Physics 2112
Unit 5: Electric Potential Energy
Today’s Concept:
Electric Potential Energy
Unit 5, Slide 1
Where we’re headed….
Force
2111
Energy
2112
E Field
???
Unit 5, Slide 2
Recall from Mechanics:

r2
 
W =  F dr

r1
F
dr
WTOT = DK
W>0
Object speeds up ( DK > 0 )
W<0
Object slows down ( DK < 0 )
F
dr
or
F
dr
F
dr
W=0
Constant speed ( DK = 0 )
Unit 5, Slide 3
Prelecture Question
Masses M1 and M2 are initially separated by a distance Ra.
Mass M2 is now moved further away from mass M1 such that
their final separation is Rb.
Which of the following statements best describes the work Wab
done by the force of gravity on M2 as it moves from Ra to Rb?
A. Wab > 0
B. Wab = 0
C. Wab < 0
Unit 5, Slide 4
Potential Energy
DU  Wconservative
If gravity does negative work, potential energy increases!
Same idea for Coulomb force… if Coulomb force does negative
work, potential energy increases.
+
+
+
+
Dx
F
Coulomb force does negative work
Potential energy increases
Unit 5, Slide 5
CheckPoint: Motion of Point Charge Electric Field
A charge is released from rest in a region of electric field. The
charge will start to move
A) In a direction that makes its potential energy increase.
B) In a direction that makes its potential energy decrease.
C) Along a path of constant potential energy.
It will move in the same direction as F
F
Dx
Work done by force is positive
DU = Work is negative
Nature wants things to move in such a way that PE decreases
Unit 5, Slide 6
Example: Two Point Charges
Calculate the change in potential energy for two point
charges originally very far apart moved to a separation of “d”
d
q1q2
DU =  k 2 dr
r12

d
q1
q2
q1q2
DU = k
d
(Charged particles with the same sign have an increase in potential
energy when brought closer together.)
For point charges often choose r = infinity as “zero” potential
energy.
qq
U =k
1 2
d
Unit 5, Slide 7
Example 5.1 (Velocity after a long time)
The two charges shown below are held in place and
then released. What is their final velocity after they
have
d = 10cm
q1
q2
m1 = 5X10-10kg
q1 = +6nC
m2 = 7X10-10kg
q2 = +8nC
Unit 5, Slide 8
CheckPoint: EPE of Point Charge
A charge of +Q is fixed in space. A second charge of +q
was first placed at a distance r1 away from +Q. Then it
was moved along a straight line to a new position at a
distance R away from its starting position. The final
location of +q is at a distance r2 from +Q.
What is the change in the potential energy of charge +q
during this process?
A.
B.
C.
D.
E.
kQq/R
kQqR/r12
kQqR/r22
kQq((1/r2)-(1/r1))
kQq((1/r1)-(1/r2))
Unit 5, Slide 9
Potential Energy of Many Charges
Two charges are separated by a distance d.
What is the change in potential energy when a third
charge q is brought from far away to a distance d from
the original two charges?
Q2
qQ1 1 qQ2 1
DU =
+
40 d 40 d
d
d
(superposition)
Q1
• Don’t “double count”
• No sines and cosines
q
d
Electricity & Magnetism Lecture 5, Slide 10
CheckPoint: EPE of a System of Point Charges 1
Two charges which are equal in
magnitude, but opposite in sign, are
placed at equal distances from point A
as shown. If a third charge is added to
the system and placed at point A, how
does the electric potential energy of the
charge collection change?
A.
B.
C.
D.
Potential energy increases
Potential energy decreases
Potential energy does not change
The answer depends on the sign of the third charge
Unit 5, Slide 11
CheckPoint: EPE of a System of Point Charges 2
Two point charges are separated by some distance as shown.
The charge of the first is positive. The charge of the second is
negative and its magnitude is twice as large as the first. Is it
possible find a place to bring a third charge in from infinity
without changing the total potential energy of the system?
YES, as long as the third charge is positive
B. YES, as long as the third charge is negative
C. YES, no matter what the sign of the third charge
D. NO
A.
Unit 5, Slide 12
Summary
For a pair of charges:
qq
Just evaluate U = k 1 2
r
r
Q1
Q2
(We usually choose U = 0 to be where the charges are far apart)
For a collection of charges:
Sum up
U =k
q1q2
r
for all pairs
Unit 5, Slide 13