Fields, Patterns, Maxwell’s Equations and Begin
Induction/Faraday’s Law
2049
SCALE-UP
Monday
14
Wednesday
Friday
16 (Read rest of
18
chapter)
QUIZ
Chapter 22
Lentz & More
Chapter 22
Gauss
2 WebAssigns
Chapter 22
Gauss
21
23
Chapter 23
Faraday
QUIZ
Chapter 23
Faraday
28
30
Chapter 23
Faraday
Chapter 24
EM
Saturday
HOLIDAY
2
Chapter 24 EM
Optional Exam
(22-24)
3
FINAL EXAM
THE EVAN SHOW
Diverging Field
Point Sources
“Curly Field”
No diverging source
Electrostatic Fields
Magnetic Fields
q

E  ndA 


B • ndA  0

E  dl  ? =Faraday's Law of Induction - Next Topic

B  dl    I
(One additional term)

inside
0
0
inside. path
B

d
s


i
0
enclosed

Let’s apply this to the gap of a capacitor.
i
i
CHARGING OR DISCHARGING …. HOW CAN CURRENT
FLOW THROUGH THE GAP
In a FIELD description??
I=0
T heELECT RICFLUX throughS2
 E  EA 
q
0
d E 1 dq

dt
 0 dt
Let
dq
 I d (in gap)
dt
Displacem ent Current
dq
d E
Id 
 0
dt
dt
q

E  ndA 


B • ndA  0

E  dl  ? =Faraday's Law of Induction - Next Topic

d
B  dl   (  I
+
)

dt
inside
0
E
0 inside. path
0

E  dl  ? =Faraday's Law of Induction -
Galvanometer
Coil
Integral over a SURFACE
A
Observation
Variables
Direction
Polarity
Pitch
Velocity
Meter Deflects
There must be an
emf
around the loops!
Aluminum
Pipe
S
N
N
REPEL!!
Induced Current
B
Aluminum
Pipe
There must be
an Electric Field
in the metal that
is pushing the
current!!
You said that there is a conducting loop.
You said that there is therefore a current
induced around the loop if the flux through
the loop changes.
But the beginning and end point of the loop
are the same so how can there be a voltage
difference around the loop?
Or a current???
‘tis a puzzlement!
DID I LIE??
Electric fields that are created by static charges
must start on a (+) charge and end on a (–)
charge as I said previously.
Electric Fields created by changing magnetic
fields (NON-Coulombic) can actually be shaped
in loops.
STILL
Because you said that an
emf is a voltage so if I
put a voltmeter from
one point on the loop
around to the same
point, I will get ZERO
volts, won’t I? How can
there be a current??
Yes … but
this doesn’t make
me a liar!
Let Me Explain.
Is the WORK that an external agent has to do
to move a unit charge from one point to
another.
But we also have (neglecting the sign):
V   Es
s
em f   Es  E  s
x
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em f  2RE  zero
Conductor
E
x
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E

A
Conductor
A
B
C
The emf
Zero
Can’t tell
em f  
MINUS????
Through
the loop
t
Michael Faraday
(1791-1867)
Q: Which way does E point?
A: The way that you don’t want it to point! (Lenz’s
Law).
Lenz’s Law Explains the (-) sign!
In this case, 2 coils, each have
the SAME emf so we add..
Ohm’s Law still works, so

em f  N
t
em f
i
Rcoil
Faraday’s Experiments
?
?
Insert Magnet into Coil
Remove Coil from Field Region
That’s Strange …..
These two coils are perpendicular to each other
All Involve Changing The Magnetic
Flux through the Loops
Remember the Definition of TOTAL
ELECTRIC FLUX through a CLOSED
surface:
 E  
surface
d E
T otal Flux of theElectric
Field LEAVINGa surface is
 E   E  n out dA
Magnetic Flux
 Applies to an OPEN SURFACE only.
 “Quantity” of magnetism that goes through a surface.
 B   B  dA
surface
In the figure below a 120-turn coil of radius 1.8 cm and resistance 6.8 W is
coaxial with a solenoid with 209 turns/cm and diameter 3.2 cm. The solenoid
current drops from 1.5 A to zero in time interval Δt = 25 ms. What current is
induced in the coil during Δt?
0.0224 A
DONE