# Chapter 34. Electromagnetic Induction

```Chapter 34. Electromagnetic Induction
Electromagnetic induction
is the scientific principle
that underlies many
modern technologies,
from the generation of
electricity to
communications and data
storage.
Chapter Goal: To
understand and apply
electromagnetic induction.
Chapter 34. Electromagnetic Induction
Topics:
• Induced Currents
• Motional emf
• Magnetic Flux
• Lenz’s Law
• Induced Fields
• Induced Currents: Three Applications
• Inductors
• LC Circuits
• LR Circuits
Stop to think 34.1
page 1044
Stop to think 34.2
page 1045
Stop to think 34.3
page 1048
Stop to think 34.4
page 1054
Stop to think 34.5
page 1058
Stop to think 34.6
page 1067
Stop to think 34.7
page 1073
Faraday found that there is a current in a coil
of wire if and only if the magnetic field passing
through the coil is changing. This is an informal
Magnetic data storage encodes information in a pattern
of alternating magnetic fields. When these fields move
past a small pick-up coil, the changing magnetic field
creates an induced current in the coil. This current is
amplified into a sequence of voltage pulses that
represent the 0s and 1s of digital data.
Motional emf
FB  qvB
E 
F
q
 vB
m o tio n al em f
l
l
  vlB
 V  Vtop  Vbottom   0 E y dy   0 (  vB ) dy  vBl
Potential difference along a rotating bar
 V  V tip  V pivot 
l
 0
E r dr 
l
 0
(   rB ) dr 
1
2
l B
2
Induced Current in a Circuit
I 

R

vlB
R
F p u ll  Fm a g  IlB  (
vlB
R
2
) lB 
vl B
R
2
P 1046
Magnetic flux can be
defined in terms of an area vector
The magnetic flux measures the amount of magnetic
field passing through a loop of area A if the loop is tilted
at an angle θ from the field, B. As a dot-product, the
equation becomes AB cosθ
Example 34.5 Magnetic flux from the current in a long
straight wire (P1051)
From the Chapter 33. we know the magnetic field at distance x from a
long straight wire :
B 
0I
2 x
The infinitesimal flux through a little area is
d  m  B  dA  BdA 
m   dm 
 
dm
dt

 0 Ib
2
ca
c
0I
2 x
dx
x

b  dx
 0 Ib
2
 c a 
ln 

c


 0 Ib
  0 Ib
 c  a 
 d 
ln 
d
  / dt 
2
 c

 2
 0 Ib a
V
2
c (c  a )
 ln (1 
a / c  / dt )
The Induced current for six different situation
Tactics: Using Lenz’s Law
 coil   N
dm
dt
  ABN
d (cos  t )
dt
  A B N sin( t )
V em w ave 
1
 00
Inductors
• Capacitors: as devices that produce a uniform electric field.
• Capacitance: C = Q/ΔV
• Capacitor stores potential energy UC =1/2 C(ΔV)2
• Inductors: A coil of wire in the form of a solenoid is a device that
produces a uniform magnetic field. An idea inductor is one for
which the wire forming a coil has no electric resistance .
• The magnetic filed inside a solenoid having N turn and length l
B 
0 NI
• We define the inductance L as: L   m
I
• The inductance of the solenoid:
l
• L (solenoid) =
N
0 N A
2
per coil
I

l
  N
dm
 N
d ( BA)
dt
L so len o id 
dt
0 N
l
2
A
 N
d (  0 N I / lA )
dt
  0 N A / l
2
dI
dt
Inductance of a solenoid
The inductance of a solenoid having N turns,
length l and cross-section area A is
Here we also used the magnetic field B (solenoid) :
B 
0 NI
l
(equation 33.16, P 1017)
Energy density:
The potential difference across an inductor
The potential difference across an inductor
with an inductance of L and carrying a current I
measured along the direction of the current is
  IR  L
dI
dt
o r   IR  L

Q
 0
C
dI
dt

Q
C

C
Q
 L
C
Q
dI
 0
dt
 L
C
dI
2
 L
dt
Q ( t )  Q 0 cos( t )
P 1070
d Q
dt
2
 
1
LC
LR Circuits
L
dI
 IR  0 
dt
I  I0e
dI

I
 t /( L / R )
 I0e
R
dt
L
t /
 =L / R
A current-carrying wire is pulled away from a conducting loop in
the direction shown. As the wire is moving, is there a cw current
around the loop, a ccw current or no current?
A. There is no current around the loop.
B. There is a clockwise current around the loop.
C. There is a counterclockwise current around the loop.
```