Download Electric Potential Energy

Electric Potential Energy
Recall, for point masses, the force of gravity
and gravitational potential energy are:
GMm and
Fg  2
r
GMm
Eg  
r
For point charges, it would follow that:
kq1q 2
F  2
r
and
kq1q 2
E  
r
Electric Potential Energy
However, how are electric fields and
gravitational fields different?
Unlike charges attract
+q
-q
Like charges repel
+q
+q
Therefore, electric potential energy can be
positive or negative:
kq1q 2
E  
r
Electric Potential Energy
How do you increase the electric potential
energy for charges?
UNLIKE CHARGES
+q
-q
Increase the
separation between
the charges.
LOW potential
HIGH
potential energy
energy
LIKE CHARGES
+q
+q
HIGH
LOW potential
potential energy
energy
Decrease the
separation between
the charges.
Electric Potential Energy
Electric potential energy is defined as zero
when two charges are an infinite distance apart
E g  0 as
r
In other words, our reference “point” is infinity.
The change in potential energy is the work
done by the electrostatic force when moving a
point charge from infinity to a distance r from
another point charge.
W  E 
r
+q
Electric Potential Energy
Electric potential energy
versus separation graph
kq1q 2
E 
r
E
Like charges
0
E  0
r
Unlike charges
E  0
Electric Potential
All charges have the potential to store energy
in their electric field.
+q2
+q1
There is no potential
energy stored until
another charge is
placed in the field of
the first charge.
Electric Potential
The electric potential is defined as the
electric potential energy per unit charge.
E
V
q2
For point charges:
kq1
V
r
units: volt (V)
1 V = 1 J/C
Electric Potential
Potential difference is the difference in
electric potential from one point to another.
V  VB  VA
B
A
+q1
Also referred to
as “voltage”
Potential difference
is path independent
Electric Potential
Electric potential can be positive or negative
depending on the sign of the charge producing
the potential.
kq1
V
r
A positive charge produces a positive potential.
A negative charge produces a negative potential.
Electric Potential
Case 1: q1 > 0 and q2 < 0
q1
q2
+
-V
A
B
A
 2V
VB  1V
V  VB  VA
 1V  2V
 1V
E   qV
  1C  1V 
 1J
If a negative charge (-1 C) is placed at A and then
moved to B, potential energy should increase.
Electric Potential
Case 1: q1 > 0 and q2 > 0
q1
q2
+
+V
A
B
A
 2V
VB  1V
V  VB  VA
 1V  2V
 1V
E   qV
  1C  1V 
 1J
If a positive charge (+1 C) is placed at A and then
moved to B, potential energy should decrease.
Electric Potential
Case 1: q1 < 0 and q2 < 0
q1
-
q2
-V
A
A
 2V
V


1V
B
B
V  VB  VA
 1V   2V 
 1V
E   qV
  1C  1V 
 1J
If a negative charge (-1 C) is placed at A and then
moved to B, potential energy should decrease.
Electric Potential
Case 1: q1 < 0 and q2 > 0
q1
-
q2
+V
A
A
 2V
V


1V
B
B
V  VB  VA
 1V   2V 
 1V
E   qV
  1C  1V 
 1J
If a positive charge (+1 C) is placed at A and then
moved to B, potential energy should increase.
Electric Potential
The potential difference is related to the
electric field strength.
d
A
B
Two points, A and B, are
separated by d and have
a potential difference of:
V  VB  VA
V

d
or
V  d
Electric Potential
Recall, Ohm’s Law:
I
V  IR
+
V
-
Here, “V” actually refers
to potential difference.
Why is current proportional to voltage?
R
Electric Potential
Equipotential lines can be drawn around
charges to indicate constant electric potential.
+q1
At every point on this
line, the electric
potential is the same.
At every point on this
line, the electric
potential is the same.
Example Problem
For a point charge of 5e C, determine the following:
a) electric field strength 5.0 cm away from the charge
b) electric potential 5.0 cm away from the charge
c) electric potential energy if a -2e C charge is placed
5.0 cm from the 5e C charge
d) the work required to move the -2e C charge from
5.0 cm away to 10. cm away from the 5e C charge
Answers:
a) 2.9x10-6 N/C
b) 1.4x10-7 V
c) 4.6x10-26 J
d) 2.3x10-26 N/C
Example Problem
Summary
In general:
F

q
E
V
q
V

d
W  E 
For point charges:
kq1q 2
F  2
r
kq
 2
r
kq1q 2
E 
r
kq
V
r