Download Document

Electricity
Electric Potential
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
1
Electric Power
Electricity
Electric Potential
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
φ


W  F  r
W  F r cos 
2
Electricity
Electric Potential

Example of Work

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
3
Electricity
Electric Potential

Example of Work

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
Electricity
Electric Potential
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.
5
Electricity
Electric Potential
Example of a Conservative Force
Gravity as a mass is raised and lowered
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
Electricity
Electric Potential
Example of a Non-conservative Force
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 )
Electricity
Electric Potential
Consider the work necessary to put together two point charges.
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

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.
8
Electricity
Electric Potential
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,Ethen we see that
U  qV
9
kq
V
r
Electricity
Electric Potential
What if there are more point charges?
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
Electricity
Electric Potential
2nC
Example
1
3nC
2m
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

9
11
Electricity
Electric Potential
What about potential?
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
12
Electricity
Electric Potential
2nC
Example
1
3nC
2m
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 
 
 


Electricity
Electric Potential
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
14
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
Electricity
Electric Potential
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/
15
Electricity
Electric Potential
Common SI Units in Electricity
Electric
Potential
Electric
Field
Energy or
Work
16
V
J/C
V/m
N/C
eV
J
Electricity
Electric Potential
Relationship Electric Potential and Electric Field
The electric field is the slope of the electric potential.
slope of this
line is -E
V
s
17
Electricity
Electric Potential
Relationship Electric Potential and Electric Field
The electric potential is the area under the curve of electric field.
positive
area
E
s
negative
area
18
Electricity
Electric Potential
What is electric power?
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.
19
Electricity
Electric Potential
What is electric power?
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.
20