WEEK 18 PHYS 31 CE 1ST YEAR

0:04 [Music] hey good afternoon class so i will be having my pre-recorded lesson um about columns low so columns low class is uh one of the law that was uh formulated in relation to the to electrostatics okay so this was uh developed by columns okay so the column law relates the force between two single charges separated by a distance okay so the previous topic not

0:51 in class for electrostatics and fundamental concept is if you have like charges there will be repulsive or repulsion okay and then if you have unlike charges so there is an attraction okay so the attractive forces there or the repulsive forces will be computed uh by applying columns low okay so we have here the formula for columns law so this is the um force which is equal to the constant

1:37 times first charge so it means that the charge of the first object times the charge of the second object divided by the square of their distance okay so again uh the formula of column slow is f or force is equal to the constant which is equal to 9 times 10 raised to 9 unit is newton meters squared per column square so q1 is the charge of the first object and then q2 is the charge of the second object okay divided by the distance between the two objects or the between the two charges okay now

2:23 uh unit for [Music] charge class is columns okay and then a unit pattern for distance is meters so um if we're going to compute for the force and tendency and cell native new meters squared as well as column squared okay so the remaining unit now for force is newton okay so this is the illustration class so we have here two charges so q1 [Music] and then uh q2 okay so there is an attraction if you have noticed class the arrow are facing with each other so if the arrow are facing with each other so it means

3:10 that there is an attraction uh between the charges so it follows that they have uh charges okay now if the arrow are in opposite direction so it means that the charges will repel or the object will repel i see they have the same charges and then the distance between the charges is what we call our a so formula okay so column slow gives the electric force between two point charges so again this is the formula so young k not n denotes columns constant which is nine point

3:57 nine and nine times ten raised to 9 and newton meters squared per column squared so q sub 1 is charged on mass 1 and then fuse of 2 is charged on mass 2. so this is being referred to the thermos is being referred to um the object or the choice itself so your r is the distance between two charges so we are going to prove glass that the electric force is much stronger than the gravitational force so the gravitational force was developed or formulated by newtons okay so we're going to compare if uh the electric uh force is uh really stronger than the gravitational force so

4:43 we're going to check that later okay so dito we have an illustration so the force between two charges gets stronger as the charges move closer together so the closer the charger the charges and the stronger the force between them okay so the force also gets stronger if the amount of charge becomes larger so if the amount of charge um is getting bigger so it follows that the electric force is also stronger or higher so directly proportional your force and distance directly proportional i see the force between two charges

5:32 inversely proportional rather i see the force between two charges get stronger as the charger move closer or as the charges move closer together so if the charges are moving closer it means that the distance is decreasing but the force between the two gets stronger so inversely proportional so again the force is inversely proportional to the distance between the charges i see the closer the closer the charger the charges the higher or the stronger the force so inversely proportional now the force

6:17 also gets stronger if the amount of charge becomes larger so the force not end is directly proportional to the amount of charges so the higher the charges the stronger the force between them [Music] and then another one so the force between two charges is directed along the line connecting their centers okay so it means again considering uh center young line at their centers okay a cd bomb pakistan atom made of of protons and electrons so

7:05 pico considered a center part of the protons and the neutrons so electric forces always occur in pairs according to newton's third law like all forces so they are in pairs always okay so either in agripoles either in metal repulsion or attraction they come in ears okay so if there is an attraction as mentioned canina you object are you in charges nothing are getting closer aggregation they are in opposite direction okay so it means that they are getting far and far from each other because they have the same charges are signed

7:50 so additional concept so the force between charges is directly proportional to the magnitude or amount of each chart so the force between charges is directly proportional to the magnitude or the amount of each charge so the higher the force the higher the magnitude or the higher the magnitude the higher the force so doubling one charge double the force so if you're going to double positive charge the force will double if you are going to double negative charge still the force will double but if you're going to double both charges uh quadruples the four the force so double positive actually negative charges

8:35 nothing four times force okay so i say directly proportionally on force nothing and charges or the magnitude of charge so you know once you double one charge so it doubles the force doubling both charges so w positive w negative force okay additional concept for columns law so the force between charges is inversely proportional to the square of the distance between them okay so as you mentioned by the closer the charges of course the

9:22 smaller the distance peron effect inversely proportional so doubling the distance reduces the force by a factor of two squared or equal to for doubling the distance reduces the force distance it means that you have now a longer distance between the charges so your force of attraction done is decreasing so doubling the distance the effect of the

10:09 force is magicking 140 okay this relationship is called an inverse square law because force and distance follow an inverse square relationship so take note of that so the relationship between the distance and the force um is inverse square law okay because it follows or it is an application of an inverse square relationship so you double the distance the effect of the force is it reduces to 1 4. okay calculating force so two balls are each given a static

10:56 electric charge one ten thousand or point zero zero one of a column okay so in charges nila i point zero zero one so calculate the force between the charges when they are separated by one tenth of a meter or equivalent to 0.1 of a meter so compare the force with the weight of an average 70 kilogram person so your formula number four is nothing class is k times uh charges first charge and second charge divided by the distance so you know 10 is equal to 9 times 10 raised to 9 newton meters squared per

11:42 second per um column squared times q1 charge which is 0.001 c so q2 charge is also point zero zero one column divided by the distance the point one meter uh raised to two so i could compute nothing in class so calculator young times ten raised to 9 and that's a lower part okay so double checking allah's calculator in you so 9 times 10 in enter your time standards at bottom part of the calculator and then exponent nothing is nine that was times point zero zero

12:30 one times point zero zero zero one is equal to okay square of 0.1 so 0.1 raise to 2 or direct square so answering atom is 9000 newton okay 9000 newton okay next is i we're going to compare daw indicate it compare the force with the weight of an average 70 kilogram person so when you say a weight that is equal not equal to the exact or the actual mass okay so

13:16 mass of a person is 70 kilograms so in order to solve for the weight which is a downward force if you multiply the matter you must add acceleration due to gravity so we have here uh weight or the downward force is equal to mg so 70 kilograms that is 9.8 so 70 times 9.8 then we have 686 kilograms meter per second squared or newton let's see one one kilogram meter per second square is also equivalent to one okay so the force between the charges is 13 times of an average uh person so check nothing so nine thousand divided by 686

14:05 okay so the force between the charges is certain times the weight of an average person okay okay so again we have two charges are separated by a distance r and then of course f on each other so q one nothing is f q two is f so if r is doubled it picks up um one fourth of the original force nala okay so but if q1 is double then uh your foreign becomes twice of the original

14:51 now if q1 and q2 are doubled then r is half [Music] times force okay

15:37 so here we have another example so 240 grams so the same masses each with a charge of three micro columns are placed 50 centimeters apart so you knew atom symbol this is mu or that is the symbol for the unit micro so paksinami micro column that is 1 times 10 raised to negative 6 of a column micro so you column is equivalent to one times micro column not an equivalent opinion is uh one times ten raised to negative six column okay

16:23 so dito you are go we are going to compare the gravitational force between the two masses so the electric force between the two masses so class maritime the long are also equal which is equal to three micro columns so the distance between them is 50 centimeters apart so if force is stronger than the gravitational force so we're going to prove glass by computing uh the gravitational as well as the electric force okay now for the gravitational force this is the formula so fg or the gravitational force is

17:10 equal to g which is constant 6.67 times 10 raised to negative 11. so mass one mass of the first object m2 mass of the second object so diva para hola mas milan of 40 grams so uh kilograms so 40 divide one then we have point zero four divide one thousand and unit casinos we are going to convert the mass into kilograms 40 kilograms divided by 40 grams divided by 1000 is equal to 0.04 kilograms okay since

17:57 value so 0.04 to 0.5 let's see 100 centimeters is equal to so you're recalling your conversion nino so one one meter is equal to 100 centimeters so if you have

18:48 [Music] [Music] so if you have 50 centimeters so times 100 long times the factor calling [Music] we have 100 centimeters so then we have now 0.5 meters okay so use a kilogram

19:34 we have 40 grams so times the factor so factoring atom is one kilogram it's equal to one thousand grams so that is why don't point for kilogram okay and then take note of this so per unit of force we have a newton is equal to kilogram meter

20:31 [Music] okay so let's go back here regardless exponent so 6.67 times 0.04 times 0.04 equals opposite divide nothing's squared on point five so square root of point five is point twenty five i'm answering nothing is point zero four two six eight eight okay and then times times ten the same exponential again nothing negative eleven direct calculator so your answer is

21:16 4.27 right times 10 raised to negative 13 okay so 6.67 times point zero four times point zero four equals the reclamatized calculator divide square now point five is .25 so 4.268 times 10 raised to negative 13 or

22:03 point 27. dominant decimals but three places so 4.27 times n raised negative 13 newton okay so this is the gravitational force between the two objects weighing uh 40 grams okay now for the electric field for instance of course we are going to use the charges so you charge us nothing i micro coconino times 1 times 10 raised to negative 6 columns 3 not 10 given since micro colombian times ten raised to six longer than okay so q sub one at n is three times n raised to six q sub two three times ten raised

22:48 to six sodium multiplied in so nine times exponent the positive nine times three non-exponential exponent is negative 6 divided by so the same long point 25 so the answer is three two four newton so in the initial round of class case around those two places

23:49 so no gravitational force between the two objects compared on selected force so the electric force between the two objects class is three to four so we have proven that the electric force is much greater than the gravitational force that is at all times for any object okay object mass malagas electric foreign

24:40 [Music] [Applause] i [Music]

25:26 [Music] so nine times three years basis multiply nothing and then your exponents exponents [Music] so nine times three times three and then your exponents union first exponent pattern is nine

26:13 plus a negative sharp a minus or not n that was minus another six so i'm a digging result this is for the numerator and nine times three times three is eighty one eighty one apples times anomaly exponent pattern so nine minus six so negative twelve negative twelve plus nine so negative twelve plus nine is negative three [Music]

27:21 [Music] so divide like nothing by 25 so if you divide nothing by 10.25 yarn now give me answer 81 times 10 raised to negative 3

28:46 [Music] minus six so nine minus six minus six is negative three nine times three times three of course is at the numerator divided by 0.25 still the answer is 0.324 okay times 10 raised to x jones calculator okay let's say most of the problems class are expressed with uh exponent values okay so we have another example here so two charge particles as shown in

29:32 figure below a qp which is being referred to the charge at point p 10 micro column and qq so this is the charge for point q is equal to positive 20 uh micro column are separated so unseparated guess diet cell and separate it's because they have the same charges so on tendency are separated by a distance r which is 10 centimeters 12 centimeters rather we're going to change so what is the magnitude of the

30:18 electrostatic force classion given that is uh 12 centimeters okay so i'm given a 10 the charge of point p is positive micro column or 10 times 10 raise to negative 6 column and then of course a 0.2 so 20 times 10 raise to negative 6 column of course some k nathan is 9 times 10 raise to 9 newton meter per column square indeed

31:12 [Music] i am from the denominator to the numerator you have to change the sign or decay a numerator to denominator once you change current design okay so r nathan is 12 so to continue and formula nothing of course i a k q p plus q q times q q over r square so nine times ten and then we have positive ten times ten

32:00 raised to negative six so positive twenty times ten negative six divided by um is equivalent to so 12 over to l place to two magicking point zero one four four this is exponential but

33:21 so this is 10. in denominator 10 raise to 6 10 raised to 6 and then this one is 20. positive sign understood the manitoba so this is six and then i'm denominator in attendance is point twelve so point twelve raised to two and this is now equal to

34:17 so 9 9 times 10 raised to 9 times 10 times 10 raised to negative 6 times 20 times 10 based on the negative six only is equal to 1.8 divided by 12 times 2 12 times 12. divided

35:11 is [Music] so the magnitude of the electrostatic force between point p and point u is 120 newtons okay some technique also sold so 9 times 10 times 20 [Music] and then

35:56 for the exponent but if ever in uh 20. three school nine nine minus six minus six

36:45 9 times 10 times 20 is 1 8 plus 9 times 10 raised to 3 times exponential 11 so times 10 raised to negative 3.

37:34 0 1 4 4. so 1 8 0 0 times 10 raised to negative 3 divided by point zero one four four then you have 125 newtons okay on the scientific notation so if ever

38:25 zero one four four still the answer is 125. so 1.8 divided by 0.0144 [Music] then you have this one at the young magikin solution

39:27 minus six that is now negative three that was a divide muchas a square of twelve so one twenty five or so punta lagang exponents [Music] one point eight over point zero one four four then still your answer okay so next so another example so we have here one charge of two

40:14 column is 1.5 meters away from uh the second charge which is negative three column so determine the force they exert on each other and then negative question determine the force they insert on each other the same tendency if they have different um different charges or different sign they will attract with each other okay so in distance and then of course the constant latin

41:02 so times q1 which is two columns times negative three columns so two times three is negative six canceling nothing new columns and columns a square meter square meter so one point five square is two two five two point twenty five so it will remain in values so divided by 2.25

41:48 plus times 10 raised to 9 so 9 times 6 25 [Music] so negative times positive of course you have now negative okay so negative um they are [Music] the two charges will attract with each

42:36 other it's because they have different or unlike charges okay so you know if so we're done with two uh problems having two charges so how about now if we have three charges so dipo class might complicate major complicated conte with regards to science and direction so keeping manhattan classical again direction so

43:27 [Music] so we are going to use the positive sign and of course the direction is going to be okay so c and b our result nothing is negative we are going to um reverse the direction

44:16 negative result negative your result is the following three charges are arranged as shown so determine the net force acting on the charge on the right okay so on the right we are referring it to q sub c or charge um

45:03 charge three okay let's see if they can consider nothing i charge one two and then three okay so that we have to determine the net force acting on the charge on the right so he picks a b and c a will up to c and then b will also up to c so i have no direction okay so first they go consider nothing of course ion charges or electric force between point a to point c okay that is why we have here a force ac or electric force from a to c so using the formula nine point nine this is the constant

45:50 and then q a not n is one point five times then there is a negative seven column and then q c not n is negative 3.5 times 10 raised to negative 4c okay all over so on distance from a to c i 3.1 3.1 a to b not and we are talking about point a and point c so the total distance from a to c is equal to 1.4 plus 1.7 or 3.1 meters okay next is

46:40 and then remind us on an exponent so 9 times 1.5 times negative 3.5 then this is equal to negative 47.24 9 times 1.5 times 3.5 so 47.25 times positive 9 negative 7 negative 4 so minus seven minus four then we have negative two so you exponent nothing's a product not n times ten raised to negative two square of three point one so three point one square is 9.61 so class i cancel

47:26 narrating my units on meters squared columns and columns cancel and the remaining units is remaining unit is newton okay so i simplify further so i'm giving you 47.24 times 10 raised to negative 2 divided by then the answer is point zero forty nine one five or a round of nine point zero nine okay now the bang answer class data is negative okay the correct answer here is negative negative negative you answered some direction

48:13 is a acting on c or a acting towards c so on direction is a arrow going to the left so it mixes um [Music] electric charge known f ac okay direction a to c a to c not n is right going to the right negative your result no computation nothing so if you change that in your direction okay based on the third law of newtons

49:00 uh in every action there is always an opposite reaction okay so a acting on c is going to the right since the result is negative the direction of this electric force now is going to the left okay so check nathaniel b to c okay we're going to consider now the um forces between b acting on c or a to c a c r sorry b c so b acting on c so the same london formula so you check nothing again

49:49 3.5 times 10 raised to negative 4 so distance from b to c is 1.7 so a young dynamite not an eye one point seven so i checked nothing on nine times two point three times three point five is 72.45 so negative and negative becomes positive okay so positive so simplifying along method excuse me so simplifying it further

50:36 72.45 negative 2 divided by 2.89 the answer is positive 25.069 or 0.25 newtons so the amount direction is from b to c is going to the right since the answer is positive we are not going to change the sign so in direction of no force bc not n is going to the right okay now we are going to solve the net force between um the three points so we're going to add f c f a c and f b c okay one forces but of course we have to

51:22 indicate the direction for us to determine the correct answer okay so dito di on point 25 nothing is positive going to since they are in opposite direction it means that we're going to subtract the numbers is always negative okay so um i'm answering a 2.01

52:09 copy the sign of the higher value so a higher value nothing is 0.25 where in the direction is to the right and final answer nothing i point two zero one newton to the right so this is the final answer or the net force uh the total net force acting uh on the charge on the right side are acting on c [Music]

53:10 ah so foreign

54:05 uh um [Music]

54:51 oh [Music] [Music] my god

55:51 okay so dress down for a while so we're done with this we'll proceed to the next example so still it has three charges so three charged particles are arranged in a line as shown in the figure below charge a so it has negative five times ten raised to negative six columns you'll be in a month ten times ten raised to negative six columns and then you'll see it's negative times then raised to negative six columns and then you know then of course is 9 times 10 raised to 9 newton meters squared c negative squared or if you want over

56:38 c squared so your answer not n is so first is a b okay calculate the net electrostatic force on particle b so i'm adding parallel reference point or you can't get point at an is point so from a to b direction at an is to the right and c to b direction nothing is to the left check nothing so for a b uh negative five times ten so i'm a gigging result not in class is negative so negative 125 okay

57:24 the bound direction is next is for b and c so from c to b because you're acting towards b okay so 10 times 10 is negative 6 negative 12 times 10 raised to negative 6 so your magicking result need to question 9 times 10 times negative 12 is negative okay divided by the distance so answer is negative 675.

58:14 so from c to b because we are our charges are acting on particle b so you see to be in a direction since negative sha change nothing new direction on c75 okay 125 direction is left sodium left that is negative and then in 675 direction right

59:03 i know it's minus and then the answer is 550 newton but we are going to follow the sign of the higher value direction is to the right so the net force between uh these three charges where in they are both acting on point b um is equal to 550 newtons and the direction is to the right so if ever six centimeters

59:56 plus down [Music] check nothing so nine times five times ten is equal to four hundred fifty four hundred fifty uh raised to negative two negative two divided by

1:00:43 point zero six square is equal to [Music] nine times five times ten [Music] forty divided by 0.06 [Music] and then the exponent pattern is negative two so 125

1:01:32 point zero six lambda plus i indication erasing [Music] so so i double check nothing and 9 times 10 times 12 so 1080 exponent is negative 2 tables divided by

1:02:17 0.04 square six point zero four and it's point zero four so 9 times 10 times 12 divided by times negative raised to negative divided by 0.0016 [Music] checking the limit

1:03:29 in [Music] so

1:04:29 queen 036 oh [Laughter] again it should be 0.06 squared that was 0.04 squared so mobile in zero okay and then since we're done with the

1:05:16 charges in a straight line how about now if we have non-cooling non-collinear charges we can consider this as uh collinear charges okay let's say they are acting in one line so no they are acting on different lines okay or they are considered as non-collinear charges so if we have non-collinear charges and then we can form a right triangle uh we are going to apply pythagorean theorem okay so to recall pythagorean theorem states that the square of the hypotenuse is equal to this to the sum of the squares of the

1:06:04 two sides okay so in mathematics or in mathematical equation that is now equal to hypotenuse or c squared is equal to a squared plus b squared so it is statement now categorian theorem that this um the square of the longest side which is the hypotenuse is equal to the sum of the squares of the two sides okay so we have here a right triangle okay and then we can consider this as our a to say a for altitude or height and then this is our b for the base and then of course the longest side is c or the hypotenuse

1:06:50 and then okay which is angle now if you are going to solve for the missing side or the hypotenuse or younger sultan charges [Music] okay and then extract is equal to [Music]

1:07:39 happy so if ever you are going to find for a are you missing side mo let's [Music] [Music] squared minus a squared okay now if ever

1:08:25 you are asked to find for the angle if you are asked to find for the angle you are going to use this formula although you can also use sine cosine so in this figure your opposite side not endito is a considered as adjacent because young longest side is always the hypotenuse of a right

1:09:12 triangle so again you side a dito is the opposite side of angel then we can also use other letters so to solve for angle theta using tangent function so it is opposite divided by the adjacent side so stands for tangent opposite side divided by adjacent side so in this figure um opposite side not n is side a and then the adjacent side is

1:09:57 [Music] foreign shapes shapes

1:10:50 yeah so still this is our a so if uh ingleta and and then of course so if you have this uh angelna or if you're this triangle where in english is on the upper part your opposite monadito is

1:11:44 opposite side of the angle here is b and then an adjacent side is a okay [Music] hmm [Music] [Music] again [Music]

1:12:34 and then we nail adjacent sides this is based on the second so based on the second triangle we're in ingol theta is on top uh

1:13:22 [Music] is always on the starting point okay so always on the starting point [Music]

1:14:08 in order to solve for the angle is always opposite side over adjacent side so it's not always a over b so it can be b over a if you have this figure so you can add the second figure so i'm going to discuss now the next example so three charges are arranged in a right angle so now indicate that in a range in a right angle so miranda i didn't write okay so as the following diagram shows so determine the force on q2 so acting on q2 so on starting point at and of course on q1 is from the top

1:14:56 then you have your q two that was q two uh to the right naman then we have q three so you know that's the right side nothing is q three so marana time corresponding values so i'm charged one atom is two columns charge two is one and then charge three is four and the new distance from q1 to q2 is three meters um distance from q [Music]

1:15:45 okay so since we have now arrived in gal we can apply pythagorean urine tapos tangent in order to find the angle but of course before we can solve for that charges between q1 and q2 that was three and two um the forces now are on uh q2 so f1 2 so force from one to two uh your first one nothing is two columns you force kuna negative six because the given unit

1:16:32 there is micro column okay so compute so nine times two times one is eighteen divided by the square of three so square of three is nine okay i'm a gigan result from the figure we have q two is ones one taposium q three is four distance is four meters so you have now uh constant and nine times ten raised to nine and then q201 column q3 of four columns divided

1:17:20 by the square of four which is sixteen so if i go compute nothing and we have now nine times one times four is thirty six so 36 divided by 16 is two point and put it in what nine times four divided by sixteen so 2.25 or the round of nothing so 2.25 so 2 squared plus 2.25 squared then you have 9.06 square root mode so approximately

1:18:08 3.01 so point zero one or approximately nothing and that is now equal to three [Music] times ten raised to nine so this is the final answer okay so since we have now values for uh the total force we are going now to find the angel

1:18:55 okay so balik is a figure this is the angel starting point starting point in [Music] considered nothing as adjacent side and then your result patterns are q2 and q3 equal consider that and as um [Music] opposite side so the best computation at n between f1 and 2 so 2 times 10 raised to 9 so this is our adjacent side in a notebook in this

1:19:41 problem adjacent side problem and then this is the opposite side you uh the total charges nothing from two and is 2.25 times 10 raised to 9 divided by 2. so 2.25 divided by 2 then we have

1:20:30 1 2 five shift pan shift pan 1.125 the answer is 48.48.36 8.36 or so i better not need

1:21:17 so approximately 48 degrees so in this problem we have three different three non-coplanar charges where in it is indicated in a problem that one of the angle is a right angle so therefore we can have a right triangle now if we have a right triangle then we can we can get the the net force or the total force by applying categories urine okay so that is why in our formula we have this one okay in applying that pythagorean theory before that we have to find first the total uh charges between

1:22:04 two points or two charges which are q1 and q2 so for q1 and q2 2 times 10 raised to 9 which is considered as the adjacent side and then for charges q2 and q3 we have 2.25 times 10 raised to 9 okay which is considered the minus the opposite side of the indian

1:22:51 and then to solve for the angle so we're going to use arctan opposite divided by adjacent side so opposite is 2.25 divided by two so we have 1.125 so also reflex calculator is 48.37 palatoplasty 366. um [Music] as a full number okay so we're done with

1:23:39 our problem solving um by applying column slow okay so so if you ever know my concern some next week sample problems examine the next week because okay so

1:24:26 bye class so thank you [Music] like

1:25:12 all right [Music] okay bye everyone get this