Physics 212 Lecture 7, Slide 1

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Physics 212 Lecture 7
Today's Concept Conductors and
Capacitance Exam 1 in 8 days! Review Session
next Monday at 400 in 100 Noyes
PLEASE HELP!!! SOOOOO MUCH INFORMATION TO DIGEST
did god know he was making phys 212 ridiculously
hard when created earth?
2
How confident are you in your understanding of
the concepts presented in the prelecture? A  I
am confused by all of it. B  I understand a
little but I am confused by most of it. C  I
understand some parts and I am confused by other
parts. D  I understand most of itE  I
understand everything
3
Your Thoughts
BRING THE HEAT!!!! HARDCORE PROBLEMS!!!!!!
More Gauss plzzz
capacitance! charges moving around between plates
and within and outside of conductors depending on
where charges are located. basically everything
)
how introducing an uncharged plate affects a
parallel plate capacitor.
Differences between voltage and capacity. .
just do your thing in lecture and I'll tkae some
more notes.
I feel like the examples given in the
pre-lectures are WAY simpler than the homework,
and I have a sickening feeling that the test
questions will be more like the homework. Can we
do more complicated problems in lecture in order
to prepare us better?
why is this lecture only 50 minutes while PHYS
211 was 75 minutes?
4
Summary of your questions

• Adding conductor between the plates of a
  capacitor
• We have prepared exercises to understand this
  example

2) Capacitors and Calculations What is a
Capacitor? Calculation of Capacitance ? We
will calculate the capacitance of a cylindrical
capacitor
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Conductors
I'd love a list of things we're supposed to
assume when we see metal or conducting or
non-conducting sphere in a problem.

• Charges free to move
• E0
• Equipotentials

5
6
Preflight 2
Since, relative to V0 at infinity, VkQ/r, the
potential at the surface of A will be smaller
than that at the surface of B since A has a
larger radius.
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7
Preflight 4
Once the two sphere conductors are connected, the
entire system is essentially one conductor.
Charges will flow until there is no electrical
potential difference
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8
Preflight 6
The charge will tend to flow "downhill" from the
sphere with the larger potential to the sphere
with the smaller potential, which means from
sphere B to sphere A.
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Example Problem
Two parallel plates of area A separated by a
distance d carry equal an opposite charge Q0. An
uncharged conducting plate having thickness t is
slipped midway between the plates. How does the
voltage between the plates change?
Q0
d
-Q0
d
t
the whole business with inserting the plate
between two charged plates
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As in Pre-Lecture 7
First figure out DV without conductor
Q0
Integrate from the bottom plate to the top plate
DV Ed
d
-Q0
so
Also, since
not too sure about how E, C, and V differ.
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After the conductor is inserted, the charge on
the plates is Q1. Compare this to Q0.
Q0

• Q1 lt Q0
• Q1 Q0
• Q1 gt Q0

d
-Q0
We haven't touched the plates so Q cant change.
Q1
d
t
-Q1
The green thingy in between the red and blue
thingies. I've never had to pluralize "thingy"
before and it doesn't look right.
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12
Q0
d
t
-Q0
What is the total charge induced on the bottom
surface of the conductor?

• Q0
• -Q0
• 0
• Its ve but the magnitude is not known
• Its ve but the magnitude is not known

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13
Q0
E
E 0
E
-Q0
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14
Now figure out V out as a function of distance
from the bottom conductor. Choose V0 to be at
the bottom conductor
Q0
r
E 0
d
t
-Q0
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15
Preflight 8
Suppose the electric field is zero in a certain
region of space. Which of the following
statements best describes the electric potential
in this region?
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Now figure out DV with conductor
Q0
Again, integrate from the bottom plate to the top
plate DV E(d-t)
t
d
-Q0
so
So to make DV the same as before you have to make
Q bigger
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17
Preflight 10
Two parallel plates carry equal and opposite
charge Q0. The potential difference between the
two plates is measured to be V0. An uncharged
conducting plate (green) is slipped into the
space between the plates without touching either
one. The charge on the plates is adjusted to a
new value Q1 such that the potential difference
between the two plates remains the same as
before.
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18
Now figure out new capacitance
Q0
t
d
DV E(d-t)
-Q0
We just showed
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Preflight 12
Two parallel plates carry equal and opposite
charge Q0. The potential difference between the
two plates is measured to be V0. An uncharged
conducting plate (green) is slipped into the
space between the plates without touching either
one. The charge on the plates is adjusted to a
new value Q1 such that the potential difference
between the two plates remains the same as
before.
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Why is energy density important?
BANG
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What are you doing to me man!!! Could you please
include more of the worked examples in the
lecture, or include some examples from the
homework, because I fell like I am helpless
because most of the homework refers you to a
worked problem for help, but I cannot figure out
what they are doing in order to get the answers
that they do. They don't really show you how to
get an answer to a problem, because they tell you
how to solve a specific problem and do not show
you how to get it from the problem on the
homework. Could you give us some shortcuts in how
to solve for a certain quantity, and then show us
the various steps to go about attaining each of
those quantities? I would greatly appreciate it.
Thanks!
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Calculation
cross-section
a4
a3

• A capacitor is constructed from two conducting
  cylindrical shells of radii a1, a2, a3, and a4
  and length L (L gtgt ai).
• What is the capacitance C of this device ?

a2
a1
metal
metal

• Conceptual Analysis

But what is Q and what is V.. They are not given??

• Important Point C is a property of the
  object!! (concentric cylinders here)
• Assume some Q (i.e., Q on one conductor and Q
  on the other)
• These charges create E field in region between
  conductors
• This E field determines a potential difference V
  between the conductors
• V should be proportional to Q the ratio Q/V is
  the capacitance.

33
23
Calculation
cross-section
a4
a3

• A capacitor is constructed from two conducting
  cylindrical shells of radii a1, a2, a3, and a4
  and length L (L gtgt ai).
• What is the capacitance C of this device ?

a2
a1
s
metal
metal

• Conceptual Analysis
• How will Capacitance depend on separation sa3-a2
  between shells?
• A) C increases with increasing s
• B) C decreases with increasing s
• C) C wont depend on s

35
24
Calculation
cross-section
a4
a3

• A capacitor is constructed from two conducting
  cylindrical shells of radii a1, a2, a3, and a4
  and length L (L gtgt ai).
• What is the capacitance C of this capacitor ?

a2
a1
metal
metal

• Strategic Analysis
• Put Q on outer shell and Q on inner shell
• Cylindrical symmetry Use Gauss Law to calculate
  E everywhere
• Integrate E to get V
• Take ratio Q/V should get expression only using
  geometric parameters (ai,L)

25
Calculation
cross-section
a4
a3

• A capacitor is constructed from two conducting
  cylindrical shells of radii a1, a2, a3, and a4
  and length L (L gtgt ai).
• What is the capacitance C of this capacitor ?

Q
a2
a1
-Q
metal
metal
Why?
26
Calculation
cross-section
a4
a3

• A capacitor is constructed from two conducting
  cylindrical shells of radii a1, a2, a3, and a4
  and length L (L gtgt ai).
• What is the capacitance C of this capacitor ?

Q
a2
a1
-Q
r gt a4 E(r) 0
metal
metal
Where is Q on outer conductor located? (A) at
ra4 (B) at ra3 (C) both surfaces
(D) throughout shell
Why?
We know that E 0 in conductor (between a3 and
a4)
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Calculation
cross-section
a4
a3

• A capacitor is constructed from two conducting
  cylindrical shells of radii a1, a2, a3, and a4
  and length L (L gtgt ai).
• What is the capacitance C of this capacitor ?

Q
a2
a1
-Q
-
r gt a4 E(r) 0
metal
Where is -Q on inner conductor located? (A) at
ra2 (B) at ra1 (C) both surfaces
(D) throughout shell
Why?
28
Calculation
cross-section
a4

• A capacitor is constructed from two conducting
  cylindrical shells of radii a1, a2, a3, and a4
  and length L (L gtgt ai).
• What is the capacitance C of this capacitor ?

a3
Q
a2
a1
-Q
-
r gt a4 E(r) 0
metal
Why?
29
Calculation
cross-section
a4

• A capacitor is constructed from two conducting
  cylindrical shells of radii a1, a2, a3, and a4
  and length L (L gtgt ai).
• What is the capacitance C of this capacitor ?

a3
Q
a2
a1
-Q
-
r gt a4 E(r) 0
a2 lt r lt a3
metal
r lt a2 E(r) 0 since Qenclosed 0

• What is V?
• The potential difference between the conductors

What is the sign of V Vouter - Vinner? (A)
Vouter-Vinner lt 0 (B) Vouter-Vinner 0
(C) Vouter-Vinner gt 0
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Calculation
cross-section
a4

• A capacitor is constructed from two conducting
  cylindrical shells of radii a1, a2, a3, and a4
  and length L (L gtgt ai).
• What is the capacitance C of this capacitor ?

a3
Q
a2
a1
-Q
-
r gt a4 E(r) 0
r lt a2 E(r) 0
a2 lt r lt a3
metal
V proportional to Q, as promised