# Lecture 5 - PowerPoint 5

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```					           Physics 212
Lecture 5
Today's Concept:

Electric Potential Energy

Defined as Minus Work Done by Electric Field

Physics 212 Lecture 5, Slide 1
Main Point 1

First, the Coulomb force is a conservative force. By that, we mean that the work
done by the Coulomb force on a charged particle as it is moved between any two
points is independent of the path taken between those two points.
Physics 212 Lecture 5, Slide 2
Main Point 2

Second, since the Coulomb force is a conservative force, we can define an electric
potential energy associated with this force. In particular, we defined the change in
electric potential energy of a charged particle moved from point A to point B to be
minus the work done by the Coulomb force on that particle as it moves between the
two points.                                                  Physics 212 Lecture 5, Slide 3
Main Point 3

Third, the electric potential energy of a system of fixed charged particles is just
equal to the scalar sum of the electric potential energies due to each pair of
particles.
Physics 212 Lecture 5, Slide 4
r2
Recall from physics 211:   W   F dr          WTOT  K
r1

F                   Object speeds up ( K > 0 )
dr         W

F
dr
or
W        Object slows down ( K < 0 )
F
dr

F
W        Constant speed ( K = 0 )
dr
Physics 212 Lecture 5, Slide 5
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
U    k 2 dr                       d

r12              q1                  q2

For point charges often choose r=infinity as “zero” potential energy.

Physics 212 Lecture 5, Slide 6
Physics 212 Lecture 5, Slide 7
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

d               d

Q1                        q

d

Physics 212 Lecture 5, Slide 8
Physics 212 Lecture 5, Slide 9
Checkpoint 1

A
B
C
D
E

34
Physics 212 Lecture 5, Slide 10
Physics 212 Lecture 5, Slide 11
Checkpoint 2

A   B   C     D

31
Physics 212 Lecture 5, Slide 12
Physics 212 Lecture 5, Slide 13
Checkpoint 3

34
Physics 212 Lecture 5, Slide 14
Physics 212 Lecture 5, Slide 15
Checkpoint 4
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

34
Physics 212 Lecture 5, Slide 16
Example

A positive charge q is placed at x=0 and a negative charge -2q is placed
at x=d. At how many different places along the x axis could another
positive charge be placed without changing the total potential energy of
the system?

q                   -2q
x
X=0                  X=d

40
Physics 212 Lecture 5, Slide 17
Physics 212 Lecture 5, Slide 18
Physics 212 Lecture 5, Slide 19

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