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In this video, we begin our investigation of the
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exact nature of the electric force. French physicist Charles
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Augustin Nakoula took a charged metal object and attached it
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with a wire toe on identical metal object that was
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uncharged. This allows charge the flow from one to
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the other and because the objects are identical by symmetry
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, they end up with the exact same charge.
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You can then disconnect them and they end up with
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two orbs of unequal charge in each. And we'll
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call this charge que He then measure the force.
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Between these charges at some distance are what he found
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was a certain size force which will just call f
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not. He then took thes equally charged orbs and
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he moved him further apart. And if you move
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these further apart to a distance of say to our
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, then you'll see that the force between them has
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changed. And more specifically, it is now f
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not over four. Mhm. Next he moved.
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He moved the orbs in relation to each other again
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. Except this time he placed him closer to each
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other. So he measures the force between them again
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. This time the distance is our over to,
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and what he found was, the force was equal
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to four F not, and by repeating this again
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and again and measuring the force between these two equally
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charged orbs at different distances, he finds that the
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force is proportional toe one over R. Squared the
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inverse square of their distance from each other, and
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you'll notice that this in inverse square law is the
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same thing that's in. That's obeyed by the gravitational
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force. Having determined how the distance between two charged
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objects affects the force, Coolum next investigated how the
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size of each charge would affect that force. So
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, using a similar method of charging two equally charge
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balls, he could take one of those orbs and
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charge it with another equal one to get half the
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charge that he originally had. And when he measures
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this force, he sees that it equals the original
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force over to, and he could repeat this again
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and get a ball with a quarter of the charge
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and find that the force is equal to F not
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over four. And by repeating this and repeating this
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, you'll see that the forces linear with the charge
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and it's linear with each charge. So now our
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force is proportional to the charge on each orb.
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And of course, as we've already seen to the
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inverse square of the distance between them and this leads
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us to cool arms law. That force is equal
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to some constant times. The charge on the first
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object, the charge on the second object, all
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divided by the distance between them squared. Our next
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part will investigate more about the nature of this constant
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of proportionality, k so cool and discovered that the
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electric force between two charge objects, as we see
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on the right here, is equal to the charge
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on the first object times. The charge on the
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second object divided by the square of the distance between
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them. Time some constant K in this case is
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the electric constant, and it has the value of
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about 8.988 times 10 to the ninth. Newton's times
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meter squared per Coolum squared que is often also written
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as one over four pi epsilon. Not where Epsilon
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not has a value of 8.854 times 10 to the
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negative 12 Cool, um, squared per newton meters
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squared the use of either K or Epsilon not is
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acceptable. Absalon, not is often Ah, lot
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easier to deal with, depending on what units you're
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using. But in S I either K or Epsilon
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not works very well. However, we know that
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forces a vector and so electrostatic force must also be
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a vector. So more appropriately, we write that
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the force of actor is equal decay Q one que
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two over r squared in the direction of our hat
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where our hat is just the unit vector in the
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direction between q one and Q two or more precisely
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, our hat is simply are divided by the magnitude
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of our. We'll also notice that if Q One
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and Q two have the same sign, then if
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it's positive, if they different different Insein, then
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our force vector is negative. And so we say
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that a positive force is repulsive and a negative force
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is attractive, which we would expect opposite. We
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charged particles should attract each other and similar, like
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part charges should repel each other. So we might
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ask ourselves how strong is the electric force in particular
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? How strong is it to something we've studied a
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lot, such as gravity well to answer that.
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We look at each force. We've shown that the
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electric force is equal decay. Times Q. One
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Q two over r squared while the gravitational force will
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recall is equal to G M one m two over
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R squared mhm. When we look at the ratio
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of these, we see that the distance square,
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the inverse square law drops out because it applies to
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both the electric force and the gravitational force. And
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so we're left with Korg Times Q. One Q
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two over M one M two. Now this leading
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term a k a. Burgess simply constant. So
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what will determine the relative sizes of these forces are
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charges and our masses, and we'll see that for
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very, very small mass particles such as electrons,
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protons, atoms, nuclei. This is a very
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, very small mass, which means that this ratio
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of the electric force of the gravitational force is very
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large. And so we expect at small mass objects
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the electric force will dominate. However, as masters
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get bigger and bigger, we'll see that the gravitational
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force begins to dominate and this whole ratio becomes a
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lot smaller. So the electric force will dominate.
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When we have small masses and large net charges.
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Meanwhile, the gravitational force dominates when we get to
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a larger bodies people, planets, solar systems.
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In other words, when the masses are much larger
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than the charges come to further explore in the nature
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of the electric force versus the gravitational force, we
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look at the concrete example of the hydrogen atom.
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So here on the left, we see a typical
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hydrogen atom which contains a positively charged proton and its
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nucleus and a Nilla negatively charged electron. At some
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distance from the nucleus, I've written here all of
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the constants we need to discuss the gravitational electric forces
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, the electric constant, the gravitational constant G,
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the masses of the electron and the proton. And
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of course, their charges which are equal but opposite
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in charge and sign. It's also gonna We're also
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going to need the typical distance between the proton and
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the electron, which is about half an angstrom or
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5.29 times 10 to the L. A. In
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the meters. This varies in actuality, but that
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is an average value that we can use for the
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purposes of this. So we calculate our electric force
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as the electric, constant times the charge of the
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electron, the charge of the proton over R squared
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. And we get something along the lines of 8.24
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times 10 to the negative. Eighth eight Newtons.
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Negative because the forces attractive between them. Our gravitational
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force, which is G times the masses divided by
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the distance squared, is 3.63 times 10 to the
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negative 47 Newton's now. Typically, there is no
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sign in the gravitational force equation. That's because the
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force is always attractive. There is no such thing
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as negative mass so far as we know. And
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so we'll put a negative sign here to make sure
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that these agree in concept. We can see if
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the ratio of these the electric force over the gravitational
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force is about 2.3 times 10 to the 39.
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Until that thes scales with these tiny masses on these
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short distances, the electric force far outweighs the gravitational
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force. It's only when we get up to macro
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scales of planets. Uh, solar systems stars that
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the that the gravitational force will far outweigh the electric
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force