In this video we're introducing coulomb's law describing the force between two
electrical charges and then we're going to apply coulomb's law to two examples
as a starting point i wanted to remind you of the direction of force between two charges so
over here on the left we see that if we have two positive charges they repel each other
if we have two negative charges they also repel each other and when the signs are different
they attract each other so there's the directionality of the force between the charges
but what about the magnitude of the force well i think this makes a lot of sense
that the closer the charges are to each other the stronger the force between them so coulomb's
law includes that piece of information but more specifically it works like one over the distance
between the two charges squared the force between the charges is also proportional to the magnitude
of each charge and then there's a constant k out in front that's equal to 8.99 times 10 to the
ninth newton meter squared per coulomb squared i want to make a couple points about coulomb's law
before we apply it and the first one is that if i put in like charges here so each one of these is a
plus charge coulomb's law would give me a positive force that must mean a repulsive force between the
two charges now try it with minus signs if i put it in two negative charges that also
comes out positive giving me a repulsive force if i put in one positive charge and one negative
charge into coulomb's law it's going to come out negative which means an attractive force between
the charges the second point i wanted to make before moving on is to look at the units of
k so it has these odd units of newton meters squared per coulomb squared
and i just wanted to check that that makes sense so when i'm looking at coulomb's law on the left
hand side if i examine the units i could say the units of force should be equal to the units of k
times the units of q1 units of q2 over the units of r squared
and so that gives me the units of k times coulombs times coulombs or coulombs squared over meters
squared and i know that the units of force are newtons so newtons have got to be the units of k
times coulombs squared per meter squared so i could just solve for k real quick and say well
k better have units of newtons in order to get the newtons popping out on the left-hand side and i've
got to cancel the meters squared and the coulomb squared and that's why k has these odd units
moving on to a couple examples first i'm asked to compute the force between two one micro coulomb
charges separated by one meter so this prefix is read micro and that means one millionth or 10
to the negative six so let's get a picture of our charges there it is two one micro coulomb charges
separated by one meter and i plug into coulomb's law just to remind you k q 1 q 2 over r squared
and we plug in k i'm not going to write the units since we already discussed them at length
both of my charges are the same so i can just write it like this remember a micro coulomb is
10 to the negative 6 coulombs so i can just write it as 10 to the negative 6 squared since there's
two of them and then my distance is 1 meter squared when i crunch the numbers on this i get
.0089 newtons of force in my second example i want to find the force of attraction between
the proton and the electron in a hydrogen atom and i'm given some useful numbers here
the diameter of hydrogen is about one angstrom that's the a with the
little circle over it and that's 10 to the negative 10th meters and that means the
radius which is really what i'm interested in because that's the separation distance
the radius is going to be half the diameter or 0.5 times 10 to the negative 10 meters
i'm also told the elementary charge is 1.6 times 10 to the negative 19 coulombs now
that's the charge magnitude on the proton and the electron the difference is that the electron
has a minus sign so if i write that into my picture my proton has a charge of plus qe
my electron has a charge of minus qe so we plug into coulomb's law
and again i can streamline things a little bit
because my charges have the same magnitude there is a minus sign
out in front but i have the same magnitude of charge for each one so i can just write it as 1.6
times 10 to the negative 19 coulombs all squared and then the distance between them squared so 0.5
times 10 to the negative 10 meters all squared so this is going to come out
negative indicating that it's an attractive force between these two because they're unlike
charges and when i run the numbers i get negative 9.21 times 10 to the negative eighth
newtons again in coulomb's law the minus sign means we're talking about an attractive force
in some versions of this question you might just be asked for the magnitude of the force and then
you just ignore the minus sign if you find the physics content on zack's lab helpful click on the
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