Electric Potential Energy
As in all other interactions in physics, energy is closely related to electrical
interactions.
When a charge moves it must do work or have work done on it.
In either case there is a change in the charge's
PE or KE or both (TE will remain constant)
The absolute PE cannot be measured but
changes in PE can.
PE = W, W = Fd so
PE = Fd, E = F/Q, F = QE so
PE = QEd Dec 7­11:28 AM
Dec 7­11:34 AM
When work is done there is a change in PE so the difference in electrical PE between two points equals the work. Also
F = (kQQ) / r2, and PE = Fd
Fr = (kQQ) / r so
PE = (kQQ) / r
Dec 7­11:44 AM
The amount of work needed to move a charge from one point to the other is an extremely important concept and quantity called potential difference or just potential.
Jan 9­6:55 AM
In most cases the sign of V can be ignored
V = W/Q measured in J/C However in some cases ­ 1J/C = 1V (Volt)
V = V ­ Vo = W/Q
V = potential difference (V)
W = work (J)
Q = charge (C)
potential & field.asx
When work is done on the charge against the electric field, V is positive
When work is done by the charge in the same direction as the electric field, V is negative
Dec 7­11:47 AM
Jan 9­7:17 AM
1
Potential difference and electric potential energy are similar.
Potential difference always involves comparing
the electric potential energy at two locations.
There is no absolute zero potential but a reference can be selected to be zero.
The earth or ground is usually selected to be
zero.
Dec 7­11:47 AM
Dec 7­11:47 AM
E = F/Q or F = QE (field theory) for point charges
The effects of charge distribution can be described equally well by field theory as well
as by electric potential difference.
W = Fd so W = QEd (1)
V= W/Q or W = QV (2)
setting 1 & 2 equal to each other
QV = QEd or E = V/d (potential difference)
for charged surfaces
Jan 9­7:05 AM
Jan 18­11:57 AM
E = V/d in V/m
Electric field in terms of potential difference is called potential gradient.
+
+
Would work be done to move
the smaller charge along each of the colored arrows?
work done on the charge
work done by the charge
no work
Jan 18­12:06 PM
Jan 19­12:39 PM
2
Potential difference can be represented by drawing equipotential (equal potential) lines (2D) or surfaces (3D).
Equipotential lines are perpendicular to the field at all locations.
No work is required to move along the equipotential line.
Field lines have a beginning and an
end, equipotential lines are continuous.
A conductor must be at the same potential everywhere in a static situation. The surface of a conductor is an equipotential surface.
Jan 19­12:46 PM
Jan 19­2:52 PM
Potential difference has been related to work.
V = W/Q
Potential difference has been related to electric field V = Ed
Dotted lines are equipotential
Jan 19­2:54 PM
Potential difference can also be related to charge.
E = (kQ)/r2 and V = Ed
Combining the two formulas:
V = (kQ)/r2(d) so V = (kQ)/r (for point charges)
It is easier to work with V than E.
E is a vector, V is a scalar. Jan 22­7:03 AM
Jan 22­6:59 AM
1 J is the energy gained by moving a 1 C charge across a potential difference
of 1 V.
The Joule is too large when dealing with atoms and molecules.
Later in nuclear physics we will need to work
with small energy changes and the electron volt has been designed for this purpose.
Jan 22­7:07 AM
3
The electron volt (eV) is the energy acquired
by moving 1 electron through a potential
difference of 1 V.
W = VQ = 1V(1.6 x 10­19C) = 1.6 x 10­19J = 1 eV
Practice ­
FOC ­ Pg. 592 # 2, 4, 6, 9, 11, 12
HO ­ 22 16 17 18
An electron that moves through 1000 V will
gain or lose 1000 eV as an example.
eV is not an SI unit.
Jan 22­7:09 AM
Jan 24­8:29 AM
4