Download Electric Potential Lecture

Electric Potential Energy
and Electric Potential Difference
Mike Maloney
AP Physics
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Potential Energy in General
o Remember from last year, things on Earth
have a Gravitational Potential Energy
[GPE] based on their height, or distance
from the surface of the Earth.
o Charged objects in an Electric Field act
very much the same way, they also have
an Electrical Potential Energy [EPE,U]
based on their position, or distance from
a charge.
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GPE vs. U (going from A to B)
+++++++++++++++
A
A
q
Fg= mg
ha
Fe= q0E
d
B
hb
B
d
q
Fe= q0E
Fg= mg
--------------
• GPE = mgh
• GPEA > GPEB
• ΔPE = PEB – PEA= - WAB
• WAB = Fg•d = mgΔh
• U A > UB
• ΔU = UB - UA = -WAB
• WAB = Fe•d = qE•d
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Electric Potential Energy (U)
o Electric Potential Energy decreases when
charges are brought into more favorable
conditions.
ΔU < 0
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Electric Potential Energy (U)
o Electric Potential Energy increases when
charges are brought into less favorable
conditions.
ΔU > 0
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ΔU, Work and Energy
For a positive test charge to
be moved a distance d
against the field, work must
be done against the electric
force, or you could say the
electrical field does negative
work.
The electric potential energy
has increased, and ΔU is
positive, U2 > U1
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ΔU, Work and Energy
For a negative test charge to
be moved a distance d
against the field, the opposite
is true, the electrical field
does positive work.
The electric potential energy
decreases, and ΔU is
negative, U2 < U1
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Electric Potential Difference for 2 Plates
o Since F = q0E, the work done to move the
charge depends on the charge itself. Since
charges can change, it is useful to determine the
Work per unit charge.
WHAT
DOES
THIS
o The is called
the Electric
Potential
Difference [ΔV].
W AB U A U B
W AB qEd
IN WORDS?
=
= Ed
= MEAN
−
q0
q0
q
q
q
o The U/q0 value is called the “electric potential” [V]
U
V=
q
ΔU
ΔV = VB − V A =
= − Ed
q
The units are joules/coulomb or VOLTS (V).
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Milikan’s Oil Drop
o Robert Millikan received a
Nobel Prize for determining the
charge on the electron. To do
this, he set up a potential
difference between two
horizontal parallel metal plates.
o He then sprayed drops of oil between the plates and
adjusted the potential difference until drops of a certain size
remained suspended at rest between the plates, as shown
above.
o When he measured the charge of thousands of drops, they
all ended up being an integer multiple of
1.6 x 10-19 coulombs.
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Solving Milikan’s Oil Drop
E = 10,000 N/C
mdrop = 3.27 x 10-16 kg
a) What is the magnitude of the
charge on this drop?
b) Is it a multiple of 1.6 x 10-19?
c) The electric field is downward, but the electric force on
the drop is upward. Explain why.
d) If the distance between the plates is 0.01 m, what
potential difference between the plates?
e) The oil in the drop slowly evaporates while the being
observed, but the charge on the drop remains the same.
Indicate whether the drop remains at rest, upward, or
moves downward.
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Electric Potential and U from One Charge
o Since ΔV = E • d, if we assume
¾ VB = 0 (grounded), so ΔV = V
¾ d = r (for E at a distance r from a charge)
r
q
¾E=k 2
r
» So,
V =k
q
r
[Electric Potential due to a point charge]
This is a scalar quantity, so you can
Add them algebraically, not vectorly
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Potential Energy of a Pair of Charges
o If we now add a second charge [q2], we can
get the potential energy due to the two
charges interacting with each other by finding
You can also think of the work as Force x displacement
the work done to bring the charge from infinity
q ⋅ q2
(V=0) to a distance “r” from charge “q”
W = −U = F ⋅ d = q2 E ⋅ d = k
r
q ⋅ q2
q
W = −U = q2V = q2 ⋅ k = k
r
r
[Electric Potential due to a point charge]
This is a scalar quantity, so you can
Add them algebraically, not vectorly
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Equipotential Lines/Surfaces
o All points have the same potential difference on an
equipotential line or surface.
o ΔV between any two points on an equipotential
surface is 0.
o So, NO Work is needed to move along an
equipotential surface
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Equipotential Lines of 2 Plates
Draw field lines for the charge configuration below. The field is 600 V/m,
and the plates are 2 m apart. Label each plate with its proper potential, and
draw and label 3 equipotential surfaces between the plates. You may ignore
edge effects.
V1 > V2 > V3
------------------ -------------------
Vlow
V3
E-field
V2
V1
+ + + + + + + + + + + + + + + + + + + + + + + ++ +
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Vhigh
Equipotential Lines of a Point charge
o Draw a negative point charge of -Q and its associated electric field.
o Draw 3 equipotential surfaces such that ΔV is the same between the
surfaces, and draw them at the correct relative locations.
o What do you observe about the spacing between the equipotential
surfaces?
-Q
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