Download Ch. 20: Electric potential energy, electric potential, voltage

Ch. 20: Electric potential energy, electric potential, voltage
(Dr. Andrei Galiautdinov, UGA)
2014FALL -
PHYS1112
PLAN:
1.
2.
3.
4.
5.
6.
Electric potential energy, electric potential, voltage
Parallel plate capacitors
Parallel plate capacitors with dielectrics
Electric energy storage
Electrons accelerated in an old TV picture tube
Extra problems on “Electrostatic potential energy of point
charges”
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PART 1
Electric potential energy, electric
potential, voltage
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Strategy:
•
We have some charge distribution, producing some electric field in its vicinity. We take a point
charge qtest and bring it into that field. We then notice that the point charge qtest sitting at point
A “might” have some electrostatic potential energy, UA, stored in it. How can we justify that?
•
We justify that by, first, simplifying the situation. The charge distribution is taken to be pointlike, Q. So we have Q and qtest some distance apart. We compare this situation with two other
situations from mechanics: a mass attached to a compressed spring (elastic potential energy),
and a mass held above the ground (gravitational potential energy). By analyzing our
electrostatic situation and comparing it to the mechanical examples, we conclude that qtest
does indeed have electrostatic potential energy UA stored in it.
•
By using the general prescription for calculating U in mechanics, we find that in our simple (Q,
qtest) situation,
UA = kqtestQ/rA.
•
We then go back to the general situation and define the electrostatic potential φA at point A to
be
φA = UA /qtest (general definition).
•
As a result, in our simple (Q, qtest) situation,
φA = kQ/rA.
•
Now, if we have two points, A and B, the voltage between them is defined as the difference
between the two potentials,
VAB = φA - φB (general definition).
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(a single source charge, Q>0)
some charge distribution
(this result also works for
charges of any signs, + or - )
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PART 2:
Parallel plate capacitors
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What we ultimately want is to find out how the voltage V across the capacitor is related to the
amount of positive charge +Q stored on the positive plate (the negative plate will store the
same but negative amount of charge -Q).
This formula shows how the
voltage V across the capacitor is
related to the electric field E
inside it.
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This is how you
calculate capacitance C
if you know A and d.
To increase C, roll it up into a cylinder! Just
make sure the plates don’t touch!
This is what we really
wanted, how Q depends
on V (or vice versa).
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unit of capacitance
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Estimating voltage, V, b/w Earth
and cloud during a thunderstorm:
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Estimating voltage, V, b/w Earth
and cloud during a thunderstorm:
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PART 3:
Parallel plate capacitors with
dielectrics
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Dielectric is a material that cannot conduct a steady current. Charged particles
(electrons and atomic nuclei) inside a dielectric can only shift by a tiny amount
under the action of the externally applied electric field, which leads to polarization.
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Typically, the dielectric constant қ ranges from 1 to a
few 100’s.
Vacuum: қ = 1
Air: қ = 1.00059 (almost like vacuum for all practical
purposes)
Paper: қ = 3.7
Mica: қ = 5.4
Pure distilled water: қ = 80
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PART 4:
Electric energy storage
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This is for the capacitor and the battery that are used to build our own
camera flash
a
Here we are comparing the electrostatic energy
stored in the capacitor with the gravitational
energy stored in our textbook held above the
ground.
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RECALL OUR PLAN:
1.
2.
3.
4.
5.
Electric potential energy, electric potential, voltage
Parallel plate capacitors
Parallel plate capacitors with dielectrics
Electric energy storage
Electrons accelerated in an old TV picture tube
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PART 5:
Electrons accelerated in an old TV
picture tube
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ASIDE #2. LCE
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The only reason for small q is b/c I don’t want this q
to push around the charges that produced φ at
locations A, B, and everywhere else. If those charges
got pushed, then the φ they produce would change
everywhere, which wouldn’t be good…
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Problem
3) The electrons in a TV picture tube are accelerated
from rest through a potential difference of 25 kV.
What is the speed of the electrons after they have
been accelerated by this potential difference?
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How can an electron freely “fall” from lower φA to higher φB, while increasing
its speed and kinetic energy? “Preposterous!”, you say.
Well, that’s because you developed your intuition about potential energy using
gravity as an example.
With gravity, the only possibility to pick up speed is indeed to fall from high φB
to low φA.
But electricity is a little different. In electricity you have two kinds of charges. If
gravity (where the role of the “gravitational charge” is played by the mass m of
the object) had two kinds of charges, then a negative mass m < 0 would
spontaneously fly up in the air increasing its speed the moment you let it go antigravity!
So, roughly speaking, an electron is like a negative mass in gravity. It speeds
up from low φA to high φB, all by itself.
As the electrons fly off, the
external circuit keeps
supplying new electrons to
the negative plate, so no,
the plate is not losing
negative charge. It stays at
the same potential at all
times.
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Problem
3) The electrons in a TV picture tube are accelerated
from rest through a potential difference of 25 kV.
What is the speed of the electrons after they have
been accelerated by this potential difference?
9.4 x 107 m/s
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The End
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