Transcript Class #12 - Department of Physics | Oregon State

Summary of Electrostatics
Field “payload”
E
·q
Effect
=
E = –dV/ds
V
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F
F = –dUE/ds
·q
=
UE
Oregon State University PH 213, Class #12
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The Voltage Difference Created by
a Set of Parallel Plates
Since the E-field between two plates is a constant, it’s easy
to find the work necessary to move a charge against that
field (just like moving a mass against a constant local g)
for a distance Dd:
|DW| = |DUE| = |qEDd|
So the potential difference (also called the voltage
difference) magnitude is |DV| = |DUE/q| = |E||Dd|
But you are moving a displacement Dd against the field to
increase voltage:
DV = DUE/q = –|E|Dd
So in general (not just between plates): |E| = –dV/ds,
where ds is an incremental distance moved along the
direction of E.
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Oregon State University PH 213, Class #12
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A capacitor is essentially a pair of parallel,
oppositely-charged conductive plates.
The electric potential inside a capacitor…
1. is constant
2. increases linearly from the negative to the positive
plate
3. decreases linearly from the negative to the positive
plate
4. decreases inversely with distance from the
negative plate
5. decreases inversely with the square of the distance
from the negative plate
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Oregon State University PH 213, Class #12
3
The electric potential inside a capacitor
1. is constant
2. increases linearly from the negative to
the positive plate
3. decreases linearly from the negative to
the positive plate
4. decreases inversely with distance from
the negative plate
5. decreases inversely with the square of
the distance from the negative plate
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Oregon State University PH 213, Class #12
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Rank in order, from largest to smallest, the
potentials Va to Ve at the points a to e.
1.
2.
3.
4.
5.
Vd = Ve > Vc > Va = Vb
Vb = Vc = Ve > Va = Vd
Va = Vb = Vc = Vd = Ve
Va = Vb > Vc > Vd = Ve
Va = Vb = Vd = Ve > Vc
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Oregon State University PH 213, Class #12
5
Which electric potential
graph describes this
electric field?
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Oregon State University PH 213, Class #12
6
Which electric potential
graph describes this
electric field?
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Oregon State University PH 213, Class #12
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Summary of Electrostatics
Field “payload”
E
·q
Effect
=
E = –dV/ds
V
4/22/16
F
F = –dUE/ds
·q
=
UE
Oregon State University PH 213, Class #12
8
The Strength of the Electric Potential Field
(Voltage) Created by a Point Charge
Q: It’s all well and good to look at simple, uniform electrical
fields between parallel charged plates, but what about when the
fields are not uniform—such as when point charges create
them? What is the electric potential (voltage) at any point in
space due to a nearby point charge, q?
A: V = kq/r, where r is the distance from q to the point in
question. This is a result of integrating Again, the sign of the
charge again indicates how the potential changes in the space
around it.
Note where we have selected V = zero only at an infinite
distance from q. (The analogy to gravity goes on.)
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Oregon State University PH 213, Class #12
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Rank in order, from largest to smallest, the
potential energies Ua to Ud of these four pairs
of charges. Each + symbol represents the
same amount of charge.
A.
B.
C.
D.
E.
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U a = Ub > Uc = Ud
U b = Ud > Ua = Uc
U a = Uc > Ub = Ud
U d > Uc > Ub > Ua
U d > Ub = Uc > Ua
Oregon State University PH 213, Class #12
10
Rank in order, from largest to smallest, the
potential energies Ua to Ud of these four pairs
of charges. Each + symbol represents the
same amount of charge.
A.
B.
C.
D.
E.
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U a = Ub > Uc = Ud
U b = Ud > Ua = Uc
U a = Uc > Ub = Ud
U d > Uc > Ub > Ua
U d > Ub = Uc > Ua
Oregon State University PH 213, Class #12
11
Rank in order, from largest to smallest, the electric
potentials (“voltages”) of these four collections of
charge [measured at the midpoint between them].
Each + symbol represents the same amount of
charge.
[Voltage is a field—a description of a certain
property—of a point in space, so we must specify
that point.]
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Oregon State University PH 213, Class #12
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