Electric Energy
Electrical Potential Energy
 Potential energy is the negative of the work done by
conservative forces.
• Potential energy DU = -Wcon
 Electrical work is done by the Coulomb force.
• Electrical potential energy
Changing State
 A charge in an electric field is
subject to a force.
 
W  F  d  -qEd
 Moving the charge against the
field requires work.
 The state of the charge is
q
d
q
E
F
changed to increase the
potential energy.
Potential Difference
 The potential energy is
expressed as a difference of
the energy of two states.
DU  qEd
 The electric potential can be
expressed with respect to a
test charge.
q
DU
d
q
E
F
DU
DV 
q
Point Potential
 Coulomb’s law is
mathematically similar to
gravitational force.
• Define potential energy
similarly
• Point charge Q
• Test charge q
 Apply the definition of the
 1 1
DU  kqQ - 
r r 
i 
 f
 1 1
DV  kQ - 
r

r
f
i


electric potential.
 Like gravity zero is at infinity.
kQ
V
r
Potential Curve
 The point potential can be attractive or repulsive.
• Attraction like gravity
Arbitrary Zero
 The zero of potential energy is
arbitrary.
 U can be defined, but DU is
what really matters.
• Compare energy to work
 We can measure the change in
Vf
electric potential V.
• No experiment reveals the
specific value
q
E
V=0
Charge Energy
 The electric force is
conservative.
• Energy is conserved
• Independent of the experiment
 Suppose that charge were not
conserved.
• An experiment would be able
to cause some charge to
vanish
• Loss of specific amount of
potential energy
• Inconsistent with energy
conservation
Vf
q
E
V=0
Conservation of Charge
 The arbitrary zero of the potential was the heart of the
preceding contradiction.
 To have an electric potential independent of the choice of
zero, and be conservative, requires charge conservation.
 This is an example of symmetry in physics.
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