Download 17.5 Electric Potential due to Point Charges

ConcepTest 16.1 Electric Charge I
Two charged balls are
repelling each other as
they hang from the ceiling.
What can you say about
their charges?
1) one is positive, the other
is negative
2) both are positive
3) both are negative
4) both are positive or both
are negative
The fact that the balls repel each
other only can tell you that they
have the same charge, but you do
not know the sign. So they can
be either both positive or both
negative.
Follow-up: What does the picture look like if the two balls are oppositely
charged? What about if both balls are neutral?
ConcepTest 16.2 Conductors I
A metal ball hangs from the ceiling
1) positive
by an insulating thread. The ball is
2) negative
attracted to a positive-charged rod
3) neutral
held near the ball. The charge of
4) positive or neutral
the ball must be:
5) negative or neutral
Clearly, the ball will be attracted if its
charge is negative. However, even if
the ball is neutral, the charges in the
ball can be separated by induction
(polarization), leading to a net
attraction.
remember
the ball is a
conductor!
Follow-up: What happens if the metal ball is replaced by a plastic ball?
ConcepTest 16.3 Conductors II
Two neutral conductors are connected
1)
0
0
by a wire and a charged rod is brought
2)
+
–
3)
–
+
4)
+
+
5)
–
–
near, but does not touch. The wire is
taken away, and then the charged rod
is removed. What are the charges on
the conductors?
While the conductors are connected, positive
0
0
?
?
charge will flow from the blue to the green
ball due to polarization. Once disconnected,
the charges will remain on the separate
conductors even when the rod is removed.
Follow-up: What will happen when the
conductors are reconnected with a wire?
ConcepTest 16.4 Coulomb’s Law I
What is the magnitude
1) 1.0 N
2) 1.5 N
of the force F2?
3) 2.0 N
F1 = 3N
Q
Q
F2 = ?
4) 3.0 N
5) 6.0 N
The force F2 must have the same magnitude as F1. This is
due to the fact that the form of Coulomb’s Law is totally
symmetric with respect to the two charges involved. The
force of one on the other of a pair is the same as the reverse.
Note that this sounds suspiciously like Newton’s 3rd Law!!
ConcepTest 16.5 Coulomb’s Law III
The force between two charges
1) 9 F
separated by a distance d is F. If
2) 3 F
the charges are pulled apart to a
3) F
distance 3d, what is the force on
4) 1/3 F
each charge?
5) 1/9 F
F
Originally we had:
F
Q
Q
Fbefore = k(Q)(Q)/d2 = F
Now we have:
Fafter = k(Q)(Q)/(3d)2 = 1/9 F
d
?
?
Q
Q
3d
Follow-up: What is the force if the original distance is halved?
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17.1 Electric Potential Energy and Potential Difference

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Review of work and energy
The electrostatic force is
conservative.
W = Fd = qEd
PEb – PEa = -W
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17.1 Electric Potential Energy and Potential Difference

The electric potential is the electric potential energy
per unit charge.
PEa
Va 
q

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Voltage
PEb  PEa
Vba 
q
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17.2 Electric Potential and Electric Field


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If we have uniform electric field, then W = -qVba
and W = qEd
Therefore Vba = -Ed
or
Vba
E
d
In general, the electric field is the rate at which the
electric potential decreases over a distance.
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17.3 Equipotential Lines
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17.3 Equipotential Lines
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No work is required to move along an equipotential
line and E is perpendicular to the line.
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17.4 The Electron Volt

The energy acquired by a charge (± e) after passing
through a potential difference of 1 volt.
1 eV = 1.6 x 10-19 J
Lichtenberg Figures
and
Lightning
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17.5 Electric Potential due to Point Charges

If V = 0 at r = ∞ then
Q
V k
r

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The principle of superposition
allows us to determine the
potential due to multiple
charges
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17.5 Electric Potential due to Point Charges
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