WEBVTT
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This is College Physics
Answers with Shaun Dychko.
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We're going to find the ratio
of the electrostatic force
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to the gravitational force
between two electrons
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and then do it again for
between two protons.
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So the electrostatic force is Coulomb's
constant times the two charges,
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both of which are the elementary charge
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and so we square them,
square the elementary charge,
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and divide by the distance
between the two charges,
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and the gravitational force
is the gravitational constant
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times the mass of each
electron multiplied together,
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divided by the distance
between them squared.
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The ratio of these two forces is going
to be the electrostatic force
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divided by the gravitational force.
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Now instead of dividing
a fraction by a fraction,
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I'm going to multiply by the
reciprocal of this fraction,
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so multiplying by *r* squared
over *g m e* squared.
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This works out to *k q e* squared over *G m e*
squared and the *r* squareds cancel.
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Then we substitute in numbers
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and we have the Coulomb's constant times
the elementary charge squared,
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divided by the gravitational constant,
times the mass of an electron squared.
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We get 4.16 times ten to the forty-two
which is a very massive number.
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This means electrostatic
force is way bigger
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than the gravitational force for electrons.
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Now when it comes to protons, the expression
is basically going to be the same
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but we'll have mass of a proton down
here instead of mass of an electron.
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So we substitute in all the
same numbers as before
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but now the mass of electron which was 9.11
times ten to the minus thirty-one kilograms,
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is replaced instead with 1.67 times ten
to the minus twenty-seven kilograms,
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mass of a proton.
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This works out to 1.24 times
ten to the thirty-six
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is the ratio of the electrostatic force
to the gravitational force for protons.
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The reason these ratios are different
is because the masses are different.