Electricity and Magnetism
• Today
– Kelvin Water Drop Generator
– Electric Potential Energy
– Electric Potential
Feb 22 2002
Recap: In-Class Demos
• No field inside
• No charge on
inside surface
Faraday Cage
Large E; E~1/r2
+
++
++
++
+
+
Figure by MIT OCW.
Van der Graaf Generator
Kelvin Water Drop Generator
Water pipe
Metal can
• No battery, motor,
anything...
• Start water flow
• Water ‘flares out’
– like tinsel
• Spark!
• Cycle repeats...
Metal Bucket
Feb 22 2002
Puzzles
• Spark
– Spheres have opposite charge
– Asymmetry!
– But apparatus is symmetric!?
• Where does the energy come from?
Feb 22 2002
Kelvin Water Drop Generator
Water pipe
Metal can
Metal Bucket
Feb 22 2002
Kelvin Water Drop Generator
Water pipe
Metal can
+
Metal Bucket
Feb 22 2002
Symmetry is broken
+
by Fluctuation
Kelvin Water Drop Generator
+
Water pipe
Metal can
+
+
+
-+
+
+
Metal Bucket
Feb 22 2002
-
-
-
Kelvin Water Drop Generator
++ + - - Water pipe +
+
+
-- + Metal can + - +
+ +
+
+
+
+
+ + +
+
+
+
Metal Bucket
Feb 22 2002
---
- --
Positive Feedback
Loop
Kelvin Water Drop Generator
Water pipe
Metal can
Metal Bucket
Feb 22 2002
Spark neutralizes
system
Final question
• Spark is like a small lightning
– contains energy (like lightning)!
• Where does this energy come from?
Gravitational potential energy of water
(Epot = m g h)
• Where was it before the spark?
Feb 22 2002
Electric Potential Energy
• Massive objects in Gravitational Field
have potential energy
• What about charged objects in E-Field?
• Let’s review some concepts from
8.01x....
Feb 22 2002
Work and Potential Energy
F(l)
b
x
dl
Note: In general,
x
a
Feb 22 2002
Example
F || dl
Work and Potential Energy
F(l)
dl
b
x
α
x
a
Feb 22 2002
Work:
Work and Potential Energy
(2)
(1)
x
a
b
x
(3)
Conservative Force:
Wba independent of path
Wba(1) = Wba(2)= Wba(3)= Wba
Feb 22 2002
Work and Potential Energy
• IF
F conservative:
– Define Potential Energy
Example - Gravity
y
b
a
dl
F(l)
Feb 22 2002
Work and Electrostatic Force
Charge q at point a
in Coulomb field of Q
+Q
b
a
+q
Feb 22 2002
How much work to
move to point b?
Is FES conservative?
(1)
i.e. is Wab =
+Q
b
(1)
Feb 22 2002
a
+q
(2)
Wab(2) ?
Is FES conservative?
+Q
b
a
dl
+q
α
r
Feb 22 2002
Electric Potential Energy
• Found Potential Energy associated with
Electric Force between two charges
• Can only observe differences in potential
8
– often set U( ) = 0
– U(r) energy needed to bring q,Q together
from infinity
Feb 22 2002
Electric Potential
• Electric Potential Energy proportional to q
• Again, define
V = U/q
• Electric Potential V:
– Units are Volt [V] = [J/C]
Feb 22 2002
Electric Potential for many
charges
• Superposition principle....
V(r) = Σ1/(4πε0) Qi/ri
• Sum of scalars, not vectors!
• Integral for continous distributions
Feb 22 2002
Electric Potential for many
charges
• Electric potential depends on charges that
create field, not the test charge!
V(r) = Σ1/(4πε0) Qi/ri
• V tells us how much energy a charged
object can aquire when moving from a to b
Feb 22 2002
Electrical potentials
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•
•
•
•
Feb 22 2002
Battery:
Power outlet:
HV power line:
Accelerators:
Thunderstorm:
1.5 V
120 V
106 V
108 V
108 V