Upload
roz
View
20
Download
0
Embed Size (px)
DESCRIPTION
Review of Work. 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. - PowerPoint PPT Presentation
Citation preview
TOC
1
Physics 222Electric Potential Difference
Review of Work
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
Electric Power
Potential Surfaces
SI Units
Field and Potential Graphs
TOC
2
Physics 222Electric Potential Difference
Definition of Work
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
F rW
cosW F r
φ
TOC
3
Physics 222Electric Potential Difference
Example of Work
The following is an example of the work done by gravity on a mass.
Δh2
Δh1
Δw
y
x
F rW
m
2121 00 hmghmghmghmgW
TOC
4
Physics 222Electric Potential Difference
A2
A1
Example of Work
This is an example using the the fact that integrals are areas under a curve.
JNmbhA 5252
1
2
11
JNmbhA 6432
1
2
12
JAAW 121
F (N)
0
1
-1 X (m)
0 1 2
F rW
TOC
5
Physics 222Electric Potential Difference
Definition of a Conservative Force
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.
TOC
6
Physics 222Electric Potential Difference
y
x
Example of a Conservative ForceGravity as a mass is raised and lowered
1
2
3
5Δh2
Δh1
11 hmgW
02 W
123 hmghmgW
04 W
25 hmgW
WTOTAL = 0
4
m
TOC
7
Physics 222Electric Potential Difference
11 LfW s
WTOTAL = - fs (2ΔL1 + 2ΔL2 + 2Δw )
y
x
2
1
3
45
ΔL2
ΔL1
Δw
wfW s2
123 LLfW s
wfW s 4
25 LfW s
m
Example of a Non-conservative ForceFriction on a block that is moving around a table
TOC
8
Physics 222Electric Potential Difference
Consider the work necessary to put together two point charges.
The force is given by Coulomb’s Law.
1 22
12
kq qF
r
The work needed to bring one charge from infinity to within a distance r12 of the other is
12
21212
2112
12
r
qkq
r
qkqdr
r
qkqW
rr
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.
TOC
9
Physics 222Electric Potential Difference
The potential energy held between these two point charges is then
Now we consider the same relationship, but with electric field instead of force. This we call the potential.
F E U r V r
12
21
r
qkqWU
Since , then we see that
EF q
qVU r
kqV
TOC
10
Physics 222Electric Potential Difference
3
12
What if there are more point charges?
12
3
1 212
12
q qU k
r
1 313
13
q qU k
r 2 3
2323
q qU k
r
1 3 2 31 212 13 23
12 13 23
q q q qq qU U U U k k k
r r r
1
2i j
i j ij
q qU k
r
TOC
11
Physics 222Electric Potential Difference
3
12
Example 12
3
1
2i j
i j ij
q qU k
r
2nC3nC
4nC
2m
2.1m 2.1m
1 3 2 3 3 1 3 21 2 2 1
12 13 21 23 31 32
1
2
q q q q q q q qq q q qk
r r r r r r
1 3 2 3 1 3 2 31 2 1 2
12 13 23 12 13 23
12 2 2
2
q q q q q q q qq q q qU k k
r r r r r r
29
2
2nC 4nC 3nC 4nCNm 2nC 3nC8.99 10
C 2m 2.1m 2.1mU
TOC
12
Physics 222Electric Potential Difference
What about potential?
12
3
0P
12
3
110
10
qV k
r
220
20
qV k
r
330
30
qV k
r
31 210 20 30
10 20 30
qq qV V V V k k k
r r r
TOC
13
Physics 222Electric Potential Difference
3
12
Example 12
3
00
i
i
qV k
r
2nC3nC
4nC
2m
2m 2m
31 2
10 20 30
qq qkr r r
29
2
Nm 2nC 3nC 4nC8.99 10
2 2 2Cm m m
3 3 3
V
0P
TOC
14
Physics 222Electric Potential Difference
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 EquationEquation for
Point Charges
Electric Field
Force
Potential
Potential
1 212 2
12
q qF k
rF qE
2
qE k
r
FU r qV
1 2
1212
q qU k
r
EV r
q
V kr
TOC
15
Physics 222Electric Potential Difference
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 AppletThis Applet can be found at http://www.slcc.edu/schools/hum_sci/physics/tutor/2220/e_fields/java/
TOC
16
Physics 222Electric Potential Difference
Common SI Units in Electricity
Electric
Potential
V J/C
Electric Field
V/m N/C
Energy or Work
eV J
TOC
17
Physics 222Electric Potential Difference
Relationship Electric Potential and Electric Field
The electric field is the slope of the electric potential.
V
s
slope of this line is -E
TOC
18
Physics 222Electric Potential Difference
Relationship Electric Potential and Electric Field
The electric potential is the area under the curve of electric field.
E
s
positive area
negativearea
TOC
19
Physics 222Electric Potential Difference
What is electric power?
Power is the change in work over time
We will use this latter when we reach the topic in circuits.
qVU qP V IV
t t t
TOC
20
Physics 222Electric Potential Difference
Review of Work
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
Electric Power
Potential Surfaces
SI Units
Field and Potential Graphs