Today 3/3

1
Today 3/3

• Read Ch 19.4
• Practice exam posted
• Energy of Assembly
• Calculating Velocities
• HW Charge Assembly 2 Due Thursday
• Lab Mapping Equipotential Lines (get E
  field lines from these)

2
Potential Energy Difference and Potential
Difference
Potential Energy Difference ?PEA,B is the change
in PE the particular charge feels when it is
moved from one location to another. This is also
the Work required to move the charge.
Potential Difference ?VA,B is the change in PE a
positive 1C charge would feel if it were moved
from one location to another.
3
Calculating ?VA,B
Q is the source charge.A is a location (field
point) near the source charge.r is the distance
from the source charge to point field point.
?VA,B ?V?,B - ?V?,A
?VA,B is negative!
4
More than one source
What is the potential difference ?VAB? All
distances are 5cm.
Q1 4 x 10-9 C
Q2 10 x 10-9 C
A
B
VA kq1/r1A kq2/r2A Sum potentials at A
VA (9x109)(4x10-9)/.05 (9x109)(10x10-9)/.10
VA 720V 900V 1620V
VB (9x109)(4x10-9)/.10 (9x109)(10x10-9)/.05
VB 360V 1800V 2160V
?VAB 540V potential is higher at B
5
More than one source
A 4g particle with charge 6?C is released from
rest at B. What is its speed at A?
Q1 4 x 10-9 C
Q2 10 x 10-9 C
A
B
?VAB 540V
?VBA -540V
?PEBA q?V (6 ?C)(-540V ) -3.2 x 10-3 J
?KEBA -?PEBA 3.2 x 10-3 J 1/2 mv2
v 1.3 m/s at location A
6
More than one source
What is the potential at point A midway between
these two charges? (different charges than before)
Q1 4 x 10-9 C
Q2 -4 x 10-9 C
A
VA 0 Two contributions add to zero
Is there an E-field at A?
Yes, Enet points right. Two contributions add as
vectors, yet the potential is zero!
The potential is negative just right of A and
positive just left of A. There is E if V changes.
7
More than one source
How much work do I have to do to bring a 6?C to
point A from very far away?
Q1 4 x 10-9 C
Q2 -4 x 10-9 C
A
?V?A ?
?V?A 0
The work equals zero also since V? 0.
Depending on the particular path we chose there
will be and - work done along the way but the
net work done will always be zero for any path
from far away to point A.
8
Energy stored
How much energy is stored in the assembly of
charges? All are 1 x 10-3C and 1g (1 x 10-3kg).
Energy stored is the same as the work required to
assemble the charges.
3m
4m
Move them all very far away, bring them in one at
a time, and total up the work done.
5m
9
Energy stored
First moves in for free. Work ?PE?r 0
Upper left requires work.
Work 9/4 x 103 J
Upper right also requires work, two contributions.
3m
Work (9/3 9/5) x 103 J
4m
Energy stored in the system is the sum of the
work done.
5m
Energy Stored 7 x 103 J
1 x 10-3C and 1g
10
Energy stored
What happens if we let go of the charges?
They accelerate away from each other.
When they are very far away from each other the
system will have 7 x 103 J of kinetic energy
shared among these three charges. (energy is
conserved)
3m
4m
5m
Energy Stored 7 x 103 J
1 x 10-3C and 1g
11
Energy stored
What happens if we let go the upper right charge?

Buckets!
0
3m
4m
PE after ?
5m
PE after 9/4 x 103 J
?PE 19/4 x 103 J
or - ?
?KE 19/4 x 103 J , speeds up
1 x 10-3C and 1g
v 3082m/s
12
Energy stored
How fast are these charges moving after they are
released and they are very far away from each
other?
1.8 x 103 J
Energy stored
Each charge has 0.9 x 103 J of kinetic energy.
(split 50/50 by symmetry)
5m
0.9 x 103 1/2mv2
v 1340m/s
1 x 10-3C and 1g
13
Energy stored
What about the case where one is now a negative
charge?
-q
When the energy is negative we call it the
binding energy.
Binding energy is the work required to separate
the charges to infinity.
5m
Electrons are bound to protons in this way.
q
Both are 1?C in magnitude.