hello welcome to simplified Minds to0 68 we have going to know I'm going to start this the first video on the entire physics now on 25 to 30 hours of9 out of0 in physics numer electric charges and Fields so this chapter we discuss completely today one discuss der I mean Theory understanding I assume that not only about you know there are some more videos on this chap related one the mcqs I I also prepare mcqs for you and phys chap almost 100 mcqs so those 100 mcqs also you can solve that is also f so with this you are completely once you understand this lecture okay take one not any this chapter is completely done okay so and you know I think for 2025 boards we have three blueprints I'm do not worry about because in this chapter you also have two marks and three markers also Ander electrostatics that may be electric potential that may be an electric charge or from this chapter first chapter second chapter do not worry on that that will beasy everything is easy for you separate notes only for you can write simplified Min physics and RP sir you can put by RP I'm going to complete entire chapter entire we discuss definition the everything in this and also we discuss numericals and also discuss KCT on this chapter so the order that's very important first so what is there but if I ask someone for examp Optics get up and what is there R Optics and at least you should able to tell the chapters in order I mean the topics in order opsi you should have overall picture of the chapter that's very very important soap B disc form we'll discuss it okay discuss electric field this is very important electri we discuss about gos La gos we discuss abouts other related application discuss this overall picture anytime en chap can make a flowart or formulas and all the things that's very important important and before I start this we have some Basics so basic because my intention is to make you get out of in physics in board exams for example charging by induction charging by conduction for example made ATS the the body which loses electrons it will become positively charged the body which gains electron become negatively charged and positive POS sorry like charges basic and if you want to find the magnitude of the charge we also have gold so if you keep if you come and depending how muching we can say magnitude Basics discuss because it's not that important also and also and discuss but this one sh will become then four hours six hours okay and then this chapter is very very important before I start this because what is this studing electric charge next start running charge is running we call it as we we call it as current charge rate flow of charges is called current third chapter is current electricity always produce magnetic field around that a moving charge will produce a magnetic field that's called moving charge and magnetism mag fifth next what is magm how when something this magnetic is prod if this magnetic field is you know continuously changing it will produce Emi electr Force because it's continuously changing there something called alternating current is produ it's not not a regular DC current what is the alternating current what is the application no that all next to seven chapters understand perfectly all are related that's why you should study this chapter is very important and also of course uh uh this chapter is very important because if you're doing it uh okay disc because if I tell about all the why to study a chapter practical application real life application so we not discuss on that we come to the theory okay proper of but you can't add all the things like that Char so you can add adding it for example this is addition ad of charges charges can be added algebraically that's simple that's all examp additivity of charges charges charges can be added algebraically because scal quantity you can add it like that forces you can't add forces algebraically because again so you have to add them vector vector is consed because you're not creating any charge or neither be nor be destroyed just going from one body to other body so one becomes positive other becomes negative so in isolated system the total charge always remains the constant that is called as charge is conserved okay so next to quantization of charge quantization important Quant small quanti ation what is what is quantization simple example simple very simple it basically says that for example simple so what it says is the total charge in the total charge is always represented as integral multiple of basic unit of charge but not Reed most of the time if they ask in exam properties of charges just write three properties if you want you can write one one sentence for both ad additivity of charges means charges can be added algebraically conservation means in isolated system total charge remains constant quantization of charge in the total charge can be represented as integral multiple of integral integers one 2 3 multiple of basic unit of charge that is e so the value of e is basically 1.6 into 10^ -9 so what does it means very simple example I tell for example what is this taking some fruits for example if you take a box of fruits on the box total number of fruits if you say total weight the weight of the Box is always basically either 10 apples or n apples or eight apples like this you will not have 8.5 apples no you have 8.5 apples .5 think Wasing that guy will put exactly the total weight is always integral multiple of number you not have half or little like that that is a basic that's meaning of this example steps if you want to climb the steps so total height between the two floors the total height that whatever height can be always a number a number into height of each step the total height H is equal to the number 10 steps into height of each steps decimal points what is the meaning of this deci 1.6 not possible that is a basic meaning that's meaning quation means toal charge is always equal to or it can be represented as integer multipl integral multiple integral multiple of basic unit of charge that's the basic things let's go for next topic now law very simple so like charges attract unlike charges sorry like charges repuls unlike charges attracts basically so what is so that force is proportional to product of the charges and it's inversely proportional to square of the distance between them so we call this as inverse Square law so it's inversely proportional square of the distance between them and whenever we have proportionality to remove that we should put a constant proportionality constant f is equal to K into q1 Q2 / r s this is a form R square or d square whatever it may be okay so what is a k it's a proportionality constant it is found to be it's 1 1 by 4 Pi Epsilon whose value is 9 into 10^ 9 so if you want to find the unit of this k that c rad distance rad distance meter M Square so I am keeping this as it is this goes this side that means this is Newton m squ per square that's the formula newon Square per square you get it this a value this value is very important and 85 into 10us and since is 1 by 4 that means reciprocal so whatever the unit of K that me S this is a formula this value is not required Val value but this value is very very important you should understand this value it is very very very important what is the Kum slot definition the force of attraction or repulsion between two charges is directly proportional to the magnitude of proportional to product of the magnitude of the charges and inversely proportional to square of the distance between them I written this formula also sent so the force between two charges directly proportional to the product of the product of the charge is inversely proportional square of the distance between them the force always acts along the line joining charge q1 Q2 so along the line so this Force whatever the force attraction whatever repulsion whatever it is along the line either it can be in this way or it can be in this way it can act however it want I think I think C they asked one question like this so uh force on one due to two is something F12 force on two due to uh due to one is F21 the relation between fub1 to F2 it's very simple question sometimes C question questions so they asking what is the relation between F12 and F21 they say F12 is minus of F21 question basically you to answer equal both are equal so I don't remember question okay this is a simple formula you should know how it came and then it acts along the formula ask Define one for examp one Kum Define one Henry Define one they can ask anything one Henry Define [Music] if you want one that means what 1 one that means distance should be one and this value already we know it's 9 into 10^ 9 9 into 10^ 9 F equal to what is the value of f f is 9 into 10^ 9 1 into 1/ 1 9 into 10 9 F 9 into 10 9 so one of if ask to Define one Kum one Kum of charge one sorry one Kum is that amount of charge which is kept a distance of 1 M which is kept at a distance of 1 M and exerts a force equal to 9 into 10^ 9 the Bas whatever the value you get that you define so what is one it's that it is that amount of charge I mean that amount of two charge which is kept at distance of 1 met from same charge exerts a force which is equal to 9 into 10^ 9 and that is called as you know one definition you can mug up from somewhere ifine one terms are very important distance 9 into 10 key are important next we have force between multiple charges again is there's nothing to worry about this simple actually imagine there's a Char q1 and there's a charge Q2 charge Q3 I need to find what is a force on the q1 okay what's the force on the q1 so due to charge Q2 there's a force let us imagine both are positive okay so plus plus repulsion out like this it will be and force on one due to three force on one due to two the force M when we have two forces like this and I want to find the resultant of the two forces you always have to use law of par vectors everywh F2 between root of fub1 s + FS2 s + 2 fub1 F2 when we go to numeric that time we'll do it question they ask you find the net force what is the net force at the at one of the corner at one of the diagonal same questions with they repeat electric potential also do not worry on this topic anything but textbook they have given some kind of vector notations force on one is nothing but force on 1e to 2 plus force on 1e to 3 1 4 it is q1 Q2 divid by R12 it's a vector notation R12 square into R12 the unit Vector disc like that you can have again 1 by 4 Pi Epsilon into q1 Q3 force on one due to two and due to three and again they have one more formula r13 squ R 13 the unit Vector you can have it for n number for example there so many charges are there what's the force on this and add it's not like adding like this you to add vectors because a vector addition it is there AIT Vector I cap JC K cap R cap R1 2 cap R12 you can't add because it's a vector it is what answer you going to get the total force is a vector you to add as per the law of vector this par of vectors a B+ 2 a COS next electric field what is electric field simple what is electric field so it has area of influence for example like this sometimes you know they have their own area and they'll tell what is that meaning is so that is my area it's my area of influence so there are two ways two ways of dealing that okay can tell in two ways sorry I don't use that okay so you'll be in struggle that means you have love know and someone guys like you want to hit someone there two ways that means when a charge comes inside right so this charge can can show two kinds of forces one is what it can show attraction or repulsion but there is some kind of force right Al influence so that Force itself is actually electric field so what is electric field electric field at any point so what is electric field electric field at a point so we can Define electric field at particular Point only electric field at a point is defined as electric field at point is defined as Force per unit charge e is equal Al to F by Q so basically what is a force experiened by a charge when it's kept at that point that is electric field at that point electric field is continuously changing it is more at the nearer and as it goes far electric field becomes less e equal to F by q e equal to F by what electric field is is nothing but Force per unit charge they may ask Define electric field electric field is nothing but it's Define electric field so we can say electric field at a point is defined as so the force experien uh force force experienced by the charge definition electri point is defined as the force experienced by unit power unit positive charge why we taking unit because Q is equal to 1 if I put Q is equal to 1 so e becomes f e equal F by q q is equal 1 e equal F so what is the electric field electric field at the point is defined as Force per unit charge Force experienced by unit unit charge kept at that point we call test charge to find the electric field of this if I see electric field formul I mean so you can experience that field by bringing another magnet you can experience the field it's basically an imaginary uh you know lines drawn to present the what I can say electric field okay simple e equal F if form in f e to Maro relation between the force electric field and the charge next there's a definition I already told you so the other way of defining the electric field is limit Q tends to zero as a q is become smaller and smaller e is equal to F basically the formula is again what is the force formula how you going to get so when there's a source charge Q there you know test charge small q there the force between them what's the formula 1X 4 Pi Epsilon Q 2 by r² distance between them if I want to find electric field e f the test charge Q I'll get the answer 1 by 4on 2 by R that's a formula for electric you can remember the unit is again simple it's e f by Q so it's Newton perum the answer is Newton per again if they ask to Define one one they won ask that one okay not required e equal to F by Q next next this representation Q is more than Z sketch electric field lines for Q is less than Z electric field L negative negative and it will comeing towards this and positive and it goes away and then you have dipole and also you have the properties of electric field lines it's very important electric field L basically they start from if it's a positive and negative they usually start from positive and go towards a negative and then if a single chart they start and they go infinitely somewhere okay so you can see they continuous curves that's very important they're continuous curves and no two electric field lines electric fi L inter in because see what is electric field line basically that is that IM we are drawing it is like a you know Direction so if I take a point somewhere if two electric field intersect at the point of intersection you have two direction simultaneously that's not possible like in case of magnetic field if you give compass compass can't show two two don't keep your leg on that's very important anyway so never intersect each other I just wrote the key this happens you have to write sentences you can say electric field lines electric field lines start at positive charge and ends at the negative charge sent electric field lines are continuous curves the electric two electric field lines can never intersect and then uh the electric fi do not form a closed Loops the center next we have so what is electric flux electric flux is nothing but simple I was giving example of Ries something Bangalore okay everyone have you know what you call I mean so so there'll be a gang leader and then there'll be 20 guys going behind him there's one more gang leader 30 30 people going behind him okay flux if a gang has more number of people I mean 50 60 and all we call flux flux means basically number it indicates the density flux electric field electric you can flux density I mean what is that ter uh we can have magnetic flux electric flux flux and is a general term which tells about the number of something number of field lines density flux is more number of people I say anywh so if someone fine so coming to Electric flux and know number of number tell about density so number of field lines passing through a given area perpend so many fields are coming so if I take a small unit area if I take a small unit area here or if I take a small somewhere here so I'm taking same area same area maybe I'll take DS area DS surface or da whatever okay is more 52 51 is more than 52 the number of field lines entering perpendicularly that's called flux magnetic it can be anything magnetic flux electric flux number people flux anyway what is flux means that it should enter perpendicularly the electric field should enter perpendicular imagine they're not perpendicular so maybe maybe the surface is you know maybe the surface is land or field lanes are not coming perpendicular they're coming at an angle we have to for example if we take e angle is Theta so e has two components one is e cos Theta which is along the axis towards the Theta is e cos Theta away from the Theta towards the COS Theta away from the you can just draw a triangle and put Theta this X and Y use cos Theta sinet you get it f towards from what is definition is we take a component of the so that is DS is surface Vector surface though into e cos Theta so therefore it is DS cos Theta into e or E cost into DS or you can do anyways either you can align you can take component of DS along the e or you can take component of e along the DS actually okay so e DS cos Theta formula is it's basically I equal to e Vector do DS Vector we also call this as scalar quantity SC vectors scal vectors product maap can go that also it'll be very very easy vectors so this called dot product that's why you need to understand soct scal product exactly when I'm teaching that chap you that so basically formula is e DS cos Theta e into DS e vector. DS this is a flux formula is for example thet equal 90° what the fluxes Z 0 Theta equal to 0° flux is maximum so again you understand for example you may think sir what is this I'll take the NCR book okay so you may think get maximum of is a vector it is the direction of area is nothing but a a line perpendicular to it so we have a chap 3D geometry and the we discuss something planes okay last I think this won't ask okay V of the plane you can see clearly this makes 0 de with the line This is a unit Vector perpendicular to this this is the direction of the surface or DS get maximum so undera you should not see direct you should not compare angle between plane and the field you should not compare this you should compare the angle between the plane Vector that's n vector and the e n and E both are in the same direction so the basically angle is THX okay me you can go to can see okay any next let's go dipole quick go next topics elect dipole so so basically again there's so many definition short dipole and all the things we not discuss too discus that means and they separate by distance 2 because we take all all the calcul from we also have dipole moment P that is nothing but either of the charge that is q into distance between them that's called as dipole moment of the dipole so we also you also should know direction of the dipole basically so direction of dipole is given by it's from minus Q to plus Q the direction is where it's from [Music] of it has a direction direction is from where to where from minus Q to plus Q next so coming to next one electric field a point on a line what we should discuss now discuss what is electric field to dipole electric field formul we discuss at two different locations one is at the equatorial plane somewhere here one is along the axial plane somewhere disc so what about some angle is there of course they can ask some angle also that we discuss in C not here exam 0 or 180 depending on that side or this side so we'll discuss this and also we'll take this dipole and keep it in the magnetic field sorry keep it in electric field and see how it behaves the next so coming to here is electric field at a point on axal line okay I want to find dipole minus Eli [Music] [Music] remember only some steps remaining all you can do by yourself minus plus point always take plusus see this is towards this direction this is towards this direction so what is the effective field at this location obviously the that is what it is that means field here electric electric field for examp 10- is 6 towards this how going to dislocation that is e+ Q minus eus because it is that side normally have this distance 2 a all the distance are measured from Center since we measuring distance of this Q from the center the total BND so this point is taken a distance of R so if you want to find this distance it is Rus a sorry R if you want to find distance between the plus q and the P so distance between plus q and the point the test posi charge is this small distance that is R minus a that means plus Q Rus a 1 by 4 Pi Epsilon I for time being I'll just keep field that is plus q that Q / by q and distance between them that is r - A the whole Square minus you need to find distance between now this and this minus Q basically if it is r + a so it is basically r + a so 1 by 4 Pi Epsilon not into Q / r + a the whole S Plus Q minus Q you don't have to put minus Q again because we got the sign by considering we got this direction we got the direction by considering the sign only the positive therefore it is repulsion the negative therefore it is attraction opposite subtracting it some books they plus Q minus they plus here but they'll take charge as negative here plus into minus is fine but always writey because this is more easy for me in the C okay very so this only 1 r 1 r s simplif r a r a A plus bqu aare formula 4 A divid by a plus b a a square B Square simple that's it all I not repeat all those things I written all the steps already so a plus b a 4 a a s b² + 2 a a sare b s- 2 a so if I remove the bracket minus 2 4 general formula a a sare b sare is the formula and the formula going to get that is 4 a r into r s a square we know already formula is that dipole moment is either of the charge and distance between them that is 2 a 2 into 2 so so basically it is 2 into 2 that is becomes p and you get basically again simplified or you can simp r s into p and you get 2 p r the formula so again so basically you have for R much much greater than and what's the meaning of this r s aare imagine compar to a and first of all imagine is2 R is 10 10 square minus 02 the whole Square 10 square is 100 become fur 1 by Square 1 it's 144 square so the value always red understand for solving C questions R we have R here that's it so we have again simple so distance is 2 a we take R somewhere Point here perpendicular to this again due to this it pushes minus ATT and angle some angle is AA basically it is an it's going to form kind of isoc triangle or you can sayle a problem actually basically so is 90° it will be there and this will be equal to this so just 2 it is yeah this angles also will be equal I'm okay not required okay plus Q again individually we can take this one so let us take this angle as something five we'll take this as Theta these two angles will be equal equ again we can use Z shape and all the things something corresponding angles are equal and it can have Z shape alterate Ang are equal and these two Ang are equal because is triangle andely okay Q two components components Force components so towards the angle away from the simple Q component notice one comp like this one component like this one component like this one component like this compon compon because they'll be equal and they'll get cancel because we can find the magnitude also now if you want to find the magit we can find it Square because this is 2 a this is a and a distance we always take measure distances from the center to a point where you finding the field and that we take it always R so by using right angle theorem right angle triangle this is a this is R this is root of r² + a s py theorem r a sare if I want to find electric field due to plus Q I mean here plus Q in the that's nothing but K the charge qide by distance distance between the charge and the point that is this that is root of root of R square + a square the square into Q of course minus we taking the magnitude and root of R square + a squ square so you can clearly see both are same of all obviously therefore this is like this and this is like this so magnitude same that becomes horizontal components but this if I add sin Theta they'll become vertical components vertical components opposite e component eus component add so that means what you have it's coset component compon we have got the direction by using plus and minus only so again you don't have to put the plus sign same WR twice then whatever you have cos Theta you have to get the COS Theta from this formula obvious this will adjacent by hypotenuse a / rooot r s + a sare this becomes a / root r s + a square so something into root that become half + 1 3x2 3x2 again for a much much greater than shortes you can neglect the numerator you have 2 a into q that becomes p and p / r² + a s so you can neglect the a squ you get RQ directly P / RQ that's so this is very very important notice for axial plane okay electric field electri it will be along the direction minus q q electric field will be along the line in case of in ofor E aial is basically opposite both are opposite e a is negative of e equatorial not just negative it's also you can notice that for axial we have two for we don't have two we don't have two two either tce is nothing but e aial the tce e 2 * of e equatorial is e AAL not just that it's also negative negative but field opposite to each other but if you take aial so both in same direction it's positive question they can ask MC also next so we will take dipole keep it in the electric field may be force of attraction or there may be force of repulsion there force of attraction force of repulsion what I'm saying is when dipole is kept in an you know in an electric field it experiences the kind of force what is the force that's going to experience let's check out here now okay so what is the force you're going to exp let keep a dipole in this case now this is electric field netive so that means going like this from positive to negative that's the meaning of this so plus Q minus Q it is going in this direction the electric field I'm going to keep a dipole in this what happen basically so this plus will always get attracted towards where minus this minus will attract towards the PO plus you now first of all it's kept angle someone is trying to pull like this some is trying to pull this so the dipole will experience a torque dipole experience a torque whenever a dipole is kept in a uniform electric field it will experience a torque so I thinki or nonform like this is only application I think questions session it experience a torque how do you find a torque is equal to torque is nothing but Force into perpendicular the defition of is something which rotates a rotational Force something rotates like this torque how do you find you know T to equal to force into the perp either of the force since both are equal either of the force into perpendicular distance between them you to find this distance if this Theta if the distance is 2 a or something like you know we can call it as you know 2 basically so if you want to find this distance that is 2 a sin Theta 2 a sin thet perpendicular distance f is nothing but e into Q so basically it is e into Q into 2 a into sin thet and you already know Q into 2 is nothing but P that is p sin Theta the formul the if they ask you to derive this for three Mark in the board exam I diagram torque definition torque is force into perpend either of the force into perpendicular distance between them there's a one force like this there one force like this and distance between them is what there a perpendicular distance this is 2 a this is 2 a sin Theta so that is how it is you're going to get P into sin Theta this is basically this is nothing but a scalar product P into e scalar product see scal sorry multiply the answer a vector that's called as that's called as basically your you know Vector product right that that is where your left hand flamings law right hand sorry right hand flamings law left hand flamings law left hand flamings law and you know that you have rule left hand Flemings rule not law right hand Flemings Rule and left hand Flemings Rule and you have that right andle I mean when two forces are multiplied when two forces are multiplied you'll get a one more Force which also has Direction the direction is perpendicular to these two forces that is only Vector product we'll discuss that in the physics sorry mathematics mathematics yeah okay next so this is about we discuss about allision all this till now next before we go to the gos law we have something called charge distribution simple nothing it's just a term system when you have some you know charge divid maybe it's a long infinite wire but I want density density Cal charge divid by length the charge per unit length is called linear charge density surface charge density volume have some kind of solid box Char I need to find what is the charge per volume that's called volume charge density I need to find charge per unit volume charge per unit volume that's called as surface charge dity right next next next we have gos so what is gosla simple very simple till now what we discussed we found the charge due to Point Char we found electric field to point charge electric field due to a dipole we found electric field discuss in the c section not in the board exams charge configurations for example you have you know you know some kind of charge distribution charge distribtion you have some sheet on the charges distributed everywhere random charge distribu or some volume is there or some some you have some charge q1 and you need to find a very beautiful electric field due to any kind of charge distribution not exactly kind again there some conditions are there conditions that that's not requir all those things simple what it says that they want the charge distribution the for example if you want to find a electric field what gosla says is that very simple you consider goian surface which covers the entire charge distribution which covers the entire charge distribution so the electric field coming out of this the total electric field or you can say electric FL the flux coming out is always 1 by epon * what is the net charge inside very beautifuland distrib Al how do you find the you know total flux what how you going to electric field so we can find the flux using this formula then equal to some other formula we can get the electric field simple by usings you can find electric field to different kind of charge distribution not just only single point or two two charges whole wi charge there other you can find the flux you can find you know electric field that's a beauty of gos that's very this guy is very famous gos gos engineering you have all the theor Divergence Theorem convergence theorem very famous guy okay next famous person salute okay next ask State gos law and then using gos law derive some things first thing is they ask you to derive using a charge distribution for example you have some kind of wire infinitely long wire what is I think students are very good conting two steps to 10 steps there be sometimes small question will be asked for you know 10 five marks you students are very good from from making small thing to bigger it so I think very good obviously and since it a wire the goian surface suitable goian surface circular goian surface for examp Tu you don't want light to come out of tube light what are you going to do you want to cover it with some sheet for example you have some kind of yeah you for example you have some for example this a wire go in surface something which is like this something like this it cover everything I keep a light inside so it will cover everything so it take a suitable goian surface of course you may light bir but that is very Less almost negligible or you can say so you get all the electric field lines flux like this you not get flux like this one reason so there won't be flux any side so flux comes only on the uh the circumference of the this cylinder so if you want to find the total you know electric field simple how you going to find so first of all there are three surface we can just divide three surfaces here there is no flux you can you can Define that in the exam in the three region there's no flux here there's no flux here because the field lines like this TS is like this so electric field is like this D is like this so Theta is equal 90° therefore flux is equal to Z flux is equal to EDS cos Theta 0 but e and DS they are in the same direction so Theta B 0° only along this surface if you take any small area along the surface not get like this much other that thet is equal to Z only flux will be coming from here because that is e into cos 0 get cos 0 is 1 a small area than the DS you want to find total area total flux integrated we call this a small d e DS toal integr integration you get circumference circumference formula is 2 pi r into length of this where finding that's length L 2 pi r this is the total flux this we got through integration we got this answer but according to GS law we know flux is equal to 2 by Epsilon by equating these two what are you going to get now if you want electric field e e into 2 RL should be equal to Q by Epsilon e q / 2 R lilon 2 is basically Sigma and linear charge density then it becomes 2 pi r Epsilon that is basically e eal Lambda 2C simple usings flux is Q by Epsilon and we will take small DS area small D it's very simple okay simple using gos La QEP fluxes using integration you'll find the flux Eli you get the form simple same steps already all the steps both and then do it do this by yourself next have surface then you take like this no problem or who who knows this this is maybe bigger than this so we going take some kind of in surface so why see because surface surface like this F going like this just take only they rectangle rectangle like this they done rectangles here don't worry on that we'll just take the area as this a and this also as a and electric field is going only through this field is going because why the DS area DS and the electric field both are in same direction Theta 0° out the same thing using integration we take small DS so we the total flux is equal to electric field into integration of the small D so we not use any formula just write 2 a usings law 2 usings get Q byepson E into 2 AAL to Q by Epsilon your e becomes QX 2 a into Epsilon so Q by is Sigma surface Sigma by 2 form this formula is very important simple all things next you have you have again we have only this in board exam but C you also have conducting spear non-conducting spear to find out all these things but here is not re but non so since it's a plastic charge is localized Char itself distribute so that it will always have the least Force so just come to this location shell to find electri have choose like this again at every Point here you can see e and Ds are to each other basically soal again you have it again same you should do Tak small R so basically it becomes into area area of the entire thing is 4 Pi r² area of your circle is I means sphere is 4 * of P r² you can prove this mathematically also not required using gos we have q by Epsilon get the answer that's it so that's it basically so that's how it is you can get the answer steps and some statements here and there you have to write that's very important that's all about I think oh yeah that's it I hope you understood that that's all about this you know derivations so majorly go to the first so you have to yeah coming to so finally this is all we discussed disc so always do revision never forget again you have to understand all the things elect field now you watch the lecture that means you really the chapter MC all some extra topics I'll cover there and then again do questions on that in the session confident you can do other questions also okay that's I hope you understood comment com SE that's very important and see you in the next videos bye-bye and take care