Coulomb’s Law (with example)

Coulomb’s Law (with example)

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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!

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