Transcript Chap21
21 Electromagnetic Induction
Induction Experimental
Magnetic Flux
B BA 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
LN
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 Pt LII
1 2
U LI
2
Energy per unit volume (using solenoid)
B2
uB
20
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 Pt LII
1 2
U LI
2
B2
uB
20
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
LN
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