p>\n\n\n\n<\/p>\n<p>E,g If system have four charges 2\u00b5C, 3\u00b5C, 4\u00b5C, -5\u00b5C<\/p>\n<p>\n\n\n\n<\/p>\n<p>Then total charge q = 2\u00b5C+ 3 \u00b5C+ 4 \u00b5C+( -5 \u00b5C)= 4 \u00b5C<\/p>\n<p>\n\n\n\n<\/p>\n<p><strong><em><u>9. comparison of charge &amp; mass :-<\/u><\/em><\/strong><\/p>\n<p>\n\n\n\n<\/p>\n<figure>\n<table>\n<tbody>\n<tr>\n<td><strong>\u00a0<\/strong><\/td>\n<td><strong>Electric charge<\/strong><\/td>\n<td><strong>Mass<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td>\u00a0Electric charge may be + ve, -ve or zero.\u00a0\u00a0\u00a0<\/td>\n<td>The mass of a body is always a positive.<\/td>\n<\/tr>\n<tr>\n<td><strong>2<\/strong><\/td>\n<td>Electric charge is always quantized.<\/td>\n<td>Quantization of mass is yet not obeyed.<\/td>\n<\/tr>\n<tr>\n<td><strong>3<\/strong><\/td>\n<td>Charge on a body does not depend on its speed.\u00a0\u00a0<\/td>\n<td>Mass of the body increase with its velocity.<\/td>\n<\/tr>\n<tr>\n<td><strong>4<\/strong><\/td>\n<td>Charge is strictly conserved.<\/td>\n<td>Mass is not conserved as it may convert into energy.<\/td>\n<\/tr>\n<tr>\n<td><strong>5<\/strong><\/td>\n<td>The electrostatic force between two charges may be attractive or repulsive.<\/td>\n<td>Gravitational forces between two masses are always attractive.<\/td>\n<\/tr>\n<tr>\n<td><strong>6<\/strong><\/td>\n<td>Electrostatic force between different charges may cancel out.<\/td>\n<td>Gravitational forces between different masses never cancel out.<\/td>\n<\/tr>\n<tr>\n<td><strong>7<\/strong><\/td>\n<td>A charged body always has some mass.<\/td>\n<td>A body having mass may not have any charge.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p>\n\n\n\n<\/p>\n<p><strong><em><u>10. Coulombs law in electrostatics:- (Scalar form)<\/u><\/em><\/strong><\/p>\n<p>\n\n\n\n<\/p>\n<p>In 1785, the French physicist Charles Augustan coulomb measured the electric force between small charged spheres by using a torsion balance &amp; gave a law which is as below.<\/p>\n<p>\n\n\n\n<\/p>\n<p>Coulombs law states that the force of interaction between two stationary charge is directly proportion to the product of magnitude of charges &amp; inversely proportional to the square of distance between the charges. This force acts along the line joining among the charges.<\/p>\n<p>\n\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-19.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n\n<\/p>\n<p>Where k is constant of proportionality &amp; its value is<\/p>\n<p>\n\n\n\n<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-20.png\" alt=\"\" \/><\/p>\n<p>\n\n\n\n\n\n<\/p>\n<p>Where <img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-22.png\" alt=\"\" \/> is a another constant called permittivity of free space &amp; its value is<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-21.png\" alt=\"\" \/><\/p>\n<p>\n\n\n\n\n\n<\/p>\n<p>\u00a0<\/p>\n<p>\n\n\n\n\n\n<\/p>\n<p>So coulomb\u2019s law becomes<\/p>\n<p>\n\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-23.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n\n\n\n<\/p>\n<p><strong><u>Unite of charge:-<\/u><\/strong><\/p>\n<p>\n\n\n\n<\/p>\n<p>The S.I unite of electric charge is 1 coulomb.<\/p>\n<p>\n\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-24.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n\n<\/p>\n<p><em>Hence one coulomb is that amount of charge which repels another equal charge with a force of 9<\/em> <em>10<sup>9<\/sup>N when placed one meter distance apart.<\/em><\/p>\n<p>\n\n\n\n<\/p>\n<ul class=\"wp-block-list\">\n\n<li>\u00a0The c, g, s unit of charge is stat Coulomb ( stat C ) or electrostatic unit of charge (emu )<\/li>\n\n<\/ul>\n<p>\n\n\n\n<\/p>\n<p><em>One stat coulomb is that charge which repel an identical charge in vacuum at distance of 1 cm with a force of 1 dyne<\/em><\/p>\n<p>\n\n\n\n<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1 Coulomb =3 \u00a010<sup>9<\/sup> statCoulomb (e m u)<\/p>\n<p>\n\n\n\n<\/p>\n<ul class=\"wp-block-list\">\n\n<li>In electromagnetic c, g, s unit of charge is abCoulomb\u2019s or electromagnetic unit of charge (e m u)\u00a0 \u00a0<\/li>\n<\/ul>\n<p>\n\n\n<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-25.png\" alt=\"\" width=\"459\" height=\"78\" \/><\/p>\n<p>\n\n\n\n<\/p>\n<p><strong><em><u>Significance of coulombs law:-<\/u><\/em><\/strong><\/p>\n<p>\n\n\n<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (i) It tells us about the force which bounds the electrons around the nucleus to form a atom.<\/p>\n<p>\n\n\n<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (ii) It tells us about the force which binds the molecule to form solids &amp; liquids<\/p>\n<p>\n\n\n<\/p>\n<p><strong><em><u>Limitations of coulomb\u2019s law:-<\/u><\/em><\/strong><\/p>\n<p>\n\n\n<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (i) Coulombs law is applicable only on point charges.<\/p>\n<p>\n\n\n<\/p>\n<p>(ii) It holds good only when charges are in rest only.<\/p>\n<p>\n\n\n<\/p>\n<p><strong><em><u>11. Comparison between coulomb\u2019s force &amp;Newton\u2019s gravitational force:-<\/u><\/em><\/strong><\/p>\n<p>\n\n\n<\/p>\n<p><strong><em><u>Similarity<\/u><\/em><\/strong><\/p>\n<p>\n\n\n<\/p>\n<p>(i) Both obey inverse square law.<\/p>\n<p>\n\n\n<\/p>\n<p>(ii) Both forces are central forces.<\/p>\n<p>\n\n\n<\/p>\n<p>(iii) Both forces are conservative forces.<\/p>\n<p>\n\n\n<\/p>\n<p>(iv) Both forces are directly proportional to product of interacting Patrick<\/p>\n<p>\n\n\n<\/p>\n<p>Dissimilarity:-<\/p>\n<p>\n\n\n<\/p>\n<p>\u00a0(i) Coulomb\u2019s force is attractive as well as repulsive while Gravitational force is always attractive in nature.<\/p>\n<p>\n\n\n<\/p>\n<p>(ii) Coulomb\u2019s force is much stranger than gravitational force (10<sup>36<\/sup>times)<\/p>\n<p>\n\n\n<\/p>\n<p>(iii) Coulombs force depends upon the medium in which charges are placed while gravitational force does not depends upon medium.<\/p>\n<p>\n\n\n<\/p>\n<ul class=\"wp-block-list\">\n\n<li><strong><em>Q. How much stronger is coulombs force from gravitational force between a electron &amp; proton separated by r distance<\/em><\/strong>?<\/li>\n\n<\/ul>\n<p>\n\n\n<\/p>\n<p>I,e<\/p>\n<p>\n\n\n<\/p>\n<figure><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-26.png\" alt=\"\" width=\"416\" height=\"156\" \/><\/figure>\n<p>\n\n\n\n<\/p>\n<p>Hence Fe is 10<sup>36<\/sup> time stronger then F<sub>G<\/sub><\/p>\n<p>\n\n\n<\/p>\n<ul class=\"wp-block-list\">\n\n<li><strong>Q.6 : What is the force between two small charged spheres having charges of 2 \u00d7 10<sup>\u22127<\/sup> C and 3 \u00d7 10<sup>\u22127<\/sup> C placed 30 cm apart in air?<\/strong><\/li>\n\n\n<li><strong>Ans: 6&#215;10<sup>-3<\/sup>N<\/strong><\/li>\n\n\n<li><strong>Q.7: The electrostatic force on a small sphere of charge 0.4 \u00b5C due to another small sphere of charge \u2212 0.8 \u00b5C in air is 0.2 N. (a) what is the distance between the two spheres? (b) What is the force on the second sphere due to the first?<\/strong><u><\/u><\/li>\n\n<\/ul>\n<p>\n\n\n<\/p>\n<p>Ans:\u00a0 \u00a0 \u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-27.png\" alt=\"\" width=\"268\" height=\"28\" \/><\/p>\n<p>\n\n\n\n<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0 (b) both have equal force so F=0.2N<\/p>\n<p>\n\n\n<\/p>\n<p><strong><em><u>12. Coulomb\u2019s Law in vector from:-<\/u><\/em><\/strong><\/p>\n<p>\n\n\n<\/p>\n<p>Suppose two charge q<sub>1<\/sub>&amp; q<sub>2<\/sub> placed at A &amp; B having position vectors &amp; \u00a0from origion\u00a0 o. Now again suppose that charge q<sub>1<\/sub> exert \u00a0force on q<sub>2<\/sub>&amp; q<sub>2<\/sub> exerts force on q<sub>1<\/sub>. Then from coulomb\u2019s Law<\/p>\n<p>\n\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-29.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n<\/p>\n<p>Where \u00a0is a position vector acting from q<sub>2<\/sub> to q<sub>1<\/sub>.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n<p>\n\n\n<\/p>\n<figure><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-28.png\" alt=\"\" width=\"275\" height=\"325\" \/><\/figure>\n<p>\n\n\n<\/p>\n<p>\u00a0<\/p>\n<p>\n\n\n<\/p>\n<p>Again from Coulomb\u2019s Law force on q<sub>2<\/sub> to q<sub>1<\/sub><\/p>\n<p>\n\n\n<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-30.png\" alt=\"\" \/><\/p>\n<p>\n\n\n\n<\/p>\n<p>Where is a position vector, which acts along q<sub>1<\/sub> from q<sub>2<\/sub>.<\/p>\n<p>\n\n\n<\/p>\n<p>Clearly\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n<p>\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-31.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n<\/p>\n<p>So from eq<sup>n<\/sup> 2 we get<\/p>\n<p>\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-32.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =<br \/>Compairing eq<sup>n<\/sup> 1 &amp; 3 we get \u00a0=<\/p>\n<p>\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-33.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n<\/p>\n<p>Hence Coulomb\u2019s Law in vector from obey Newton\u2019s third Law of motion also from diagram<\/p>\n<p>\n\n\n<\/p>\n<figure><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-34.png\" alt=\"\" width=\"158\" height=\"33\" \/>\u00a0 (from\u00a0 \u00a0law of vector addition)<\/figure>\n<p>\n\n\n\n<\/p>\n<p>&amp;<\/p>\n<p>\n\n\n<\/p>\n<figure><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-35.png\" alt=\"\" width=\"123\" height=\"38\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (from\u00a0\u00a0\u00a0\u00a0 law of vector addition)<\/figure>\n<p>\n\n\n\n<\/p>\n<p>\u00a0So eq<sup>n<\/sup> 1 &amp; 2 becomes<\/p>\n<p>\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-36.png\" alt=\"\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/figure>\n<p>\n\n\n\n<\/p>\n<p>Or<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-37.png\" alt=\"\" \/><\/p>\n<p>\n\n\n\n\n<\/p>\n<p>&amp; similarly\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n<p>\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-38.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n<\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-39.png\" alt=\"\" \/><\/p>\n<p>\n\n\n\n\n<\/p>\n<ul class=\"wp-block-list\">\n\n<li><strong>Q .8: Four point charges q<sub>A<\/sub> = 2 \u00b5C, q<sub>B<\/sub> = \u22125 \u00b5C, q<sub>C<\/sub> = 2 \u00b5C, and q<sub>D<\/sub> = \u22125 \u00b5C are located at the corners of a square ABCD of side 10 cm. What is the force on a charge of 1 \u00b5C placed at the centre of the square?\u00a0<\/strong><\/li>\n\n<\/ul>\n<p>\n\n\n<\/p>\n<p>Ans: 0<\/p>\n<p>\n\n\n<\/p>\n<ul class=\"wp-block-list\">\n\n<li><strong>Q.9. \u00a0(a) Two small insulated charged copper spheres A and B have their centers separated by a distance of 50 cm. What is the mutual force of electrostatic repulsion if the charge on each is 6.5 \u00d7 10<sup>\u22127<\/sup> C? (b) What is the force of repulsion if each sphere is charged double the above amount, and the distance between them is halved?<\/strong><\/li>\n\n<\/ul>\n<p>\n\n\n<\/p>\n<p><strong>Ans: (a) <\/strong>force between the two spheres is 1.52 \u00d7 10<sup>\u22122<\/sup> N.\u00a0\u00a0\u00a0 (b) 0.243 N.<\/p>\n<p>\n\n\n<\/p>\n<p><strong><em><u>13. Dielectric constant or relative permittivity:-<\/u><\/em><\/strong><\/p>\n<p>\n\n\n<\/p>\n<p><em>Permittivity is a property of the medium which determines the electric force between the charges situated in that medium<\/em>.<\/p>\n<p>\n\n\n<\/p>\n<p><strong><em><u>\u00a0Relative permitivity:-<\/u><\/em><\/strong><\/p>\n<p>\n\n\n<\/p>\n<p>As we know coulomb\u2019s force between the two charge placed in vacuum is<\/p>\n<p>\n\n\n<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-40.png\" alt=\"\" \/><\/p>\n<p>\n\n\n\n<\/p>\n<p>\u00a0\u00a0\u00a0 Where <sub>o<\/sub> is the permittivity in free space<\/p>\n<p>\n\n\n<\/p>\n<p>Again force between the same charges, when placed in a medium is<\/p>\n<p>\n\n\n<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-41.png\" alt=\"\" \/><\/p>\n<p>\n\n\n\n<\/p>\n<p>\u00a0\u00a0 Here \u00a0is the permitivity in the medium<\/p>\n<p>\n\n\n<\/p>\n<p>Dividing eq<sup>n<\/sup> 1 &amp; 2 we get<\/p>\n<p>\n\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-42.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n\n<\/p>\n<p>Where is \u00a0is called relative permittivity.<\/p>\n<p>\n\n\n<\/p>\n<p>Hence <em>relative permittivity may be defined as the ratio of force between two charges in vacuum to the force between the charges in medium<\/em>. Or Relative permittivity may be defined as the ratio of permittivity in the medium to the permittivity in free space.<\/p>\n<p>\n\n\n<\/p>\n<p>Hence coulombs law for material medium becomes<\/p>\n<p>\n\n\n<\/p>\n<p><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/strong><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-43.png\" alt=\"\" \/><\/p>\n<p>\n\n\n\n<\/p>\n<p><strong>Q.10. What will be the Coulombs force if two charges are placed in water?\u00a0\u00a0\u00a0<\/strong><\/p>\n<p>\n\n\n<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Clearly\u00a0 \u00a0 \u00a0 <img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-44.png\" alt=\"\" \/><\/p>\n<p>\n\n\n\n<\/p>\n<p>If charges are placed in water ( =80)then force between charges becomes<\/p>\n<p>\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-45.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n<\/p>\n<p>Here we can see that force reduces by 80 in water as compare to vacuum<\/p>\n<p>\n\n\n<\/p>\n<p><strong><em><u>14. Force Between Multiple charge: The superposition Principle:-<\/u><\/em><\/strong><\/p>\n<p>\n\n\n<\/p>\n<p><em>The principle of superposition states that if there are a number of charges exerting force on a single charge, then total force on single charge will be equal to sum of all the forces exerted by individual charge on the charge.<\/em><\/p>\n<p>\n\n\n<\/p>\n<p>Suppose there are n charges q<sub>1<\/sub>, q<sub>2<\/sub> , q<sub>3<\/sub>\u2026q<sub>n<\/sub> exerting force on a charge q<sub>0<\/sub>.<\/p>\n<p>\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-52.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n<\/p>\n<p>Then from coulomb\u2019s law force on q<sub>0<\/sub> due to q<sub>1<\/sub><\/p>\n<p>\n\n\n<\/p>\n<p>Is \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0<img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-46.png\" alt=\"\" \/><\/p>\n<p>\n\n\n\n<\/p>\n<p>\u00a0<\/p>\n<p>\n\n\n<\/p>\n<p>Again force on q<sub>0<\/sub> due to q<sub>2<\/sub> is\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-47.png\" alt=\"\" \/><\/p>\n<p>\n\n\n\n\n<\/p>\n<p>Similarly<\/p>\n<p>\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-48.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n<\/p>\n<p>Adding all the eq<sup>n<\/sup> s we get<\/p>\n<p>\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-49-1024x157.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n<\/p>\n<p>\u00a0 So total force on a charge\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<strong>\u00a0\u00a0<\/strong><\/p>\n<p>\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-50.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-51.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n<\/p>\n<p><strong><em>15. <u>Force on a point charge due to continuous charge distribution:-<\/u><\/em><\/strong><\/p>\n<p>\n\n\n<\/p>\n<p><em>A\u00a0 continuous charge distribution is a system of charge lying at infinitelly small distances from each other.<\/em><\/p>\n<p>\n\n\n<\/p>\n<p><em>There are three types of continuous charge distribution.<\/em><\/p>\n<p>\n\n\n<\/p>\n<p><strong><em>(a) <u>Linear or line charge distribution:-<\/u><\/em><\/strong><\/p>\n<p>\n\n\n<\/p>\n<p>Ifcharges are arranged in such a way that they seem to be like a line then the distribution of charges is called line charge distribution.<\/p>\n<p>\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-53.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n<\/p>\n<p>The line charge density \u00a0may be defined as the charge per unit length.<\/p>\n<p>\n\n\n<\/p>\n<p>\u00a0<\/p>\n<p>\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-57.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n<\/p>\n<p><strong><em><u>(b) Surface or area charge distribution:-<\/u><\/em><\/strong><\/p>\n<p>\n\n\n<\/p>\n<p>If charge are arranged in such a way that they seems to be a surface (plane)then the distribution of charge are called surface distribution of charge<\/p>\n<p>\n\n\n<\/p>\n<p>The surface charge density \u00a0may be defined as then charge per unit area of the<\/p>\n<p>\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-55.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n<\/p>\n<p>conductor.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0<\/p>\n<p>\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-56.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n<\/p>\n<p>\u00a0<\/p>\n<p>\n\n\n<\/p>\n<ul class=\"wp-block-list\">\n\n<li><strong><em><u>Volume Charge distribution:-<\/u><\/em><\/strong><\/li>\n\n<\/ul>\n<p>\n\n\n<\/p>\n<p>If charges are arranged in such a way that they seems to be like a volume, then the distribution of the charges is called <em>volume distribution of charge<\/em>.<\/p>\n<p>\n\n\n<\/p>\n<p>The volume charge density \u03c1 may be defined as the charge per unit volume of the conductor.<\/p>\n<p>\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-59.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-58.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n<\/p>\n<p><strong><em><u>16 force due to continuous distribution of charge:<\/u><\/em><\/strong><\/p>\n<p>\n\n\n<\/p>\n<p><strong><em><u>(i)\u00a0 Forces at a point due to continuous line distribution of charges<\/u><\/em><\/strong>:-<\/p>\n<p>\n\n\n<\/p>\n<p>Suppose a point P having r distance from a point O on continuous line distribution of charge. Than small force at charge placed at P due to small charge dq on small surface ds may be given by coulomb\u2019s law,\u00a0\u00a0\u00a0<\/p>\n<p>\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-61.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n<\/p>\n<p>\u00a0<\/p>\n<p>\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-60.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-62.png\" alt=\"\" \/><\/p>\n<p>\n\n\n\n<\/p>\n<p><strong><em><u>(ii)\u00a0 Force due to continuous surface distribution of charge:-\u00a0 <\/u><\/em><\/strong>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/p>\n<p>\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-63.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n<\/p>\n<p>Where surface charge density<\/p>\n<p>\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-64.png\" alt=\"\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/figure>\n<p>\n\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-65.png\" alt=\"\" \/>\u00a0<\/figure>\n<p>\n\n\n\n<\/p>\n<p>So the force at p due to complete surface is\u00a0\u00a0<strong>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/strong><\/p>\n<p>\n\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-66.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n<\/p>\n<ul class=\"wp-block-list\">\n\n<li><strong><em><u>Force due to continuous volume distribution of charges.<\/u><\/em><\/strong><\/li>\n\n<\/ul>\n<p>\n\n\n<\/p>\n<p>Suppose a test charge is placed at point p having distance r from small volume dv having charge dq.<\/p>\n<p>\n\n\n<\/p>\n<p>Then force on due to dq \u00a0=<\/p>\n<p>\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-67.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n<\/p>\n<p>where volume charge density<\/p>\n<p>\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-68.png\" alt=\"\" \/>\u00a0 \u00a0 \u00a0\u00a0<\/figure>\n<p>\n\n\n\n<\/p>\n<figure><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-69.png\" alt=\"Force due to continuous volume distribution of charges\" width=\"499\" height=\"66\" \/><\/figure>\n<p>\n\n\n<\/p>\n<p>\u00a0Hence force at p due to complete surface is \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<strong>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/strong><\/p>\n<p>\n\n\n\n<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/vartmaaninstitutesirsa.com\/wp-content\/uploads\/2023\/03\/image-70.png\" alt=\"\" \/><\/figure>\n<p>\n\n\n<\/p>\n<p>\u00a0<\/p>\n<p>\n\n\n\n<\/p>\n<pre><code>                                                     1(b) Electric Field <\/code><\/pre>\n<p>\n\n\n<p><\/p>\n<ol start=\"17\"><\/ol>\n\n\n<\/ol>\n<p>\u00a0<\/p>\n<p>\n\n<\/p>\n\n\n\n<\/p>\n<ol class=\"wp-block-list\" start=\"17\"><\/ol>\n<p>\u00a0<\/p>\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>vartmaan institute sirsa Unit I: ElectrostaticsChapter\u20131: Electric Charges and FieldsElectric charges, Conservation of charge, Coulomb&#8217;s law-force between two point charges, forces between multiple charges; superposition principle andcontinuous charge distribution.Electric field, electric field due to a point charge, electric field lines, electricdipole, electric field due to a dipole, torque on a dipole in uniform electric field.Electric [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_uag_custom_page_level_css":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"class_list":["post-206","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_hostinger_reach_plugin_has_subscription_block":false,"_hostinger_reach_plugin_is_elementor":false,"uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false},"uagb_author_info":{"display_name":"sandeep.soni484@gmail.com","author_link":"https:\/\/vartmaaninstitutesirsa.com\/index.php\/author\/sandeep-soni484gmail-com\/"},"uagb_comment_info":0,"uagb_excerpt":"vartmaan institute sirsa Unit I: ElectrostaticsChapter\u20131: Electric Charges and FieldsElectric charges, Conservation of charge, Coulomb&#8217;s law-force between two point charges, forces between multiple charges; superposition principle andcontinuous charge distribution.Electric field, electric field due to a point charge, electric field lines, electricdipole, electric field due to a dipole, torque on a dipole in uniform electric field.Electric&hellip;","_links":{"self":[{"href":"https:\/\/vartmaaninstitutesirsa.com\/index.php\/wp-json\/wp\/v2\/pages\/206","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vartmaaninstitutesirsa.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/vartmaaninstitutesirsa.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/vartmaaninstitutesirsa.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/vartmaaninstitutesirsa.com\/index.php\/wp-json\/wp\/v2\/comments?post=206"}],"version-history":[{"count":1,"href":"https:\/\/vartmaaninstitutesirsa.com\/index.php\/wp-json\/wp\/v2\/pages\/206\/revisions"}],"predecessor-version":[{"id":4082,"href":"https:\/\/vartmaaninstitutesirsa.com\/index.php\/wp-json\/wp\/v2\/pages\/206\/revisions\/4082"}],"wp:attachment":[{"href":"https:\/\/vartmaaninstitutesirsa.com\/index.php\/wp-json\/wp\/v2\/media?parent=206"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}