Transcript 16.360 Lecture 24 Last Lecture • Dynamic Filed • Faraday’s Law

16.360 Lecture 24
Exam III, Nov. 24, Monday, 12:30 –1:30pm, SW 401, Chapter 3, 4, 5
Last Lecture
• Dynamic Filed
• Faraday’s Law
• Stationary loop in a time-varying Magnetic field
16.360 Lecture 23
Static field

  D  v ,

  E  0,

  B  0,
 
 H  J,


1
ˆ '  v dv ,
E   dE 
R
4 v '
R '2

I
H
4

dl  Rˆ
l R 2 ,
Dynamic Field

  D  v ,


B
 E   ,
t

  B  0,

  D
 H  J 
,
t
16.360 Lecture 23
Faraday’s Law

 
B 
E

d
l


C
s t  ds
  

   B  ds ,  
,
s
t
t
 
   B  ds ,
s
16.360 Lecture 23
Electromotive force
Vemf

 
B 

  E  dl   
 ds  
,
C
s t
t
tr
m
Vemf  Vemf
 Vemf
,
Stationary Loop in a Time-varying Magnetic field
tr
Vemf

B 
 
 ds ,
s t

B 
I
 
 ds ,
s t
Ri  R
tr
Vemf
Lenz’s law
16.360 Lecture 23

 


B 
Vemf   E  dl   
 ds   (  E )  ds ,
C
s t
s


B
 E   ,
Faraday’s law, differential form
t
An example:

B  B0 ( yˆ 2  zˆ3) sin t ,
(a) The magnetic flux link of a single turn
of the inductor.
(b) The transformer emf,.
(c) The polarity of the emf.
(d) The induced current.
16.360 Lecture 23
Example II

B   zˆ 0.3t ,
Determine the voltage drops across the
two resistors
16.360 Lecture 24
Today
• The ideal Transformer
• Moving Conductor in a Static Magnetic Field
16.360 Lecture 24
The ideal Transformer properties:
•=
• I = 0 in the core.
• The magnetic flux is confined within the core
Questions:
• I = ?, with applied voltage of V1and with RL
• V2, and I2=?
16.360 Lecture 24
Voltage transformer:
V1   N1
d
d
, V2   N 2
,
dt
dt
V2 N 2

,
V1 N1
Power relations:
P1  P2 ,
Why?
Current transformer:
P1  V1I1 , P2  V2 I 2 ,
I 2 N1

,
I1 N 2
Impedance transformer:
R1  V1 / I1 , R2  V2 / I 2 ,
Rin  (
N1 2
) RL ,
N2
R1
N
 ( 1 )2 ,
R2
N2
16.360 Lecture 24
Moving conductor in a static magnetic field:
Vemf

 
B 

  E  dl   
 ds  
,
C
s t
t
tr
m
Vemf  Vemf
 Vemf
,
m
Vemf
 
  

( B  ds )


 (u  B)  dl ,
t
t
  
ds  w  dl ,
  
  
  
A  ( B  C )  B  ( A  C )  C  ( A  B),
16.360 Lecture 24
Another way to look at it:
Fm
 
E

,
Fm  q(u  B),
m
q
m
emf
V

l2
l1
 l2   
Em  dl   (u  B)  dl ,
l1
Next lecture:
• The electromagnetic generator
• Moving conductor in a time varying magnetic field