Electric Potential Energy
Moving Charges in an Electric Field
When you move a charge q from point
A to B in an electric field it requires
work.
For fields that have a uniform field strength ,
the change in the electric potential energy when
a charge is moved d is given by:
EE  ( / )qd
1
The only energy transformation that can occur
when a charge moves in an electrical field is
between electric potential energy and kinetic
energy of the charge.
 Ee  Ek
Fortunately we do not need to consider
transferring energy to gravitational potential or
elastic potential energies.
Furthermore, we will limit the scope of our
energy transformation questions to electric
fields that are created by:
(A) Uniform Fields (Parallel plates)
(B) Point charges
2
Try Practice questions 1 - 3, page 349.
1. (a)
1. (b)
2.
3.
Electric Potential:
So far we have been speaking
of a quantity of electric fields
called field strength,  , which
helps to describe the force any
given charge would experience
in that particular field:
F   qt
which operates like
F  gm
for gravity.
3
The second quantity of an electric field is called
electric potential, V, which helps to describe the
electric potential energy any given charge would
experience in that particular field:
The electric potential, V, has the unit of “volts”
where 1 V = 1 J/C.
When a charge is then moved from one point to
a different area in a field (changing the potential
energy, EE) there would then be a potential
difference as well.
The potential difference is given by the
equation:
V =
Ee
qt
4
Uniform Fields (Parallel Plates)
For uniform electric fields the two
quantities of the field, field strength
and field potential, can now be
related.
W  Fd and F  Fe  q
Since W  ΔEe  qtVAB  qtd
qtVAB  qtd
VAB  d

V
d
For parallel plates, where the field strength is constant,
can now be defined as:
V

d
5
Practice Problems 1 – 2, page 353
Do # 1 – 10, page 354
6
Point Charges:
What about the electric potential energy of a
point charge in an electric field?
Recall that the equation for the
force between any two charges
(q1, q2) is:
Fe =
kq1 q2
r
2
As with gravitational potential energy (Eg) the
Electrical Potential Energy equation can be
determined from the area under the FE vs r curve
(using a weighted average) to be:
kq1 q2
EE =
r
So when a charge moves in a field created by a
point charge they transfer energy from Ee (as
shown in this graph below) to Ek (and therefore
speed of the charge)
7
Ee  Ee 2  Ee1  Ek

kqm qt kqm qt

r2
r1
 1 1
 kqm qt   
 r2 r1 
We can consider the electric potential for a unit
positive test charge qt. So the potential energy
per unit positive charge, once again called the
electric potential (V), is given by:
kqm qt
kq
V = E e = r = m (Units of J/C i.e. volts)
qt
qt
r
8
So the potential difference
between two points in a nonuniform field created by a
point charge qm is given by:
V 
E e
qt
kqm qt kqm qt

r2
r1

qt

kqm kqm

r2
r1
 1 1
 kqm   
 r2 r1 
Try Practice Problems 1 and 4, page 360
9
Do questions 1 – 8, page 361
10