[Music] hi everyone one standard physics NC electric charges and Fields chapter one one of the most important chapter for Class 12 so electric charges and field chares we have positive charges and negative charges obviously and El frictional electricity electricity electricity produced by rubbing two suitable friction conduction induction different process so because everything has its own m so friction negative chares electr in a glass are Loosely bound than the electron in a Sil right that becomes positive so when glass rod and silk are rubbed together comparatively Loosely bound electrons from glass get transferred to the silk right NE positive charge glass becomes positively charged and silk Bec negatively char is very important to know that the electrification of the body the transfer of charges so whether a positive or negative right so is due to the transfer of charges electrons from one object to the other so that is if the electron are transfer from one body to the other then the deficiency of the electron makes the body positive so deficiency of el gained by the body negatively charged silk Amper eonite rubber plastic excuse me poer of charges the properties of chares of chares the right so electric charges exist in discrete packets rather than in a continuous mopb we will discuss that also for Char negative Char so let us say that that this is N1 and this is N1 eus N2 e N1 minus N2 upon e again simp quantity of charges quantization of charges am ofes am34 1.6 3.2 4.8 1 2 3 4 5 2 1.2 1.7 so 1 2 3 4 5 6 keep on going there exists only two types of charges one positive charges and negative charges so charges like charges Ripple charges are addtive in nature so of charges we are just adding the chares becomes 5us 3 becomes 2 of charge adity of charges addition of charges so for example 2 5us 3 charges it isal multiple of charges concept basically for example it is a DOT okay like straight line lcop level discret charges it is a continuous charges which is microscopic level right charge is conserved so charge is conserved of charges object sh + 20 + 30 + 40 + 50 10 + 20 30 30 + 30 60 60 40 100 100+ 50 150 so system room charge remains same body object char of positive and negative charges in isolated system remains constant when glass rod is rubbed with the silk so negative charges appears on the silk and equal amount of positive charges appears on the glass rod chars net charge on the glass and the silk remains zero before and after rubbing it it does not change [Music] with recently the existence of less amount of charge so very minute so 1x3 of electron and 2x3 of electron has been postulated soent they have discovered existence if the quads are deducted in any experiment with concrete practical evidence strong evidence the minimum value of quantum of charges will be either 1 or 2 El good nothing but the force force between the twoes negative negative so like charges Ripple each other unlike charges attract each other be anything Force attraction repulsion attraction are repulsion so attraction repulsion is directly proportional to q1 and Q2 and force inversely proportional to distance Square so Force directly proportional to q1 and Q2 Force inversely proportional to square of distance between1 Q2 upon proportional to charge and inversely proportional to square of the distance between them of attraction it is nothing but constant Conant it is a medium in 1 by 4 [Music] Epsilon 1 epon a medium Epsilon Epsilon R so Epsilon rity becomes Oneil [Music] not it can be any value right it can be any medium overall we will discuss that also [Music] a positive constant of proportionality called electrostatic force constant or coolum constant where Epsilon not is the permitivity of a free space it says Epsilon and Epsilon r where Epsilon is Absolute Electric permitivity of a dialectric medium of a dialectric medium relity pertivity between two different medium s so inductive capacity or dialectric coefficient is given by so the equation which we have written already 1 by 4 Epsilon q1 Q2 upon R squ epon epon and Epsilon R which is the perity between the two different charges right 8.9 87 9 1 4 One One Co one so you will have only F which is equal to k k is nothing but 9 into 10 ^ 9 newon force will be equal will be equal to 9 into 10^ [Music] consider the right 600 which is very high strong compar and M2 upon r² so kg kg and then G 6.6 force and at the same time vector vector because it's a force V for example let's say this is q1 it can be it can be attractive or it can be repulsive F K * q1 Q2 by r² Vector so K q1 Q2 r² right one 2 R cap 1 force on one first charge force on one due to force on q1 charge one due to charge 2 [Music] force on one due to two is nothing but F21 Vector so you should mention that Vector symbol also f2e to one k * q1 Q2 upon second r s vector [Music] the cube term of the distance is simply because the vector form let me move to the previous slide Vector r r terms term of the distance is simply because of vector form otherwise law is inverse Square law only so even units of charge so R so1 and sta so we have certain value also right so yeah this is force between the multiple charges right so force between multiple Char we have number of charges multiple chares possibility multiple chares the total force3 multiple chares first charge second charge first charge second charge first1 Comm Q2 Q3 Q4 Q5 q6 F total which is equal to the 1 2 + 1 3 + 14 which is nothing but K [Music] common upon R * of [Music] so this will be the force between multiple charges chares summation you have summation over here Q common superposition principle superposition principle which is nothing but addition right which is nothing but addition just addition of forces right so multiple super principle multiple charge become which multiple char right so charge El 3 into 10^ 8 electrostatic units static static sta to have so relative pertivity or dialectric constant or specific inductive capacity orri coefficient definition so dialectric constant or relative permittivity or specific inductive capacity or dialectric coefficient so relectric constant relative permitivity specific inductive capacity dric coefficient absolute pertivity of the medium to the permitivity of free space right free space air one so dialectric con relative permitivity specific inductive capacity or induct dialect coefficient can also be defined as the yeah of course they representing both both the same right so SOC constant has no units okay fine it's it's a field it's a line it's an imaginary positive charges negative Char Bas we have electric field direction for positive as well as for negative charges electric field nothing but force acting per unit charge right so electric field force acting per unit charge electric field so how they defined charge Source charge sour charge which is the main charge charge so test charge charge or Point charge so right but it is positive right so it is positive Q Char small q or it can be test charge test charge effect we always imagine in the test charge electric field acting un charge so the test charge we never consider test charge okay almost equal to Z but it is not zero almost equal to [Music] so to find electric field to test the charge electri field force acting so force force is nothing but K q1 Q2 upon R q1 upon r² so Force electrostatic force F K * q1 Q2 by r r² q1 or Q generally [Music] test almost equal Z so it should not affect the source charge so is considered to be vanishingly small because its pres should not alter the configuration considered we consider it is very small quantity all of that so the charge yes and thus electric field which is intended to be measured simple right yeah of course then we have certain important points over here so you know since Q not is taken positive test charge the directions of the electric field is along the directions of the electrostatic force so positive it should in the direction of the of electric the directions of the electric field is along the directions of the electrostatic force electrostatic force on negatively charged electrostatic force on negatively Char partic will be opposite to that the of electri electric field is a vector quantity because it has Direction [Music] electri field is Vector Quan so it has magnitude as well as direction or uniquely determined at every point on the field s unit of electric field is nothing but Newton per yeah electric you will understand very easily of course right so electric field due to a point charge for exerted on how I can Define my electric field electri force acting per charge isal F upon Q * q r² but basically chares neglected charge SCE so q1 Q2 Q3 Q4 Q5 so Q 1 2 3 4 and then 5 Q5 minus one we are neglecting the sour charge sorry Point charge so how I can write for total electric field e which is equal to Q charge and charge you can add summation multiple chares so electrostatic force force multiple super position principle electric field due to a point charge hasm greater than Z positive charge Q less than Z negative charge so then the field radi outward for positive charge radially inward for negative charge so Q greater than zero says it is positive charge Q less Z it is netive [Music] charge superos principle so so far electric field in terms of coordin the given ter multiple forces right so multiple forces m of course it is a square so force is the electric field between multiple charges right so the interaction on the charge which is to be studied due to the other charges the charge on which the influence duut to the other charges found assumed to be floating charges and other are rigidly fixed the source Char because fixed example first charge floating is rled Away by Q2 and2 3 4 5 6 toward Q3 and Q the interaction between the other charges among themselves must be ignored f 2 3 4 5 6 blah blah blah 2 3 2 4 2 5 2 3 4 35 and 4 five are ignored because all are same 2 three and 32 both are same 43 and 3 4 are so we consider only one so superposition principle holds good for electric field also electric field lines right hello right so electric field lines so electric field Lin electric field sorry electric line of force is imaginary imaginary or curved path curved path along which a unit positive charge is supposed supposed to move and free to do so in an electric field electric field and force do not physically exist but they are represented represent real situations do not physically exist so magnetic we couldn't see real situations likei positive will each other negative negative each other posi negative will attract each other yeahi charges greater than is the the representation of the electric field of field the size of the arrow represents the strength of the electric field so electric are talking about strength also it can be anything okay so okay increases right coming to the point when distance increases electric field strength decreases when distance increases electric field strength decreases right which is equal to k q upon r² number electri L the given represents electric field in terms of field lines easy way to draw so just elri F line of force due to a pair of equal and unequal charges right so plus and then minus oppos electric field Direction soes unlikes like point so properties of electric L the electric field L of for are imaginary of course because but it's an imag exist a unit positive charge placed in electric field tends to flow sorry follow a path along the electric field if it is free to do so elmin and negative chares the tangent of the electric field L at any point gives the dire of the electric field at that point let's imagine okay [Music] imag electric field lines of electric field it's tent the tangent to an electric field line at any point gives the direction of the electric field at that particular two electric field L can never intersect each other but it's not possible if they do so then at point of intersection in the point there will be two tangent it means there are two values of the electric field at that point which is not possible which is not possible reason so for the electric field being a vector quantity there can only one result only one resultant field at that given point representing represented one tangent at a given point for the given line of force so direction is yeah again the same uh case electric field lines for of closed crowded where is electric field lines stronger and Lin spread out where the electric field is weak inversely proportional to r² electric field and force are perpendicular to surface of positive negatively Char body sh IM curve you know the particular which big one right the particular it's perpendicular electric field and force are perpendicular to the surface of a positive or negatively charged body right of course is contct L to represent the attraction between the unlik charges electric field exerts lateral sideways pressure to represent repulsion between the two like charges sideways moves sideways repulsion attraction right so that's what that point says in the point side waves unlike charges sorry like charges Ripple right contracts if it is unequal unlike charges so electric field and force do not pass through a conductor hence the interior conductor is free from the influence of the elect will discuss about this that is taken as electric to negative electric to negative electric fi point so interior conductor is free from the influence of the external electric field electrostatic shielding we discuss that in detail right so electric field line force can pass through an insulator also ins internal electric field will not be equal to external electric field so concept we will discuss in detail yeah we came to another topic which is electric dipole so electric dipole so electric di right so electric electric di two equal and opposite charges with same magnitude so positive and opposite plusus 100us 100 so different which mean Direction which is positive and negative opposite charges on the same magnitude right and also separated by a distance can be magnitude equal magnitude same value right OPP theid so distance should be same from midpoint electric M right Direction negative charge to positive charge right so directions of dipole we represent by a simple equation P which is equal to 2 A Q so 2 a the distance between the charge and any one charge and it is magnitude charge it can be either positive or can be negative vector quantity it has Direction so an ideal dipole is the dipole in which the charge becomes larger and larger and separations become smaller and smaller so electri field Direction sorry dipole moment Direction negative to positive so q and Q electric field certain point right so let's say in the point I have taken this point okay in the point p in the point electric field is nothing but force acting per unit charge or you can also say k Q by r² electric field it is a vector quantity we have a point p negative charge positive charge electric field for positive charge K * Q positive charge is nothing but R minus a right negative charge equal K * q r plus a minus negative charge so Square distance distance r² whole squ plus it's a minus r a s can r² + a² + 2 R plus upon r² - a² the whole s so already you have K upon 2 becom your so by R CU so this will be your final result for axial concept so axi will give both will discuss in detail bisecting point q and the minus Q same magnitude opposite direction separated by equal distance and which is very small and dipole moment Direction toid distance it can be anything anywhere but mid in the posi it's a point it's a positive charge right and also yeah we'll take this point char [Music] the positive it's a point which is a positive charge positive Point p in the charga both are separated by same it's same [Music] [Music] but BC point electri field what K * Q upon r² right which ISP the right angle Triangle hypoten Square which is opposite Square adjacent Square hypotenuse Square which is equal to opposite plus adjacent so opposite plus adjacent so let let's say that this is hypoten opposite plus adjacent Square opposite plus adjacent Square hyp sorry hpy s r² 1 by2 hypotenuse right [Music] sare distance it's already square square hypotenuse Square hypoten [Music] hqu plus r² is negative charge k q r² k q a² + Ral just add a s common plus r s common Ro R sorry a square R Square the^ 1 by 2 upon a² r² to the^ 1 by 2 same a 2 a 2 a k q a² + r² cos Theta k q a s + r² cos Theta two * of right 2 q a which is p dipole moment r² 1 3 very large when compared to dist negative charge positive charge direction of electric field sorry dipole moment Direction negative to positive so this is so if the observation is far away or when a dipole is very short then the electric field intensity of the point on the ax is doubled doubl the electric field intensity of the Equator two times of Equatorial electric field inity two we have t Electric dipole in a uniform electric field dipole right same magnitude opposite direction when you add the total charge electric dipole that becomes zero total charge of theole total charge of the dipole is zero right distance to equal opposite magnitude equal opposite charges El unifor electric on electric in unifor electric field let's imag [Music] okay we'll go with this so positive and negative side the posii are two different forces rotate [Music] rotation F Q upon e k q1 Q2 by r² r Q by r² q q q zero is the Mido theid Force so that is your Force total distance 2 2 A A Q E A Q E which is 2 a Q 2 q p in the E which is but t m in the direction in the direction dipole moment positive to sorry negative to positive electric field electric field concep One Direction of the torque is perpendicular and into the plane containing P SI unit of tar is Newton meter Newton meter T unit 0° then Z 0° t z yeah sin 0° is 0 sin 90° is 1 which is Max electric sorry max value 180 elect number electric field lines in a given area particular are electric L electri electric flux linked with any surface is defined as total number of electric field line of force that normally pass through it or through that surface which is given by EDS cos Theta which is e DS cos Theta cos Theta e do DS VOR when it is 0 de that is your maximum value when it is 90° that is your minimum value imagine right imagine EX fore Vector for this planee surf white color white color blue color white color yellow color yellow color which is dirty water [Music] minimum which is zero which is zero so electric flux is a scalar quantity because dot product of two in a straight linee dot product dot product of two Vector is a scal quantity right so it's a scalar quantity but it is a property of vector field newon squ per sare ra special cases the 0 to 90° positive 90° Z 90 less than Z and then less than 180 it ISC three dimensional equivalent of an ordinary two dimensional plain angle three dimensional object spere of radius it appears like a cone is a steradian electric flux the COS Theta and then r² right which is the distance between them stadi next we have a continuous charge distribution so continuous charge distribution 2. 3.2 4 1 continu distribution by nature is surface charge density so straight right upon upon L which is equal to Q upon l or you can also say Q Lambda time L for a straight wi for a straight wire surface surface row right row which is equal to charge upon volume v so volume v surface area and then linear charge density length it's a length length straight wire linear charge density length charge upon length surface area charge volum you can also represent Q is nothing but um the sigma time [Music] Dimension right so next one we came to another important concept which is your gasla so gasla so yeah let's discuss about this the surface the when they ask surface uh the surface integral of the electric field intensity over any closed hypothetical surface are called goian surface in a free space is equal to in the ter 1 by 1 by Epsilon * the net charge enclosed within the surface 1 by Epsilon * charge enclosed it's an integral right so charge enclosed upon epon gas so electric flux which is equal to charge enclosed by is nothing but right EDS so which can which can also be represented as EDS cos Theta in terms of magnitude when it is only closed loop draw an imaginary thing and then we assume closed surface closed Lo El q r s the electric field D is total surface is nothing but spere so 4 Pi r² K 1 by 4on r r the 4 in the 4 in the r s in the r sare which is nothing but Q upon Epsilon ened you can also say your flux is nothing but Q upon Epsilon which is gasa right so simple uh practice that becomes very easy right will understand so proof of through closed for and which is nothing but cos Theta rights cos thet because vect electric field which is 1 by 4 pepon q by r² and then surface 4 r² right so which is the closed one so 4 R squ 4 Square get cancel each other so final equation also becomes Q enclosed by Epsilon I repeat this is your electric so deduction ofum law from GS one of the most repe Q enclosed upon Epsilon equation right so obviously Kum says F which is equal to K * q1 Q2 upon r² cos Theta EDS cos Theta which isal Q enclosed byon we know it is force upon charge right Force upon charge e e we can also represent that as 1 by 4 Pi Epsilon Q upon r² is nothing but area right so area is nothing but 4 Pi r² which is equal to Q enclosed by Epsilon Q enclosed by Epsilon so simp electric field electric field which is equal to in the 4 r² [Music] which Q enclosed Epsilon R so Q enclosed Epsilon 4 p r² 4 r squ r so ter electric field which is nothing but Force upon charge Force upon charge Force Q * of e upon F which is equal to Q * of e which is K q1 Q2 by r² so beautiful relation force and then straight charged positively charged straight positively charged straight should Beed Loop VOR it's curved surface vector area Vector blue yell charged can to understand very easily here is a curv surface surface of the cinder is nothing but 2 R L surface area of the cylinder is 2 r l flux is not there your gas says electric flux which is equal to Q enclosed by ight Lambda L Lambda time L charge I'm represent that is Lambda L by epon in the fls E DS DS The Sur the remaining term e which is equal to equal to Lambda upon 2 p r epon will be your final answer straight lamb 2 they will give full Mark for sure of the electric field intensity rad outward from the positive charge and negative charge radially Inver not that the electric field intensity independent on the size of the Gan surface so independent on the size Loop the electric field intensity of the independent on the size of the goian surface surface size dimension doesn't matter constructed it depends only on the distance of the point of the consideration Right Size Doesn't Matter that is the goian surface should contain the point of consideration [Music] I don't care applications it's a sheet right so electric field intensity due to infinite long sheet positively charged one which is the closed able to use dimensional I want to make it closed one electri blue vector diens imag which it is a surface it is a Surface so is Q upon Epsilon not so we have two different surface surface Ang surface Ed is ang Theta obviously 0° 0 I can say that is 2 E A which is equal to it's a surface up Sigma a upon electric field for a single sheet Sigma upon 2 Epsilon single sheet will understand what I'm trying to say here the of the electric field is normal to the plane and away from the positive charge distributions the negative charge distributions it will be towards the plane the electric field intensity is independent on the size of the Gan surface the same point which is repeated again um it it neither depends on the distance of the point consideration or the radius of the cylindrical surface if the plane sheet is a thick plane sheet is thick then the charge distributions will be available on both sides both side so the charge enclosed within the Gan surface will be twice as before therefore the field will be twice twice right twice if it is like a double sheet sheet how the condition changes so we will try to imagine three different points so so what happens obviously always imagine that it is a positive charge if it is a positive charge it's a point charge right a positive plate and it is also a positive plate if I try to draw the electric field at three different points so positive char charges are same right if both the charges are same Sig by 2ep Sig by 2 epon Sig 2on Sig 2ep um which is exactly similar to capacitor capacitor we have two different plates and one the positive charges the negative charges we have understood right and that's what the concept says yeah and then it's a shell due to a shell um yeah one more thing so in the if it is a two sheets you will be having two different electri so obviously sing 2 epon which is Sig by 2 epon in the sheet electric field Sigma by 2 Epsilon and when we try to that becomes your Sigma by Epsilon alone Sig by epon alone [Music] 2 Sigma by 2 Epsilon plus Sigma by 2 Epsilon that becomes 2 Sigma by 2 Epsilon 2 two get cancel each other and you will have Sigma by Epsilon that's the equation says also Sigma by Epsilon two differentes which plus Sigma by 2 epon both are same denominator 2ep so when you try to add that becomes 2 Sigma by two Epsilon two two will get cancel each other and then you will have Sigma by Epsilon alone that's what I'm trying to conclude here please make a note coming to this point at a point outside the shell so electric field uniformly charged thin spherical Shell at a point outside the shell is such as the whole charge where concent at the center of the it's a simple thing um so you have a surface um it's it's like a sphere and a charge two different three different in the sphere outside in the SPH outside what says Q enclosed by Epsilon and this is nothing but eeds cos Theta which is equal to Q enclosed by Epsilon and obviously the angle between them which is zero and then Ed is so electric flux on that particular surface of the charge which IM Lo r² which is equal to Q enclosed by Epsilon which is e which is equal to Q enclosed 4 Pi r² all you can also write like this or in the charge the yellow color it is a Surface Sigma 4 Pi Capital r² upon in the Epsilon 4 r² small R the 4 4 you can also WR Sigma Capital r² Epsilon not small R squ you repeat again you will you will understand what I I have concluded here I want to the is nothing but again area 4 p r Capital Square R square 4 Pi 4 Pi cancel R square and small squ so this this is your final result suppose the surface surface the capital the small same how you can write e which isal Sig epon second chapter properties of conductors fourth point you will understand this Sigma by ep which is closed sphere electric field Sig epon on the surface yeah just have written right so e which is equal to Sigma epon Z over thank you so much I hope we can improv our lecture also and at the same time you help this with a smile