# Coulomb’s Law (with example)

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!

## 100 thoughts on “Coulomb’s Law (with example)”

I love this!

I love this!

• ### Joao Xavier Vasques Perelló Post author

Nothing…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 🙂

Great video!

• ### Yoshua Lira Post author

Thx ur saving my huge test

• ### Elvis Fernando Sánchez Nápoles Post author

Gracias (otra vez) ^_^

• ### WHATS IN THE NAME ? Post author

fell in love with coulomb's law thank u

• ### Vyshnavi Pathuri Post author

it was a nice video : ) it helped me a lot tq

• ### weirdo Post author

Hi, 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 Kaur Post author

plz 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 Aircraft Post author

is that the force of each charge on each other?

• ### William Washington Post author

Thank 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 Unas Post author

why we take product of charges instead of sum of charges.

• ### Bilal Unas Post author

why we take square of distance.

• ### Noaman Saleh Post author

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

• ### ant ena Post author

Wow. Superb!!!!!!!!!!!!!!!!!!!!!

• ### elnubnub Post author

i 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

TY..

• ### Angelbert Rosel Post author

wow youre a really nice teacher. thank you for this video. 😉

• ### Sarah Inan Post author

Can 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 Brioso Post author

I found this helpful, and you're beautiful. HAHA

• ### Usam Raza Post author

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

• ### WILIE BARORO Post author

How did u get 1.3×10^-10???

• ### mico ocares Post author

K=9×10^9 N m^2/c^2

• ### Steeven Morales Post author

honestly bless your soul home girl, glooking out

• ### insani dill Post author

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

• ### LCSWLMS Post author

Who came here from No Game No Life?

• ### Mr Saleem Post author

https://youtu.be/LMJS4GAuX2g

• ### I C Y C L E S T I C K Post author

GOOD JOB! 😮😮😮🤣🤣😂

l like u

• ### tpuryearable Post author

Jade, 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

• ### GilbertTheGreat Post author

Heres a compliment you have way more enthusiasm than my physics teacher
another compliment your explanations are dazzling

• ### Sandy _ Post author

Help me to pass my exam in science, LOL.
Pray for me :((

• ### Sandy _ Post author

I wish you were my teacher in science next SY 🙂

• ### mvolestrangler Post author

all 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 Cena Post author

it realy helped..tnx

• ### Junoon facts Post author

ek coulomb charge sambhav hai

thanks

• ### tuilika andreas Post author

i 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 Basha Post author

a just incredible video I liked your cool explanation…

• ### Lucas Dunne Post author

I heard a subaru at 8:05

• ### GANESH MALLE Post author

This video so useful for me thanks for upload😊😊😊😊😊

• ### Dhananjay Grover Post author

Best explanation

• ### Rey Carlos Post author

My exam is literally tomorrow, lol

• ### Aftab Soni Post author

You explain very well Do you know hindi Let me explain in Hindi.🤗🤗

• ### Sylvester Ongori Post author

I 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 Khan Post author

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

• ### nitesh Kumar Post author

u r reallly a excellent teacher i appreciate u

• ### electro magic Post author

I love your lesson nice don baby😙

• ### Fahim Al-Huq Post author

THANKS A LOT.

• ### Roberth Santos Post author

Speak português.
Eu sou do Brasil

• ### thomas saverio Post author

Thanx😗best explaination ever❤

• ### Michael Spurlock Post author

Excellent 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 Monroe Post author

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

• ### Raj Shekar Post author

How did they find light speed with physical example

• ### Gorgum Post author

what 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 Roy Post author

Thank u are Awesome

• ### Andrei Reyes Post author

Hi 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 Claire Post author

Very lovely Aussie girl.Merci beaucoup,ma cher amie Jade,and God bless you.

• ### 卡艺抠Kaiko Post author

needed this! thankyou for the great explanation

• ### Maths ki dunya Post author

What is actual meaning of magnitude of charge physically?

• ### YoRbOi GeLo Post author

How the fuck did you get 8.99 like WHAT THE HELL

• ### Robert Evans Post author

Exams 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 next Post 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

• ### Thembelihle Post author

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

• ### Jabulile Mngomezulu Post author

can we do the eastern cape question paper 2015 grade11?

• ### Hhh Hhh Post author

You are superb 👌👌👌

• ### Hhh Hhh Post author

You are excellent in everything 👌👌👌👌😍😍

• ### Tim Rubin Halcomb Post author

Wow! You're pretty.

• ### Zahir Jafar Post author

Something is wrong

Thank you.

• ### Gábor Králik Post author

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

• ### Souza, Marcos Antonio English with coffee Post author

Good…pretty girl…beautiful lesson…continue

• ### Sil Bombardi Post author

Merci a Monsieur Coulomb d'abord et merci à vous.

• ### Steve Doe Post author

3:12
“Don’t panic”
Words of wisdom. Also written on the back cover of a famous guide.

• ### Tom Laight Post author

Given 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 radhwan Post author

well none, thank you for the excellent explanation.

• ### Brightico Adjei Post author

thanks for the lectures

• ### Harsh Purohit Post author

You look pretty ❤️

• ### Abhishek Tripathi Post author

Force 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 Aaisha Post author

Your 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 Tripathi Post author

U are smarter mam

عربي

• ### Naf Noor Post author

Thank You dear…. This really helped a lot… God Bless You.

• ### elias salas Post author

all these nerds trying to get frisky with a girl from a chemistry video XD

• ### Aarush Kumar Post author

I really appreciate u and your work😇

• ### Mridul Maitre Post author

I 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 Maalim Post author

Splendid 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 Lewis Post author

you 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 pocasangre Post author

Can you do Gauss's Law?

• ### Physics tutorials Post author

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