Download Physics 222 Electric Potential Difference Example of Work The

Physics 222
Electric Potential Difference
Review of Work
TOC
Work Done on a Point Charge by a Point Charge
Potential Energy and Potential of Point Charges
Potential Energy and Potential of Many Point Charges
Relationship between Force, Field, Energy, Potential
Potential Surfaces
SI Units
Field and Potential Graphs
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Electric Power
Physics 222
Electric Potential Difference
Definition of Work
TOC
Work is defined as the amount of force acting over a distance.
The unit of work is either Joules (J) or electron-volts (eV)
Δr
F
φ


W  F  r
W  F r cos 
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Physics 222
Electric Potential Difference

Example of Work
TOC

W  F  r
The following is an example of the work done by gravity on a
mass.
y
Δw
Δh1
x
m
Δh2
W  mgh1  0  mgh2   mgh1   0  mgh2
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Physics 222
Electric Potential Difference

Example of Work
TOC
W  F  r
This is an example using the the fact that integrals are areas
under a curve. F (N)
1
A1
0
-1
A2
0
4

1
X (m)
2
1
1
A1  bh  5m 2 N   5 J
2
2
1
1
A2  bh  3m  4 N   6 J
2
2
W  A1  A2  1J
Physics 222
Electric Potential Difference
Definition of a Conservative Force
TOC
A force is conservative if the work it does on an object is zero
when the object moves along a path and returns to its initial
position.
Examples of conservative forces are gravity, elastic force,
electricity and magnetism.
The following are not conservative: friction, tension, normal
force.
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Physics 222
Electric Potential Difference
Example of a Conservative Force
Gravity as a mass is raised and lowered
TOC
y
Δh1
W1  mgh1
2
W2  0
1
x
m
Δh2
W4  0
5
4
6
3
W3  mgh2   mgh1 
W5  mgh2
WTOTAL = 0
Physics 222
Electric Potential Difference
Example of a Non-conservative Force
TOC
Friction on a block that is moving around a table
y
ΔL1
2
W1   f s L1
W2   f s w
1
x
m
ΔL2
3
W3  f s  L2  L1 
W4  f s  w
5
4
W5   f s L2
Δw
7
WTOTAL = - fs (2ΔL1 + 2ΔL2 + 2Δw )
Physics 222
Electric Potential Difference
Consider the work necessary to put together two point charges.
TOC
The force is given by Coulomb’s Law.
kq1q2
F
r12 2
The work needed to bring one charge from infinity to within a
distance r12 of the other is
W 
r12

8
kq1q2
kq1q2
dr


r2
r
r12


kq1q2
r12
Don’t worry about the integral in the last equation. It is only
there so that those who know calculus can see where the other
part came from.
Physics 222
Electric Potential Difference
TOC
The potential energy held between these two point charges is
then
kq1q2
U  W 
r12
Now we consider the same relationship, but with electric field
instead of force. This we call the potential.

U   F r



V   E r

Since F  q E, then we see that
U  qV
9
kq
V
r
Physics 222
Electric Potential Difference
What if there are more point charges?
TOC
1
U12  k
q1q2
r12
qq
U13  k 1 3
r13
U 23  k
2
q2 q3
r23
3
U  U12  U13  U 23  k
10
qq
qq
q1q2
k 1 3 k 2 3
r12
r13
r23
qi q j
1
U  k
2 i  j rij
Physics 222
Electric Potential Difference
2nC
Example
1
3nC
2m
TOC
2
2.1m
2.1m
3
4nC
qi q j
1
1 qq qq q q q q q q q q 
U  k
 k 1 2  1 3  2 1  2 3  3 1  3 2 
2 i  j rij
2  r12
r13
r21
r23
r31
r32 
qq qq q q 
qq
qq 
1  qq
U  k 2 1 2  2 1 3  2 2 3   k  1 2  1 3  2 3 
2  r12
r13
r23 
r13
r23 
 r12
Nm2  2nC  3nC 2nC   4nC  3nC   4nC  
U  8.99 10



2 
C  2m
2.1m
2.1m

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Physics 222
Electric Potential Difference
What about potential?
TOC
1
q
V10  k 1
r10
2
P0
V30  k
V20  k
q2
r20
q3
r30
3
q3
q1
q2
V  V10  V20  V30  k  k
k
r10
r20
r30
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Physics 222
Electric Potential Difference
2nC
Example
1
3nC
2m
TOC
2
P0
2m
2m
3
4nC
V0   k
13
qi
q q
q 
k 1  2  3 
ri 0
 r10 r20 r30 



2 
Nm
2nC
3nC

4nC

V  8.99  109 2 


C  2   2   2  
 3 m   3 m  3 m 
 
 


Physics 222
Electric Potential Difference
TOC
Relationship between Work, Potential Energy, Force
and Potential
The table below represents the fundamental equations of
electricity all of which a derived from the electric field E.
Quantity
General Equation
Ek
Electric Field
Force
Potential
Potential
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Equation for
Point Charges
q1q2
F12  k 2
r12
F  qE

V   E  r

q
r2
U   F r  qV
V k
U12  k
q
r
q1q2
r12
Physics 222
Electric Potential Difference
TOC
A surface is an equipotential surface if the electric potential at
every point on the surface is the same.
As charges move on an equipotential surface the electric force
does no work.
The electric field at a point is always perpendicular to the
equipotential surface on which the point lies.
The electric field always points in the direction of decreasing
potential.
Java Applet
This Applet can be found at http://www.slcc.edu/schools/hum_sci/physics/tutor/2220/e_fields/java/
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Physics 222
Electric Potential Difference
TOC
Common SI Units in Electricity
Electric
Potential
Electric
Field
Energy or
Work
16
V
J/C
V/m
N/C
eV
J
Physics 222
Electric Potential Difference
Relationship Electric Potential and Electric Field
TOC
The electric field is the slope of the electric potential.
V
slope of this
line is -E
s
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Physics 222
Electric Potential Difference
Relationship Electric Potential and Electric Field
TOC
The electric potential is the area under the curve of electric
field.
positive
area
E
s
negative
area
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Physics 222
Electric Potential Difference
What is electric power?
TOC
Power is the change in work over time
U   qV  q
P


V  IV
t
t
t
We will use this latter when we reach the topic in circuits.
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Physics 222
Electric Potential Difference
Review of Work
TOC
Work Done on a Point Charge by a Point Charge
Potential Energy and Potential of Point Charges
Potential Energy and Potential of Many Point Charges
Relationship between Force, Field, Energy, Potential
Potential Surfaces
SI Units
Field and Potential Graphs
20
Electric Power