Transcript Faraday Law PowerPoint
Fields, Patterns, Maxwell’s Equations and Begin Induction/Faraday’s Law 2049 SCALE-UP
Monday
14 Chapter 22 Gauss 21 Chapter 23 Faraday 28 Chapter 23 Faraday
Wednesday Friday Saturday
16 (Read rest of chapter) 2 WebAssigns Chapter 22 Gauss 23 QUIZ Chapter 23 Faraday 18 QUIZ Chapter 22 Lentz & More HOLIDAY 30 Chapter 24 EM 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
E B
dA
B • n
dA
0
l l
? =Faraday's Law of Induction - Next Topic 0
q inside
0
I
(One additional term)
B
d
s
0
i 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
The ELECTRIC FLUX through S 2
E d
E dt
EA
q
0 1 0
dq dt Let dq
I d
(in gap)
dt Displaceme nt
Current
I d
dq dt
0
d
E dt
E B
dA
B • n
dA
0
l l
? =Faraday's Law of Induction - Next Topic
q inside
0 ( 0
I
+ 0
d
E dt
)
E
d
l
? =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 There
must
be an Electric Field in the metal that is pushing the current!!
B Aluminum Pipe
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
x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
emf emf
2
E
s RE
E zero
s
E Conductor
x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
A
E Conductor A B C The emf Zero Can’t tell
emf
Through the loop
t
MINUS????
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
emf
N
t i
emf R coil
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
Total Flux of the Electric Field LEAVING a surface is
E
E
n
out
dA
Magnetic Flux
Applies to an OPEN SURFACE only.
“Quantity” of magnetism that goes through a surface.
B
surface
A
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 Δ
t
= 25 ms. What current is induced in the coil during Δ
t
?
0.0224 A
DONE