# Coulomb’s Law (with example)

Articles, Blog 100 Comments

Hi guys! Jade here. This is a video on

Coulomb’s law: the force between two charges. So this video is going to cover where

it comes from, what it’s all about, just some of the intuition behind the

equation as well, and we’re going to end with an example because I totally know

what it’s like to have read all of the theory like you can write an essay on

the theory ,and then you go to answer the very first “easy” question and you’re just

like… So theory is really important but if your exam is like tomorrow and you

just want to get to the example, I put a link so you can skip ahead. Don’t worry i won’t get offended I’ve

totally been there, but if not, let’s get started! So around the time that Coulomb’s law

was discovered the current knowledge of electricity was that people knew there

were two different types of charges, positive and negative. They knew that like charges exert this

repelling force on each other and opposite charges have this attracting

force. They also knew just by experiment that the further the distance between

two charges the weaker the force was between them. So this was a really nice observation

but there was still no real means of measuring the size of the force between

two charges. So this french guy Charles Augustine de

Coulomb came up with a really nice relationship to measure the size of the

force between two charges and it’s based on two of his findings. So the first was that the size of the

electrostatic force was directly proportional to the product of the

magnitude of the charges. In English this just means that the bigger the

magnitude of the two charges the stronger the electrostatic forces

between them. And this kind of makes sense right? I mean let’s take two

charges of pretty small magnitude, the electrictrostatic force between them is

going to be pretty weak compared to two charges of really large magnitude where the force between them will

be strong. Cool! So that was Coulomb’s first finding. His

second finding with that the electrostatic force was inversely

proportional to the square of the distance separating the charges. So again in English this just means that the further apart

to charges got the weaker the force between them, and i know we already said

that right but this was kind of like yes we can

really do a proper measurement. We can get to a more exact number than just

“the force got kind of weaker with distance” it’s like we can actually say

how much we got this is the proper relationship. Ok so now you guys have got a pretty

good understanding of the two main factors which influence the

electrostatic force between two charges. Now let’s try and transform these words

into a mathematical equation. So starting with number one: the size of the

electrostatic force is proportional to the product of the magnitude of the

charges. So don’t panic! The magnitude of the charges is just

like saying the size of the charges so not the physical size maybe strength is

a better word. So let’s say we have a charge that has a

magnitude of three coulombs and a charge with a magnitude of 300 coulombs.

Obviously the charged with three hundred coulombs is going to be stronger or

exert a stronger force anyway, so that’s all the magnitude of

the charge means like the strength of the charge. So magnitude of charge is

usually denoted by the letter q, and because we have two charges we’re going to have 2 q’s. So let’s say

q1 and q2, and the product just means one thing multiplied by another so the product of two

and three is just 2 x 3 which is six, and the products of the magnitude of the

charges is just q1 x q2. So now we’ve just got this

proportionality part which just means we need a proportionality constant. So the

proportionality constant or Coulomb’s constant is often denoted by a K, and Coulomb found it to be a 8.99 x 10^9 Newton meters squared Coulombs to the

negative 2. It’s a weird unit I know but you don’t need to remember that you can look

it up on online or any physics textbook. And the electrostatic force is denoted by F

for force. Easy! So when we translate that be scary

sentence into mathematics we get a pretty simple equation F is equal to K

multiplied by q 1 x q2. Cool! But we’re not finished yet we still

got part two. So Coulomb’s second observation: the

electrostatic force is inversely proportional to the square of the

distance separating the charges. So the distance separating the charges

is usually denoted by an r, the square of the distance is just the distance

squared so we’ll just have r squared. And inversely proportional means that as the

distance r increases the electrostatic force F will decrease. So this means that we need to divide the

equation that we have so far by r squared. If you’re having a hard time grasping this

idea what I usually like to do is just play around with different values of r,

and you will always find that as you increase the value of r, the value of F

will decrease. So yeah that’s Coulomb’s law: F is equal to K

multiplied by q 1 x q2 all over r squared. So now finally it’s time for the example.

This is a really common exam type question I just got out of a textbook

and it is: towo charges of magnitude 1.8 times 10 to the negative 17 coulombs are

separated by a distance of 150 nanometers. What is the size of the electrostatic

force experienced by each charge? So before we start looking at Coulomb’s

law or playing with numbers let’s just draw a diagram and figure out

what’s actually going on. So we have two charges, q1 and q2, and the

question doesn’t exactly tell us whether they’re positive or negative. But if we

look at the magnitude of the charges, 1.8 times 10 to the negative 17 coulombs,

it’s a positive number which means that the charges are positive. If the question

was trying to tell us that the charges were negative it would say – 1.8 times

10 to the negative 17 columns. So we have two positive charges which means they’re

repelling so we have this repelling force between these two charges. So

already just from drawing the diagram we kind of know what’s going on. So what I think it’s a really good idea

when you’re answering a question like this is just to write down everything

that the question is telling you in terms of the variables that you’re going

to need for the equation. So q1 and q2, the magnitude of the charges, is 1.8

times 10 to the negative 17 coulombs. The distance separating the charges r is

equal to a hundred 50 nanometers, and let’s just convert this into SI units

right now so we don’t forget later and get the answer wrong. So the SI unit for distances is meters so a

hundred 50 nanometers converted into meters is just 150 times ten to the minus

nine meters. And we’re looking for the electrostatic force F so we’ll just say

f is equal to ? And if we already knew we were going to use Coulomb’s law right but if we didn’t know just

writing out the information in terms of the variables gives us a pretty strong

hint that yeah we’re probably going to be using

Coulomb’s law because all the variables are kind of the same. The only one that’s

missing is k and because k is a constant we can

just look it up it’s always going to be the same we don’t need it listed in the

question. So yeah so now it’s actually pretty easy all that’s left to do is sub the numbers

into the equation. So we’ll get F the force is equal to K: 8.99 times 10 to

the 9 Newton meters squared Coulombs to the negative 2, multiplied by

q 1, 1 point 8 times 10 to the negative 17 coulombs x q 2 which is again one

point eight times ten to the negative 17 Coulombs. So we’re just going to square it

instead of writing out again because we’re just multiplying a number by the

same number. All over r squared: 150 times ten to the minus 9 meters all squared. So

if you put this into your calculator and hopefully you have your brackets correct, you should get an answer of F, the

electrostatic force, is equal to 1 . 3 times 10 to the negative 10 Newtons, and

that’s the answer! Not so bad right? Hey guys that’s the end

of this tutorial thanks so much for watching I really

hope it helps. If you have any questions or requests let me know in the comments below! I’d

love to you some of the physics topics you guys want to do together. Thanks and see you next time!

Daniel EmenikePost authorI love this!

Daniel EmenikePost authorI love this!

Joao Xavier Vasques PerellóPost authorNothing…I got confused with the letters N and m, anyways…there's no matter, in my class we simplificate the formula to "9×10^9".Thanks for the video btw it was helpful 🙂

mark vPost authorGreat video!

Yoshua LiraPost authorThx ur saving my huge test

TechDroidPost authorare you in Facebook or Instagram? what is your account?

Elvis Fernando Sánchez NápolesPost authorGracias (otra vez) ^_^

WHATS IN THE NAME ?Post authorfell in love with coulomb's law thank u

Vyshnavi PathuriPost authorit was a nice video : ) it helped me a lot tq

weirdoPost authorHi, im a grade 9 students thats just bored and saw this video. So for Coulombs law it says that theres no force of attraction between a neutral and a charged object, but isnt a neutral object attracted to both positively and negatively charged object? (they might not be related but idk lol)

Ravinder KaurPost authorplz I request u to post more videos about guesses theorum😢😖😫and other topics related to it…

I m seriously getting sick of this theorum &need ur help

The AircraftPost authoris that the force of each charge on each other?

William WashingtonPost authorThank you for your video. You will be a good teacher. Keep it up. Actually F = (k x |q1| x |q2| ) / r^2 . The equation is to calculate the magnitude of the force. It's must be the absolute value of the charge. If we don't use the absolute value, the one charge is positive and the other is negative we will have negative force. And it's wrong, we don't have negative magnitude force, but we may have forces in negative direction.

Bilal UnasPost authorwhy we take product of charges instead of sum of charges.

Bilal UnasPost authorwhy we take square of distance.

Noaman SalehPost authorAmi am studing electricity. Please can you make more videos but a little bit simple if possible.

Bilal UnasPost authorPlease ans I'm waiting.

ant enaPost authorWow. Superb!!!!!!!!!!!!!!!!!!!!!

elnubnubPost authori have a question, it might be a dumb question (the possibility exist, huhu), how come electron in a wire create magnetic field? does it mean an electrically charged wire emit photon? since photon is the vector of electromagnetism , i know a tank circuit emit radio wave, which i guess means photon, but i think i'm wrong about this, because i think electricity has nothing to do with electromagnetism, isn't electricy only the flow of an electron from hole to hole , i fell I'm missing something

or is it simpler, like , positively charged means more electron, negatively means less electron and they just try to balance themselves and doing so it would created a field ???

a crazier question, if an antenna emit radio wave, does it mean that with the right amplitude and wavelenght an antenna could potentially emit visible light ?

i never went to college, i might say dumb things

Viral UploaderPost authorTY..

Angelbert RoselPost authorwow youre a really nice teacher. thank you for this video. 😉

Sarah InanPost authorCan someone please explain how to enter in the formula into a calculator she mentions at the end. I do not get the same answer so if someone could please explain thanks

Kennard John BriosoPost authorI found this helpful, and you're beautiful. HAHA

Usam RazaPost authorwill you plz define point charge, source charge and test charge in a simplest way? waiting for answer!

WILIE BAROROPost authorHow did u get 1.3×10^-10???

mico ocaresPost authorK=9×10^9 N m^2/c^2

Steeven MoralesPost authorhonestly bless your soul home girl, glooking out

insani dillPost authori love the way you teach.. i would love to be you'r student. can u give me idea about flux of electric field lines?

LCSWLMSPost authorWho came here from No Game No Life?

Mr SaleemPost authorhttps://youtu.be/LMJS4GAuX2g

I C Y C L E S T I C KPost authorGOOD JOB! 😮😮😮🤣🤣😂

XAVIOUR XsPost authorl like u

tpuryearablePost authorJade, thank you so much for the generosity reflected in this awesome series of videos! In that spirit I would

like to ask you about your platform. Specifically how do you add the graphic layer so that we can see notes and formulas added to the video of you speaking? I would appreciate any and all details; and if you have already explained it, please just give me a link and I will learn. I want to emulate your approach but focus on the topic of Measurement Uncertainty. Thanks for helping to make the Web a better place!

Stephen

GilbertTheGreatPost authorHeres a compliment you have way more enthusiasm than my physics teacher

another compliment your explanations are dazzling

Sandy _Post authorHelp me to pass my exam in science, LOL.

Pray for me :((

Sandy _Post authorI wish you were my teacher in science next SY 🙂

mvolestranglerPost authorall made sense till I realised I have no idea how to type (8.99×10^9Nm^2C^2) into a calculator or what some of those letters actually mean.

John CenaPost authorit realy helped..tnx

Junoon factsPost authorek coulomb charge sambhav hai

Chelsea FCPost authorthanks

tuilika andreasPost authori love your videos so much. I'd appreciate it if you do some more. especially on the van der graaf generator as well as chemistry sections such as moles.

Fatma BashaPost authora just incredible video I liked your cool explanation…

Lucas DunnePost authorI heard a subaru at 8:05

GANESH MALLEPost authorThis video so useful for me thanks for upload😊😊😊😊😊

Dhananjay GroverPost authorBest explanation

Rohan veenuPost authorPlease make more videos

Ganeiz XtriPost authorTq it is so helpful..

Ganeiz XtriPost authorTq it is so helpful..

Rey CarlosPost authorMy exam is literally tomorrow, lol

Aftab SoniPost authorYou explain very well Do you know hindi Let me explain in Hindi.🤗🤗

Sylvester OngoriPost authorI want to explain to my boss how two people in an workplace can have differences using Coulomb's law…he will be like what that's ..n thats exactly my point.

Danish KhanPost authorYour teaching skills are appreciable. ..i want to learn from you..and in which country u belongs…

nitesh KumarPost authoru r reallly a excellent teacher i appreciate u

electro magicPost authorI love your lesson nice don baby😙

Fahim Al-HuqPost authorTHANKS A LOT.

Roberth SantosPost authorSpeak português.

Eu sou do Brasil

thomas saverioPost authorThanx😗best explaination ever❤

Michael SpurlockPost authorExcellent video, Thanks. I have a question that was not addressed in this video but is closely connected to the subject matter. One ampere equals 6.24 x 10^18 electrons (charges) moving past a point in one second; how did scientist determine that numeric value?

Trevor MonroePost authorYou're a wonderful teacher! I'd love to hear you explain Maxwell's Equations, or have you done this already?.

Raj ShekarPost authorYour face expression amazing mam

How did they find light speed with physical example

Please give me answer for this mam

GorgumPost authorwhat thefuck is positive? electrons move and are negative. what the fuck is charge? a coulomb per second. So this is speed. and it is equal to ampere. Load of crap is not it?

Anuj RoyPost authorThank u are Awesome

Andrei ReyesPost authorHi ma'am, according to my physics teacher , writing in scientific notation the valu of the number must be greater than 1 but less than 10 so wht is it your distance has a value of 150? it supposed to be 1.5?

Derlin ClairePost authorVery lovely Aussie girl.Merci beaucoup,ma cher amie Jade,and God bless you.

卡艺抠KaikoPost authorneeded this! thankyou for the great explanation

Maths ki dunyaPost authorWhat is actual meaning of magnitude of charge physically?

uday naikPost authorYour are great

YoRbOi GeLoPost authorHow the fuck did you get 8.99 like WHAT THE HELL

Robert EvansPost authorExams are just a celebration of your knowledge and should never be a source of angst. Focus on learning and the exams take care of themselves.

what nextPost author,必。。一。一。一。。，🚅刀子的是什么时候了解释权归纳总结婚后才能得到满足球员外界定制造商品尝尝鲜明显露珠海军官二代谎称为啥事件频繁打嗝

ThembelihlePost authorHow do I calculate the transferred when they touch each other and when the separate

Jabulile MngomezuluPost authorcan we do the eastern cape question paper 2015 grade11?

Rekha RawatPost authorI enjoyed your video

Hhh HhhPost authorYou are superb 👌👌👌

Hhh HhhPost authorYou are excellent in everything 👌👌👌👌😍😍

Tim Rubin HalcombPost authorWow! You're pretty.

Zahir JafarPost authorSomething is wrong

Puncake FuncakePost authorCan you pls upload a video about deriving Coulomb’s law

Hadiyaa ZahraPost authorThank you.

Gábor KrálikPost authorI know I'm nitpicky but the fraction line should be next to the equal sign.

Souza, Marcos Antonio English with coffeePost authorGood…pretty girl…beautiful lesson…continue

Sil BombardiPost authorMerci a Monsieur Coulomb d'abord et merci à vous.

Steve DoePost author3:12

“Don’t panic”

Words of wisdom. Also written on the back cover of a famous guide.

Tom LaightPost authorGiven that the example question asks for the size (magnitude) of the electrostatic force, am I correct in thinking that the sign of either charge is unimportant? Could have two +ve charges, two -ve charges or one of each and the force's magnitude would stay the same, just the direction would change?

hussain radhwanPost authorwell none, thank you for the excellent explanation.

Brightico AdjeiPost authorthanks for the lectures

Harsh PurohitPost authorYou look pretty ❤️

Abhishek TripathiPost authorForce between charges is medium dependent Right.ie for same magnitude of charge and same seperation force between them in air and water is different

But the que is how charges come to know that they are in different medium

Thakur AaishaPost authorYour way of teaching is really unique…

I got through many videos then finally i got to see your video and finally i m like

,oh i got it!!Roshan TripathiPost authorU are smarter mam

musaed vlogsPost authorعربي

Naf NoorPost authorThank You dear…. This really helped a lot… God Bless You.

elias salasPost authorall these nerds trying to get frisky with a girl from a chemistry video XD

Aarush KumarPost authorI really appreciate u and your work😇

Tips 4 truckersPost authorAnyone else find out about this from homestarrunner

Mridul MaitrePost authorI wish that you should be my physics teacher in high school! All my physics teacher do is sit back and say derive that and do that particular question from book

Teacher Michael MaalimPost authorSplendid video.

4:10 Polite clarification. 😊😊😊Although Coulomb's constant kE is called Coulomb's constant because it is found within Coulomb's law, he is not the one who determined the value 8.9876×10^9 which we use today under the SI Units.

The numerical value of Coulomb's constant depends on the (arbitrary) units of measure you select for force, distance and charge. The value when using the SI Units of newtons [N], metres [m] and coulumbs [C] would be different when using other units.

A clearer name would be 'the Constant in Coulomb's Law' rather than 'Coulomb's Constant'.

David LewisPost authoryou simplify the equations so that everyone can understand them, but people who don't know what magnitude is probably don't know what coulomb's law is. maybe a bit of an oversimplification there?

frank pocasangrePost authorCan you do Gauss's Law?

Physics tutorialsPost authorkindly can you mention the program you use to write this lesson …. i hope you understand sorry for my english