21 Electromagnetic Induction
Induction Experimental
Magnetic Flux
B  BA cos 
Units: Weber (Wb)
1 Wb = 1T.m2
Faraday’s Law of Induction
The magnitude of the induced emf in a circuit equals the
absolute value of the time rate of change of the magnetic flux
through the circuit:
 B

t
 B
N
t
for 1 turn or
for N turns
Generator
 B
 A sin t
 B  BA cos   BA cos t  
t
Lenz’s Law: Against the change
The direction of the any magnetically induced current or emf is
such as to oppose the direction of the phenomenon causing it.
Lenz’s Law: Example
Motional Electromotive Force
I?
 B  BLv t
 B
 
 Blv
t
“-”sign: Lenz’s Law
Recall Lorentz force on the moving part
Eddy’s Currents
Application: Damping
Application: Speedometer
Application: Hybrid Generator Brake
Mutual Inductance
 B 2
 2  N2
t
N 2  B 2  i1 or N 2  B 2  M 21 i1
 B 2
i
 M 21 1
t
t
 2  N2
Similarly,
1  N1
 B1
i
 M12 2
t 2
t
Define mutual inductance, M,
M  M 12
N 2 B 2
N1 B1
 M 21 

i1
i2
i1
i2
2  M
and  1  M
t
t
Self-Inductance
N
 B
I
L
t
t
 B
LN
I
Unit 1V.s/A = 1 Henry (H)
Examples:
Solenoid and Toroid
Transformers
 B
 1  N1
t
 2 N2

 1 N1
 B
 2  N2
t
For an ideal transformer
I1V1  I 2V2 and I 2  V2 / R
V1
R
 Reff 
I1
( N 2 / N1 ) 2
Transformer & Eddy Current
Magnetic Field Energy
I
P  VI  L
I
t
U  Pt  LII
1 2
U  LI
2
Energy per unit volume (using solenoid)
B2
uB 
20
R-L Circuit
time
I (t ) 


1 e 
R
t /
 = L/R, time constant
L-C Circuit
Summary: Electromagnetic Induction
& Faraday’s Law
Summary: Lenz’s Law
Summary: Motional EMF
Summary: Eddy’s Currents
Summary: Inductance
Summary: Transformers
Summary: Magnetic Energy
I
P  VI  L
I
t
U  Pt  LII
1 2
U  LI
2
B2
uB 
20
Summary: R-L & R-C Circuits
Homework
Ch21: 1, 4, 12, 16, 21, 25, 27, 32, 40, 45, 52.
P9-Faraday’s Law
P16&17 Lenz’s law
P21&25-Motional emf
P27-Mutual Inductance
N 2 B 2
N1 B1
M

i1
i2
P32-Self-Inductance
 B
I
N
L
t
t
 B
LN
I
P40-Transformer
V2 N 2

V1 N1
Reff
R

2
( N 2 / N1 )
P45-Magnetic Energy
Voltmeter Construction
d’
V’
V  I g ( Rg  R s )  Kd ( Rg  Rs )
If the V-meter required for maximum V’ (full scale) then
V'
V '  kd ' ( Rg  Rs ) or Rs 
 Rg
Kd '
Ammeter Construction
d’
Ig
I  I g  I sh or I max  Kd ' I sh
A
 50div  80
I g Rg
Kd ' Rg
div
I g Rg  I shRsh or Rsh 


~ 0.537
I sh
I max  Kd ' 0.75 A  0.1 10 3 A  50div
div
Rsh A Rsh 8.1 10  4 cm 2
Length 

~ 2.5m
-6

1.72 10 cm
0.1 10 3