okay so based from our previous lectures we have discussed more on the concepts concept part of electric force and electric field so on this video we would be applying those concept in computing the net electric field or rather the net electric force on a point charge exerted by a system of point charges as well as to calculate the electric field due to a system of point charges using coulomb's law and the superposition principle okay so before we start with our um mathematical computation let us recall some formulas okay previews lecture okay so let's start start with coulomb's law okay as we all know the coulomb's law measures the force reaction between charges or between point charges it finds the electric force due to um point charges and mathematically equal to k which is our coulomb's constant multiplied by um the product of two charges divided by the distance squared okay so k which is uh our proportionality constant or coulomb's constant is equals to one over four pi epsilon naught and equal to eight point nine eight eight times ten raised to nine newton meters squared per coulomb squared okay so i'm gonna go to the long negan is nine times ten raised to nine newton meter squared over coulomb squared okay so the uh the unit for force electric force is in terms of neutrons okay the second equation is for finding electric field by a charge object okay so electric field is the imaginary field that um surrounds okay that surrounds a a charge or a point charge so we can calculate the electric field magnitude of a specific charge using our electrical force per unit uh magnitude of test charge okay so the unit for electric field is in terms of neutron per column okay so deriving another equation for electric leaving an equation for electric field which is constant multiplying by the uh magnitude of the point charge over the distance between them okay squared so now uh since we have recalled some formulas that might be useful in finding the unknowns so let us make this into work with this first problem so we have to find the electric force exerted by these two point charges but first and foremost is to assign okay assign point reference okay so why does assigning point reference uh should be the first step in finding the electrical force because each or individual charges do have reaction to um the other charge on q1 in terms of q2 q2 in terms of q1 so um nothing has electric force nana experience over r squared so k is equals to nine times ten raised to nine multiply by two hundred micro coulomb times 100 micro coulomb over the distance between them which is one meter squared okay take note that micro column or micro column is equals to 10 raised to negative six yen so key input is 180 newtons but take note electric force is a vector okay so what would be the direction of the electric force at q1 so pineapple analysis so on point of reference 1961 what is the reaction of q1 the q2 so a new tendency q1 q2 positive according to love electrostatic force like charges repair so then cindy q1 take you to i put the direction that okay 1 to two okay so the electric force at charge one would be towards this direction so how about um electric force at okay at q 2 what if our point reference is at q 2 so same long then 9 times 10 raised to 9 compute magnitude 200 micro coulomb by 100 micro coulomb all over one squared one meter squared okay magnitude 180 newtons but since i'm point of reference not in ion i snatch a point two or nasa point q two any reaction eq to high q one so on tendency i mag okay this is charge number three q3 okay so align silas on horizontal plane okay so hana penaten unit force [Music] okay let's start with finding the okay effect or interaction between q2 and q3 okay so since tendency basically okay basically most probably okay how about okay how about naman q1 okay since unlike charges f3k q1 okay so f3 one so same direction distance i young distance between q1 and q3 which is 2 meters so we have to find the vector sum of [Music] k is 9 times 10 raised to 9 multiplied by 3 is negative 100 micro coulomb multiplied by 2 is 100 micro coulomb all over a one meter squared okay so the answer would be negative 90 newtons why negative okay um f3 a q3 q2 attracts q three okay so now let's move forward with f three one okay same lung then nine times ten raised to 9 multiplied by 100 negative 100 micro coulomb multiplied by 200 micro coulomb all over the distance between them is 2 meters squared so what would be the answer so the answer is negative 45 newton again negative case opposite f31 we can find f net at q 3 by adding f 3 2 and f 3 one okay so negative 90 newtons plus negative 45 newtons is equal to um 100 negative 135 newtons towards this direction so if net at q3 okay so um horizontal plane so next problem yeah okay sorry yes so i'm number four okay so if you want to try this problem you may pause the video and then start answering okay 100 microphones so um for wiz so you una is a q2 okay so secure any action yeah so pendants in eq4 q2i [Music] due to two second is secu3 so um vertical new relationship so i'm positive it will repel me q3 i sorry rather [Music] [Music] relationship so since parevo said i'm positive so on tendency the q4 q1 is a so in order for us to get f net at q4 we need to find um f of um four and two fours at between four and three and four is between four and one so uh between four and two so my kitten nothing forced between four at two is at the x axis okay so positive x axis so nothing values nine times ten raised to nine okay multiply by um 100 micro coulomb times 100 micro coulomb so this is q4 because this is q2 over the distance between them is one meters one meter then squared okay so the answer to this um relationship is f42 is equal to 90 newtons in what direction towards this direction okay next is f for three so see f43 nasa negative okay that's a negative y axis so we need to find the direction of this okay of this vector or this force vector in terms of the horizontal axis or reference with positive x-axis but first let us compute the magnitude of force four due to three okay so f43 using coulomb's law 9 times 10 raised to 9 multiplied by 100 micro coulomb times 100 a micro coulomb all over i'm one meter squared okay um one meter squared so the answer is f43 is 90 newtons but in what direction okay angle reference to x-axis so if you see f43 i 270 degrees okay angle 270 degrees okay f 43 y f x okay so yeah the new next part the man is c f 4 1 so so let's net at q 4 is equals to f 4 2 plus f for three plus f for one so my f4 f4 that was my f4 one unless nothing happened distance between f41 ff q4 and q1 can say nothing quite in the meeting one because a distance you know you won't take your three individually not in predicament so so we have to find the diagonal distance okay so according to pythagorean theorem since the form put ion 90 squared is equals to a squared plus b squared so i'm going to hand up that and it compartment is um the distance from four to one okay so equal push has a square root number a one meter squared plus one meter squared so the distance from four to one is equals to square root of two meters okay so yeah so since better time distance this is square root of 2 meters [Music] um f41 so f 4 1 is equals to nine times ten raised to nine multiplied by 100 micro coulomb times 100 micro coulomb oh a solid over one i sorry square root of two meter squared okay so key in the opinions of you the answer would be f41 45 newtons but take home eating the nut and soda gram that in okay so nathanian f41 would be most likely can be found on quadrant four nasa quadrant okay so since it oh 90 degrees 90 degrees most probably this part would measure 45 degrees at all okay f 4 1. so a new measurement angle reference to positive x axis so we have to subtract 45 from 360 and the answer would be 315 degrees okay so angle no adding f41 angle 315 degrees f41 f43 and f42 so we have to find the vector sum of this forces okay vector sum of forces summation of all forces along x axis at your summation of all forces along y axis [Music] f41 so see f42 based on the calculations not in is equal to 90 newton okay since nasa positive x axis na pusha angle 0 okay so [Music] x axis so we have to get 45 cosine 315 okay so that is equal to um that is equal to 121 okay okay that is equal to 31 point okay 31.82 newtons positive okay so 90 plus 31.82 say 90 plus 31.82 so young summation now forces along x axis is equals to 121.82 newtons okay now let's move on with um summation of all forces along y-axis so same c y-axis f for three y component f41 so see f43 i equals a 90 angle 270 degrees so since sine 270 vola components x axis so what cosine sine 270 is equal to negative 1 so f4 3 is also equals to negative 90 newtons next is um the y component for f41 f41y is equals to 45 sine 315 degrees and this is equal to negative 31.82 newtons so i'm summation of all forces along y-axis i equals um negative 121.82 newton okay now since marina putta x and y components of our force at force um net force using operating net force using fatagorian theorem net force at q4 is equals to f42 plus f43 plus f41 okay so equal push us net at q4 so no inner x and y so summation of all forces along x axis squared plus summation of all forces along y axis squared so square root now 112.82 squared plus um as squared down one point twelve point eighty two squared so equal f net net n q4 is equals two how many newtons 172 okay newtons okay since vector now see um net four so we need to find the negative one f y over f x okay equals negative one absolute value now 112.82 over 112.82 so the answer um tangent negative 1 1 is 45 so uncomputed angle nathan is 45 degrees since um if so supposedly this can be found on quadrant four so you compute nothing angle or direction [Music] 360 parameters angel reference to x axis okay so 360 minus 45 so the answer is angle reference to x axis is equal to 315 degrees okay so f net at q4 is equal to 107 newton angle 315 degrees so now um we know how to compute um electric force by point charges now we uh move forward in computing the electric field or magnitude of electric field due to point charges okay electric force electric field okay so what is is reaction so this would be our e2 okay so my mistake okay so on um direction paula okay and direction sorry the direction of our e field should focus on in terms of the point charge so i know you may experience rather knee point charge the helical test charge so you e19 a new tendency okay an independent sydney q1 tendency luma [Music] [Music] now let's compute the individual okay now let's give compute the net electric field [Music] okay q1 or q charge over r squared okay so substituting among the values 9 times 10 raised to 9. 9 times 10 raised to 9 multiplied by 1 which is 50 nano column all over the distance between them which is 1 meter squared velocity 9 times 10 raised to 9. okay multiply by you don't make question okay no negative e field or electric field since e field is a vector quantity so need the net electric field is the vector sum so we need to okay we need to take into consideration the direction of that individual filled vector so positive button direction so non-direction so we need to add okay 50 nano column [Music] okay nine times 50 is 45 450 newton per coulomb plus 450 newton per coulomb so the answer the net electric field at point p is equals to 900 newton per column okay now let's move on with our second problem for electric field we have to find all also the net electric field at the point p okay find [Music] so q1 um q1 with the types of q1 okay so it's a q1 this one okay q1 okay so since positive negative tendency in eq 1 negative b direction towards our test charge so this is e1 and the distance between q1 and test charge p is 2 meters next is ce2 icq okay so this is e2 okay so let's compute for inet [Music] so in it is equals to e1 plus e2 so same perennial 9 times 10 raised to 9 multiplied by 50 nano coulomb over the distance between q1 and p which is 2 meter squared plus 8 9 times 10 raised to 9 multiplied by 50 nano coulomb so the distance between q 2 and point b is 1 meter and then squared okay so answer d is 100 [Music] newton per column okay so since it is a direction direction so opposition direction in nella so we have to subtract okay we have to subtract the value of e2 from e1 okay so this is equal to 450 newton per coulomb so in it is equal to 300 or negative 337.5 newton per coulomb towards this direction so based from this given conclude regarding e or electric field in r or distance electric field increases a test charge is so electric field and the distance between point charge and test swords are inversely proportional okay so now let's move on with our final problem for electric field so yeah that's the x and y axis now so if you want to try to answer this um problem you may do so just pause this video okay so now let's find in it at b okay so in it at b is equals to e1 plus e okay e the equation to be used is k q over r squared okay so i'm going to pull it that i'm drawing so essentially reaction so this is our e1 next is um our e2 so you itunet and same opposite charges so this is our e2 electric field vector using pythagorean sphere okay so i compute muna natin individually let's start with e1 okay so e1 is equals to the red chocolate 9 times 10 raised to 9 multiplied by 40 and 40 micro coulomb over three okay the distance between them squared so the answer for this is um nine times 40 300 2 600 [Music] so the answer is 40 000 and 40 000 newton per coulomb okay now let's compute e2 so e2 9 times 10 raised to 9 multiplied by the value of e2 is 30 micro coulomb over the distance between them is 2 meter squared okay so the answer is 67 500 [Music] so this is e1 foreign [Music] [Music] okay square root knee e1 squared plus e2 squared okay so square root now 40 000 squared plus sixty seven thousand five hundred about square okay in it is equal to seventy eight thousand four hundred sixty-two newton per cool okay so since um vector pull let's see electric field we have to find the angle reference to x axis using soho times a negative one y over x okay or equals a tangent negative one so young y nathan is e2 okay e2 over e1 so equals a tangent negative one sixty seven thousand five hundred uh zero over forty thousand so the answer is since the answer for our direction is 59.9 degrees so final answer is in it equals 78.462 newton per column angle 59.30 degrees okay so since problems for electric field and electric forces so um if you have any questions or clarifications you may reach out through me and that would be all for this lecture so goodbye and thank you see you on to our next meeting