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!