# 8.02x – Lect 9 – Electric Currents, Resistivity, Conductivity, Ohm’s Law

When positive charges move
in this direction, then, per definition we say the current goes
in this direction. When negative charges
go in this direction, we also say the current
goes in this direction, that’s just our convention. If I apply a potential difference
over a conductor, then I’m going to create an electric field
in that conductor. And the electrons, there are
free electrons in a conductor, they can move,
but the ions cannot move, because they are frozen into the solid,
into the crystal. And so when a current
flows in a conductor, it’s always the electrons
that are responsible for the current. The electrons feel
the electric field, and then the electrons try
to make the electric field zero, but they can’t succeed, because we keep the potential difference
over the conductor. Often, there is a linear relationship
between current and the potential, in which case,
we talk about Ohm’s Law. Now, I will try to derive Ohm’s Law
in a very crude way, a poor man’s version and not
really one hundred percent kosher, it requires quantum mechanics,
which is beyond the course– beyond this course– but I will do a job that still gives us
some interesting insight into Ohm’s Law. If I start off with a conductor,
for instance copper, at room temperature,
three hundred degrees Kelvin, the free electrons in copper
have a speed, an average speed of about
a million meters per second. So this is the average speed
of those free electrons, about a million
meters per second. This in all directions. It’s a chaotic motion. It’s a thermal motion,
it’s due to the temperature. The time between collisions,
time between the collisions, and this is a collision of the free electron
with the atoms– is approximately,
I call it tau, is about three times ten
to the minus fourteen seconds. No surprise because the speed
is enormously high. And the number of free electrons
in copper– per cubic meter– I call that number n– is about ten to the twenty-nine. There’s about one free electron
for every atom. So we get twen– ten to the twenty-nine
free electrons per cubic meter. So now imagine that I apply
a potential difference– piece of copper,
or any conductor for that matter, then the electrons will
experience a force which is the charge
of the electron, that’s my little e times the
electric field that I’m creating, because I apply
a potential difference. I realize that the force and the electric field
are in opposite directions for electrons, but that’s a detail, I’m interested in the
magnitudes only. And so now these electrons
will experience an acceleration, which is the force divided
by the mass of the electron and so they will pick up a speed,
between these collisions, which we call the drift velocity,
which is a times tau. It’s just 801. And so a equals F divided by m e. F is e E [misspoken A], so we get e times E
divided by the mass of the electrons, times tau. And that is the–
the drift velocity. When the electric field goes up,
the drift velocity goes up, so the electrons move faster in the direction opposite
to the current. If the time between collisions gets larger,
they– the acceleration lasts longer, so also, they pick up a larger speed,
so that’s intuitively pleasing. If we take a specific case and I take,
for instance copper and I apply over the– over a wire, let’s say the wire
has a length of 10 meters, I apply a potential difference
I call delta V, but I could have said just V,
I apply there a potential difference of ten volts, then the electric field,
inside the conductor now, is about one volt per meter. And so I can calculate now,
for that specific case, I can calculate what the drift velocity
would be. So the drift velocity of those free electrons
would be the charge of the electron, which is one point six times
ten to the minus nineteen coulombs. The E field is one,
so I can forget about that. Tau is three times ten to the minus fourteen,
as long as I’m room temperature and the mass of the electron
is about ten to the minus thirty kilograms. And so, if I didn’t slip up, I found that
this is five times ten to the minus three meters per second, which is
half a centimeter per second. So imagine,
due to the thermal motion, these free electrons move
with a million meters per second. But due to this electric field,
they only advance along the wire– slowly, like a snail, with a speed on average
of half a centimeter per second. And this goes very much against your
and my own intuition, but this is the way it is. I mean, a turtle would go faster
than these electrons. To go along a ten-meter wire
would take half hour. Something that you never thought of. That it would take a half hour for these electrons
to go along the wire if you apply potential difference of ten volts,
copper, ten meters long. Now, I want to massage
this further and see whether we can somehow
squeeze out Ohm’s Law, which is the linear relation
between the potential and the current. So let me start off with a wire– which has a cross-section A and it has a length l and I put a potential difference
over the wire, plus here and minus there,
potential V, so I would get a current in this direction,
that’s our definition of current, going from plus to minus. The electrons, of course, are moving in this
direction, with the drift velocity. And so the electric field in here,
which is in this direction, that electric field is approximately
V divided by l, potential difference
divided by distance. In one second, these free electrons will move
from left to right over a distance v d meters. So if I make any cross-section
through this wire, anywhere, I can calculate how many electrons pass
through that cross-section in one second. In one second, the volume that
passes through here, the volume is v d times A– but the number of free electrons
per cubic meter is called n, so this is now the number of free electrons that passes, per second,
through any cross-section. And each electron has a charge e
and so this is the current that will flow. The current, of course, is in this direction,
but that’s a detail. If I now substitute the drift velocity,
which we have here, I substitute that in there
but then I find that the current– I get a e squared,
the charge squared, I get n, I get tau, I get downstairs,
the mass of the electron and then I get A
times the electric field E. Because I have here,
this electric field E. When you look at this here, that really depends
only on the properties of my substance, for a given temperature. And we give that a name. We call this sigma,
which is called conductivity. Conductivity. If I calculate, for copper, the conductivity,
at room temperature, that’s very easy, because I’ve given you what n is, on the blackboard there,
ten to the twenty-nine, you know what tau is at room temperature,
three times ten to the minus fourteen, so for copper, at room temperature,
you will find about ten to the eighth. You will see more values for sigma
later on during this course. This is in SI units. I can massage this a little further,
because E is V divided by L, and so I can write now that the current
is that sigma times A times V divided by l. I can write it down a little bit differently,
I can say V, therefore, equals l divided by sigma A,
times I. And now, you’re staring at Ohm’s Law,
whether you like it or not, because this is what we call
the resistance, capital R. We often write down rho for one over sigma
and rho is called the resistivity. So either one will do. So you can also write down–
you can write down V equals I R and this R, then, is either
L divided by sigma A, or L times rho– let me make it
a nicer rho — divided by A. That’s the same thing. The units for resistance R is volts per ampere,
but we call that ohm. And so the unit for R is ohm. And so if you want to know
what the unit for rho and sigma is, that follows immediately
from the equations. The unit for rho
is then ohm-meters. So we have derived the resistance here
in terms of the dimensions– namely, the length
and the cross-section– but also in terms of the physics
on an atomic scale, which, all by itself,
is interesting. If you look at the resistance, you see it is proportional
with the length of your wire through which you drive a current. Think of this as water trying
to go through a pipe. If you make the pipe longer,
the resistance goes up, so that’s very intuitively pleasing. Notice that you have A downstairs. That means if the pipe is wider,
larger cross-section, it’s also easier
for the current to flow, it’s easier for the water
to flow. So that’s also
quite pleasing. Ohm’s Law, also, often holds for insulators,
which are not conductors, even though I have derived it here
for conductors, which have
these free electrons. And so now, I want to make a comparison
between very good conductors and very good insulators. So I’ll start off with a–
a chunk of material, cross-sectional area A– let’s take it one millimeter
by one millimeter– so A is ten to the minus six
square meters. So here I have a chunk
of material– and the length of that material, l,
is one meter. Put a potential difference over there,
plus here and minus here. Current will start to flow in this direction,
electrons will flow in this direction. The question now is, what is the resistance
of this chunk of material? Well, very easy. You take these equations, you know l and A,
so if I tell you what sigma is, then you can immediately calculate
what the resistance is. So let’s take, first,
a good conductor. Silver and gold and copper
are very good conductors. They would have values for sigma,
ten to the eight, we just calculated for copper,
you’ve seen in front of your own eyes. So that means rho would be
ten to the minus eight, it’s one over sigma. And so in this particular case,
since A is ten to the minus six, the resistance R is simply
ten to the sixth times rho. Because l is one meter. So it’s very easy– resistance here, R,
is ten to the minus two ohms. One-hundredth of an ohm. For this material
if it were copper. Let’s now take
a very good insulator. Glass is an example. Quartz, porcelain,
very good insulators. Now, sigma, the conductivity,
is extremely low. They vary somewhere from ten to the minus
twelve to ten to the minus sixteen. So rho, now, the resistivity, is something like
ten to the twelve to ten to the plus sixteens and if I take ten to the fourteen,
just I gra– have to grab– a number– then you’ll find that R, now,
is ten to the twenty ohms. A one with twenty zeros. That’s an enormous resistance. So you see the difference–
twenty-two orders of magnitude difference between a good conductor
and a good insulator. And if I make this potential difference
over the wire, if I make that one volt, and if I apply Ohm’s Law, V equals I R,
then I can also calculate the current that is going to flow. If I R is one, then the current here
is hundred amperes and the current here is
ten to the minus twenty amperes, an insignificant current,
of ten to the minus twenty amperes. I first want to demonstrate to you
that Ohm’s Law sometimes holds, I will do a demonstration, whereby you have a voltage supply–
I put a V in here– and we change the voltage
in a matter of a few seconds from zero to four volts. This is the plus side,
this is the minus side, I have connected it here
to a resistor which is fifty ohms– we use this symbol for a resistor–
and here is a current meter. And the current meter
has negligible resistance, so you can ignore that. And I’m going to show you
on an oscilloscope, we’ve never discussed
an oscilloscope, but maybe we will
in the future. I’m going to show you,
they are projected, the voltage, which goes from zero to four,
versus the current. And so it will start here
and by the time we reach four volts then we would have reached
a current of four divided by fifty, according to Ohm’s Law,
I will write down just four divided by fifty amperes,
which is 0.08 amperes. And if Ohm’s Law holds, then you
would find a straight line. That’s the whole idea about Ohm’s Law,
that the potential difference, linearly proportional to the current. You double the potential difference,
your current doubles. So let’s do that, let’s take a look at that,
you’re going to see that there– and I have to change my lights
so that you get a good shot at it– oh, it’s already going. So you see, horizontally, we have the current
and vertically, we have the voltage. And so it takes about a second
to go from zero to four– so this goes from zero
to four volts– and you’ll see that the current
is beautifully linear. Yes, I’m blocking it– oh, no, it’s my
reflection, that’s interesting. Ohm’s Law doesn’t allow for that. So you see how beautifully
linear it is. So now, you may have great confidence
in Ohm’s Law. Don’t have any confidence
in Ohm’s Law. The conductivity sigma is a strong
function of the temperature. If you increase the temperature, then the
time tau between collisions goes down, because the speed of these
free electrons goes up. It’s a very strong function of temperature. And so if tau goes down, then clearly,
what will happen is that the– conductivity will go down. And that means rho will go up. And so you get more resistance. And so when you heat up a substance,
the resistance goes up. A higher temperature,
higher resistance. So the moment that the resistance R
becomes a function of the temperature, I call that a total breakdown of V equals I R,
a total breakdown of Ohm’s Law. If you look in your book, they say, “Oh, no,
no, no, that’s not a breakdown, you just have to adjust the resistance
for a different temperature.” Well, yes, that’s an incredible poor man’s way
of saving a law that is a very bad law. Because the temperature itself
is a function of current, the higher the current
the higher the temperature. And so now, you get a ratio,
V divided by I, which is no longer constant. It becomes a function
of the current. That’s the end of
Ohm’s Law. And so I want to show you that if I do the
same experiment that I did here, but if I replace this by a light bulb of fifty ohms
— it’s a very small light bulb, resistance when it is hot is fifty ohms,
when it is cold, it is seven ohms. So R cold of the light bulb is roughly
seven ohms, I believe, but I know that when it is hot,
it’s very close to the fifty ohms. Think it’s a little lower. What do you expect now? Well, you expect now, that when
the resistance is low in the beginning, you get this and then when the resistance
goes up, you’re going to get this. I may end up a little
higher current, because I think the resistance
is a little lower than fifty ohms. And if you see a curve like this,
that’s not linear anymore. So that’s the end of Ohm’s Law. And that’s what I want
to show you now. So, all I do is, here I have
this little light bulb– for those of you
who sit close, they can actually see that light bulb–
start glowing, but that’s not important,
I really want you to see that V versus I is no longer linear,
there you go. And you see, every time you see this
light bulb go on, it heats up, and during the heating up, it, um,
the resistance increases. And it’s the end of Ohm’s Law,
for this light bulb, at least. It was fine for the other resistor,
but it was not fine for this light bulb. There is another way
that I can show you that Ohm’s Law is not always
doing so well. I have a hundred twenty-five volt
power supply, so V is hundred and twenty-five
volts– this is the potential difference–
and I have a light bulb, you see it here, that’s the light bulb– the resistance of the
light bulb, cold, I believe, is twenty-five ohms and hot, is about
two hundred and fifty ohms. A huge difference. So if the– resistance, if I take the cold
resistance, then I would get five amperes, but by the time that the bulb is hot,
I would only get half an ampere. It’s a huge difference. And what I want to show you,
again with the oscilloscope, is the current
as a function of time. When you switch on a light bulb,
you would expect, if Ohm’s Law holds, that when you switch on the voltage–
that you see this. This is then your five amperes. And that it would stay there. That’s the whole idea. Namely, that the voltage divided by
the current remains a constant. However, what you’re going
to see is like this. The resistance goes up and then therefore
the current will go down. And will level off at a level which is
substantially below this. So you’re looking there– you’re staring
at the breakdown of Ohm’s Law. And so that’s what I want
to show you now. Ehm– so, here we need
a hundred and twenty five volts– and there is the light bulb, and when I throw this switch, you will see the pattern
of the current versus time– you will only see it once and then
we freeze it with the oscilloscope– turn this off–
so look closely, now. There it is. Forget these little ripple
that you see on it, it has to do with the way that we produce
the hundred and twenty five volts. And so you see here,
horizontally, time. The time between two adjacent
vertical lines is twenty milliseconds. And so, indeed, very early on, the current
surged towards– to a very high value and then the filament heats up and so
the resistance goes up, the light bulb, and the current just
goes back again. From the far left to the far right on the
screen is about two hundred milliseconds. That’s about two tenths of a second. And here you get a current level which is
way lower than what you get there. That’s a breakdown of Ohm’s Law. It is actually very nice
that resistances go up with light bulbs when
the temperature goes up. Because, suppose it were
the other way around. Suppose you turn on a light bulb
and the resistance would go down. Light bulb gets hot, resistance goes down,
that means the current goes up. Instead of down,
the current goes up. That means it gets hotter. That means the resistance
goes even further down. That means the current
goes even further up. And so what it would mean is that
every time you turn on a light bulb, it would, right in front of your eyes,
destruct itself. That’s not happening. It’s the other way around. So, in a way, it’s fortunate that the resistance
goes up when the light bulbs get hot. All right. Let’s now be a little bit more qualitative
on some networks of resistors and we’ll have you do
a few problems like that, whereby we just will assume,
naively, that Ohm’s Law holds. In other words,
we will always assume that the values for the resistances that
we give you will not change. So we will assume
that the heat that is produced will not play
any important role. So we will just use Ohm’s Law,
for now, and if you can’t use it,
we will be very specific about that. So suppose I have here,
between point A and point B, suppose I have two resistors,
R one and R two. And suppose I apply a potential difference
between A and B, that this be plus and this be minus
and the potential difference is V. And you know V, this is known,
I give you V, I give you this resistance
and I give you that one. So I could ask you now, “What
is the current that is going to flow?” I could also ask you, then, “What is the
potential difference over this resistor alone?” — which I will call V one and “What is the potential difference
over the second resistor?” which I call V two. Very straightforward question. Well, you apply, now,
Ohm’s Law and so between A and B,
there are two resistors, in series. So the current has to go
through both and so the potential difference V,
in Ohm’s Law, is now the total current
times R one plus R two. Suppose these two resistors
were the same, they had the same length,
same cross-sectional area. If you put two in series,
you have twice the length. Well, so, twice the length,
remember, resistance is linearly proportional
with the length of a wire and so you add them up. So now you know R one
and you know R two, you know V,
so you already know the current, very simple. You can also apply Ohm’s Law, as long as it
holds, for this resistor alone. So then you get that V one
equals I times R one, so now you have the voltage
over this resistor and of course, V two must be the
current I times R two. And so you have solved
you have the answers to. We could now have a
slightly different problem, whereby point A is here,
but now we have a resistor here, which is R one and we have
here, R two. This is point B
and this is R two. And the potential difference is V,
that is, again, given and now I could ask you, “What,
now, is the current that will flow here?” And then I can also ask you, “What is
the current that would go through one– resistor one and what is the current
that could go through resistor two?” And I would allow you
to use Ohm’s Law. So now you say, “Aha! The potential difference
from A to B going this route, that potential difference,
is V, that’s a given.” So V must now
be I one times R one. That’s Ohm’s Law,
for this upper branch. But, of course, you can also go
the lower branch. So the same V is also I two
times R two. But whatever current comes in here
must split up between these two think of it as water. The number of charges that flow
into this juncture continue on and so I, the total current,
is I one plus I two. And so now, you see,
you have all the ingredients that you need to solve
for the current I, for the current I one
and for the current I two. And you can turn this
into an industry, you can make extremely complicated
networks of resistors– and if you were in course six,
you should love it– I don’t like it at all, so you don’t have to worry about it,
you’re not going to get very complicated resistor net–
networks from me– but in course six,
you’re going to see a lot of them. They’re going to throw them–
stuff them down your throat. The conductivity of a substance
goes up if I can increase
the number of charge carriers. If we have dry air
and it is cold, then the resistivity of cold, dry air
at one atmosphere– so rho for air, cold,
dry, one atmosphere– cold means temperature
that we have outside– it’s about four times
ten to the thirteen. That is the resistivity of air. It is about what it is in this room,
maybe a little lower, because the temperature
is a little higher. If I heat it up, the air, then
the conductivity will go up. Resistivity will go down, because now, I create oxygen and
nitrogen ions by heating up the air. Remember when we had this lightning,
the step leader came down and we created a channel
full of ions and electrons, that had a very low resistivity,
a very high conductivity. And so what I want to demonstrate to you,
that when I create ions in this room, that I can actually make the conductivity
of air go up tremendously. Not only will the electrons move,
but also the ions, now, will start to move. And the way I’m going to do that is,
I’m going to put charge on the electroscope– [cracking sound] oh, that is not so good–
no harm done. I’m going to put charge
on the electroscope and you will see that
the conductivity of air is so poor that it will stay there
for hours. And then what I will do, I will create ions
in the vicinity of the electroscope. But let’s first put some charge
on the electroscope. I have here a glass rod and I’ll put some
charge on it. OK, that’s a lot of charge. And, uh, the r- the air is quite dry,
conductivity is very, very small and so the charge cannot go off
through the air to the surroundings, to the earth. But now I’m going to create ions there
by heating it up, and I decided to do that with a candle,
because a candle is very romantic, as we all know. So here I have this candle–
look how well the charge is holding, eh? And here’s my candle. And I will bring the candle– oh, maybe twenty
centimeters from the electroscope. Look at it, look at it,
away. I’ll take my candle away
and it stops again. So it’s all due to the fact
that I’m ionizing the air there, creating free electrons
as well as ions, and they both participate now
in the current and the charge can flow away
from the electroscope through the earth, because the conductivity now
is so much higher. I stop again and it stops. You see in front of your eyes
how important the temperature is, in this case, the presence
of the ions in the air. If I have clean, distilled water,
I mean, clean water. I don’t mean the stuff
that you get in Cambridge, let alone did I mean the stuff
that is in the Charles River, I mean clean water,
that has a pH of seven. That means one out of ten to the seven
of the water molecules is ionized, H plus and O H minus. The conductivity, by the way,
is not the result of the free electrons, but is really the result of these H plus
and O H minus ions. It’s one of the cases whereby not the–
the electrons are a maj–
the major responsibility for the current. If I have add three percent of salt,
in terms of weight, then all that salt will ionize, so you get sodium plus
and C L minus ions, you increase the number of ions
by an enormous factor. And so the conductivity will soar up
by a factor of three hundred thousand, or up to a million, because you increase
the ions by that amount. And so it’s no surprise then, for you,
that the conductivity of seawater is a million times higher, think about it,
a million times higher– than the conductivity
of distilled water. And I would like to give you
the number for water, so this is distilled water, that is about two times
ten to the fifth ohm-meters. That is the resistivity, two times ten
to the five oh-meters. I have here a bucket
of distilled water. I’ll make a drawing for you
on the blackboard there. So here is a bucket of distilled water
and in there, is a copper plate and another copper plate,
and here is a light bulb, and this will go straight
to the outlet [wssshhht], stick it in,
hundred ten volts. This light bulb has eight hundred
ohm resistance when it is hot. You see the light bulb here. You can calculate what this resistance is
between the two plates, that’s easy,
you have all the tools now. If you know the distance,
it’s about twenty centimeters and you know the surface area
of the plates, because remember, the resistance
is inversely proportional with A, so you have to take that
into account– and you take the resistivity
of water into account, it’s a trivial calculation, you can calculate what
the resistance is of this portion here. And I found that this resistance here
is about two megaohms. Two million ohms. So, when I plug this into a wall,
the current that will flow is extremely low, because it has to go through
the eight hundred ohms, and through the
two megaohms. So you won’t see anything,
the light bulb will not show any light. But now, if I — put salt in here, if I really manage to put
three percent in weight salt in here, then this two megaohm will go down
to two ohms, a million times less. So now, the light bulb will be happy like
a clam at high tide, because two ohms here,
plus the eight hundred, the two is insignificant. And this is what I want to–
to demonstrate to you now, the enormous importance
of increasing ions. I increased ions here
by heating the air, now i’m going to increase the ions
by adding salt. And so the first thing that I will do is,
I will stick this in here. There’s the light bulb. And I make a daring prediction
that you will see nothing. There we go. Nothing. Isn’t that amazing? You didn’t expect that, right?
Physics works, you see nothing. If I take the plates out and touch them
with each other, what will happen? There you go. But this water has such a huge resistance
that the current is too low. Well, let’s add some– not pepper–
add some salt. Yes, there’s salt in there. It’s about as much as I would put
on my eggs in the morning– stir a little– ah, hey,
look at that. Isn’t that amazing? And when I bring them closer together,
it will become even brighter, because L is now smaller,
the distance is smaller. I bring them farther apart,
it’s amazing. Just a teeny, weeny little bit of salt,
about as much as I use on my egg, let alone– what the hell,
let’s put everything in there– that’s a [unintelligible]
I put everything, then, of course, you go almost down
to the two ohms, and the light bulb
will be just burning normally. But even with that little bit of salt,
you saw the huge difference. My body is a fairly good conductor–
yours too, we all came out of the sea– so we are almost all water– and therefore,
when we do experiments with little charge, like the VanderGraaf,
beating a student, then we have to insulate ourselves
very carefully, putting glass plates under us,
or plastic stools, to prevent that the charge
runs down to the earth. In fact, the resistance, my resistance
between my body and the earth is largely dictated by the soles of my shoe,
not by my body, not by my skin. But if you look at my soles,
then you get something like this and it has a certain thickness
and this, maybe one centimeter. This, now, is l in my calculation
for the resistance, because current may flow
in this direction, so that’s l. Well, how large is my foot? Let’s say it’s one foot, long–
no pun implied– and let’s say it’s about
ten centimeters wide. So you can calculate what the surface area
A is, you know what l is and if you know now what the resistivity is
for my sole, I can make a rough guess, I looked up the material and I found that
the resistivity is about ten to the tenth. So I can now calculate what the resistance
is in this direction. And I found that that resistance then,
putting in the numbers, is about ten billion ohm. And you will say, “Wow!”
Oh, it’s four, actually. Well, big deal. Four billion ohm. So you will say, “That’s an
enormous resistance!” Well, first of all,
I’m walking on two feet, not on one, so if I would be standing one
the whole lecture, it would probably
be four billion, but if I have two feet on the ground,
it’s really two billion. You will say, “Well,
that’s still extremely large!” Well, it may look large,
but it really isn’t, because all the experiments
that we are doing here in twenty six one hundred, you’re dealing with very small
amounts of charge. Even if you take the VanderGraaff– the VanderGraaff, say, has
two hundred thousand volts– and let’s assume that my resistance
is two times ten to the nine ohms, two feet on the ground. So when I touch the VanderGraaff,
the current that would flow, according to Ohm’s Law,
would be hundred microamperes. That means, in one second, I can take hundred
microcoulombs of the VanderGraaff, but the van der Graff has only
ten microCoulombs on it. So the resistance of four billion or two billion
ohms is way too low for these experiments that we have been doing
in twenty six one hundred, and that’s why we use
these plastic stools and we use these glass plates
in order to make sure that the current is not
draining off the– the charge that we need
for the experiments. I want to demonstrate that to you,
that, indeed, even with my shoes on– that means, even with my two billion ohm
resistance to the ground– that it will be very difficult for me,
for instance, to keep charge
on an electroscope. I’m going to put charge on this electroscope
by scuffing my feet. But, since I keep my– I have my shoes on,
I’m not standing on the glass plate, the charge will flow through me. You can apply Ohm’s Law. And you will see that as I do this–
I’m scuffing my feet now– that I can only keep that electroscope charged
as long as I keep scuffing. But the moment that I stop scuffing,
it’s gone. Start scuffing again, that’s fine,
but the moment that I stop scuffing, it goes off again. Even though this resistance is something like
two billion ohms. Let alone if I take my shoes off. I apologize for that. If now I scuff, I can’t even get any charge
on the electroscope, because now, the resistance
is so ridiculously low, I don’t even have
the two billion ohms, I can’t even put any charge
on the electroscope. It’s always very difficult for us
to do these experiments unless we insulate ourselves
very well. And if, somehow,
the weather is a little damp, then the conductivity of many materials
can increase That’s why we always like to do
these experiments in winter, so that the conductivity of the air
is very low, no water anywhere. Here you see a slide of a robbery. I have scuffed my feet across the rug,
and I am armed with a static charge. Hand over all your money,
or I’ll touch your nose. This person either
never took 802, or he is wearing very,
very, special shoes. See you on wednesday.