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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.
4/28/17
Oregon State University PH 213, Class #12
1
Which electric potential graph
below describes this 
electric field?
4/28/17
Oregon State University PH 213, Class #12
2
Which electric potential graph
below describes this 
electric field?
4/28/17
Oregon State University PH 213, Class #12
3
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.)
4/28/17
Oregon State University PH 213, Class #12
4
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
5
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.
4/28/17
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
6
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.]
4/28/17
Oregon State University PH 213, Class #12
7
Summary of Electrostatics
Field “payload”
E
·q
Effect
=
E = –dV/ds
V
4/28/17
F
F = –dUE/ds
·q
=
UE
Oregon State University PH 213, Class #12
8