Fun Video: Charge on an Electron Video Lecture - JEE

let's talk about how Robert Millikan and
Harvey Fletcher discovered how much
charge electrons have by using their
oil-drop experiment now I think the
oil-drop experiment is like one of the
coolest experiments in all of science
now before this happened in 1897
JJ Thompson discovered that atoms have
electrons and he discovered that
electrons have negative charge but he
wasn't able to figure out how much
negative charged electrons have because
charge is something that can come in
different amounts so scientists wanted
to be able to put a number on it figure
out exactly how much negative charge
each electron had this was a tricky
thing to do though because you can't
just take an atom and pull out an
electron and measure its charge so
Millican and Fletcher had to do is use a
really clever technique they used tiny
drops of oil and balance them floating
in mid-air by using gravity and
electricity and believe it or not using
this technique they were able to
determine how much charge each electron
had let's talk about how here's the
equipment that Milliken use to do the
experiment this is like a big chamber
and I'm showing a cross-section of it
here now this is the atomizer it's just
like a perfume mister except instead of
spraying perfume it's spraying oil into
tiny little droplets and these droplets
spray out into this area and some of
them float down here in between these
plates and end up in this area
now these drops are really really tiny
so there's a microscope in one side of
the chamber so the people doing an
experiment can look through the
microscope and see individual drops they
try to focus on one drop at a time and
here is what they'd see they would see
one of these drops slowly floating down
here to the ground now why is that well
it's because there is a gravity force
that is acting on this little oil drop
pulling it downwards but the gravity
force isn't the only force pulling on
this oil drop there's also
electric force that is pulling it in the
opposite direction here is where the
electric force comes from as these drops
that spray out as they make their way
through the chamber some of them lose
some electrons and as they lose
electrons as they lose negative charge
the drops become positively charged so I
can indicate that here with this
positively charged this positively
charged drop here now these plates are
special because they have an electric
charge on them they're hooked up to
power here and the top one has a
negative charge and the bottom plate has
a positive charge so here it is here is
a positive charge on the bottom and here
is a negatively charged plate on the top
now the oil drop is positively charged
think about how electric charges
interact with each other well like
charge is the same type of charges repel
they push away from each other so the
positively charged oil drop is going to
be pushed away from the positively
charged metal plate that's down here and
then on the other hand opposite charges
attract
so the positively charged drop is going
to be attracted to the negatively
charged plate that's up here all of this
adds up to an electric force that is
going to be pushing in this direction
and it's going to be pushing in the
opposite direction of gravity so it's
like these two forces are going to be
battling it out one pushing down one
pushing up who wins well it depends on
how strong the electric forces and the
electric force depends on the charge
that's in these plates let me show you
two I mean let me show you what I mean
these plates have this voltage dial
that's hooked up to them so that it's
possible for the people doing the
experiments to change the amount of
power that's going to these plates so
they can turn it up or they can turn it
down alright so we've got this oil drop
here let's say that we can
crank the voltage way way up here we go
crank it all the way up to ten now
when the voltage is really high there's
a lot of power in these plates so they
have a very strong charge and because
they have such a strong charge the
electric force that that's going to
create on this drop is very big high
voltage
lots of power big charge big electric
force so the electric force you can see
is really large here and it's much
bigger than the gravity force so since
they're trying to cancel each other out
the electric force is going to win
because it's much bigger and that means
that it doesn't really matter that the
gravity force is pulling down because
the bigger force is moving up so the oil
drop is going to move upwards because
the electric force is winning so I can
kind of sum this up here where with a
high voltage the drop moves up because
the electric force is bigger than the
gravity force but on the other hand we
could turn the voltage way down here and
what that's going to mean is that
there's much less power in these plates
less charge and so the electric force
that's acting on the drop now at the
lower voltage is not very big it's just
a small little electric force and now
when it tries to cancel out the gravity
force it's much too small the gravity
force is going to win it's the bigger
force so that means that in this case
the gravity is going to pull the oil
drop down and that's what this situation
is low voltage drop moves down because
gravity wins now what if we could adjust
the voltage so that it is just right and
by just right I mean that we find a
voltage number where the upwards
electric force on the droplet gives
exactly the same amount of pull as the
downward gravity force okay so if the
voltage is a little too high the
electric force is going to be bigger
than the
gravity force so the drop moves up if
the voltage is a little too low the
electric force is going to be smaller so
then the gravity force winds and the
drop moves down but if we get the
voltage just right the drop isn't going
to move up it's not going to move down
it's just going to float in midair and
that's because the electric force and
the gravity force are both pulling but
they're pulling the exact same amount
it's like two teams trying to play
tug-of-war but both teams are equally
strong so they can't move the rope in
either direction so in the electric
force exactly equals the gravity force
the oil drop is just going to stay still
when this happens electric force equals
the gravity force this is a very
important situation and it's with the
people doing the experiment try to do
they adjust the voltage looking at a
single drop until they can get it just
right so that the drop stays still
now for each drop they do this with many
different drops for each drop they find
a way to determine the mass of it how
much it weighs so for this one let's
just say you write the mass down and
then they write down the voltage at
which it balances staying still and they
do this for many different drops they do
it for many different drops of different
sizes and for each drop they measure the
mass of it and then they measure what
the voltage is when that drop is
balanced they take these numbers and
then they're able to plug them into some
equations to figure out what the amount
of electric charge is on the drops
that's what we'll do next I'm not going
to go into all the details of how they
do the numbers and everything but I want
to give you a conceptual understanding
of how they think through the problem
now here's how they figure out what the
charge of an electron is okay they have
all of this different data
for each drop they have its mass and
they have the voltage that's required to
balance it steady okay now we can say
this that when the drop is balanced the
force of gravity equals the force of
electricity now the force of gravity
depends on the mass of the drop as well
as a few other things we don't want to
have to worry about here the force of
electricity depends on the charge of the
drop and the voltage on the plates and
remember that when the drop is balanced
these two things equal each other so in
other words this is an equation that you
can solve for one of the variables now
they know for each drop they know its
mass so this is a variable that they
know for each drop they know the voltage
that's required to balance it so they
know this and because this is an
equation they can solve for the charge
of each drop because they know this and
they know this and they know that these
two things equal each other now using
this equation they're able to determine
the charge on each drop here is a list
of some of the charges that they might
be able to come up with I've simplified
this somewhat from the actual experiment
these numbers are measured in Zepto
coulombs which is a tiny tiny amount of
charge and look that all of these
numbers are positively charged that's
because as we said earlier the oil drops
are positively charged because they've
lost some electrons on their way through
the chamber okay so they're positively
charged because they've lost electrons
when they start looking at these numbers
they notice something interesting they
notice that there is a pattern in the
numbers and here's what it is all of
these numbers are multiples of 160 okay
so look this is one times 160 this is
two times 160 three four five and so
forth
and so they say look these drops of oil
are losing charge in multiples of a
hundred and sixty so they think AHA each
electron must have a hundred and sixty
Zepto coulombs of charge because if you
lose one you have a hundred and sixty
plus charge if you lose two of them you
have a plus charge of 320 so the drop
that has this charge lost one electron
the drop that has this charge lost to
this one lost three this one lost four
this one lost five that's where the
positive charge is coming from because
the drops are losing different amounts
of electrons but they see that the
charge difference is always a multiple
of a hundred and sixty the smallest
amount of charge that you can lose when
you lose one electron so based on this
information they're able to determine
that the charge of one electron is
negative remember because electrons are
negative is negative 160 left oh cool
ohms you can also write this as negative
one point six times ten to the negative
19 coulombs coulombs are just a unit
that you use to measure charge or it can
be written as negative zero point zero
zero one six zero coulombs a very very
tiny amount that is how with oil-drop
experiment scientists were able to first
measure the electric charge on an
electron by taking tiny little drops of
oil and balancing the downward gravity
force with an upward electric force