Lecture 13.2 :!
Inductors
Lecture Outline:!
Induced Fields!
Inductors!
LC Circuits!
LR Circuits!
!
Textbook Reading:!
Ch. 33.6 - 33.10
April 9, 2015
1
Announcements
!
•HW #10 due on Tuesday, April 14, at 9am.!
•Exam #3 next Thursday, April 16.
Will cover Ch. 32 and Ch. 33.
Bring your calculators and one sheet of notes.!
!
2
Last Lecture...
All induced currents are associated with a changing
magnetic flux. Two ways flux can change:!
1.Geometry: Loop can expand, contract, or rotate.!
2.Magnetic field can change.
E=
d
m
dt
dB
dA
+A·
= B·
dt
dt
3
Last Lecture...
We know from Lenz’s law that a conducting loop in a
changing magnetic field will develop an induced current to
counteract the changing flux. There must be an E-field
present to create this current in the loop.
In this changing magnetic field, the E-field is present
whether or not the loop is there!
4
Clicker Question #1
The induced emf
around this loop is
!
A.
B.
C.
D.
E.
200 V.
50 V.
2 V.
0.5 V.
0.02 V.
5
Clicker Question #1
The induced emf
around this loop is
!
A.
B.
C.
D.
E.
200 V.
50 V.
2 V.
0.5 V.
0.02 V.
5
Clicker Question #1
The induced emf
around this loop is
!
A.
B.
C.
D.
E.
200 V.
50 V.
2 V.
0.5 V.
0.02 V.
Is the induced current flowing
clockwise or counterclockwise?
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The Can Crusher Demo
6
The Can Crusher Demo
5K20.65
Eddy Currents
6
Induced Fields
We now understand that a changing magnetic field creates an
electric field (even though no charge is present). We can
rewrite Faraday’s law to allow calculation of the electric field.
(Work done moving a
charge around a closedloop in an electric field E)
Wclosed
7
curve
=q
E · ds
Induced Fields
We now understand that a changing magnetic field creates an
electric field (even though no charge is present). We can
rewrite Faraday’s law to allow calculation of the electric field.
(Work done moving a
charge around a closedloop in an electric field E)
Wclosed
Potential difference (EMF)
crossed around that
closed-loop path.
Wclosed
E=
q
7
curve
E · ds
=q
curve
=
E · ds
Induced Fields
We now understand that a changing magnetic field creates an
electric field (even though no charge is present). We can
rewrite Faraday’s law to allow calculation of the electric field.
(Work done moving a
charge around a closedloop in an electric field E)
Wclosed
Potential difference (EMF)
crossed around that
closed-loop path.
Wclosed
E=
q
(for the case of an
unchanging loop
perpendicular to B-field)
⇥
curve
curve
dB
E · ds = A
dt
7
E · ds
=q
=
E · ds
Induced Fields
Inside a solenoid, a changing magnetic field induced an
electric field that circles around the magnetic field.
8
Induced Fields
Inside a solenoid, a changing magnetic field induced an
electric field that circles around the magnetic field.
8
Induced Fields
Inside a solenoid, a changing magnetic field induced an
electric field that circles around the magnetic field.
8
Induced Fields
Maxwell knew of Faraday’s work, and based on symmetry he
proposed that a changing electric field induces a magnetic field.
9
Induced Fields
Maxwell (~1855) also predicted that electromagnetic waves
with transverse E and B fields would travel at the speed of light.
vem
wave
=⇤
1
0 µ0
10
⇥ 3.0
108 m/s
Induced Fields
Maxwell (~1855) also predicted that electromagnetic waves
with transverse E and B fields would travel at the speed of light.
vem
wave
=⇤
1
0 µ0
10
⇥ 3.0
108 m/s
Inductors
Inductors are devices in circuits that can be used to store
energy in magnetic fields (similar to Capacitors storing
energy in electric fields). They have interesting behavior
when placed in circuits.
Inductance
L
1 henry = 1 H
11
m
I
1 Wb/A = 1 Tm2 /A
Inductors
What’s the inductance of an N turn solenoid?
Recall (from
Ampere’s Law):
Bsolenoid
µ0 N I
=
l
12
Inductors
If (and only if) the current through an inductor is changing,
a potential difference develops across the inductor.
Induced current
Induced field
13
Inductors
If (and only if) the current through an inductor is changing,
a potential difference develops across the inductor.
Induced current
Induced field
13
Inductors
If (and only if) the current through an inductor is changing,
a potential difference develops across the inductor.
Induced current
Induced field
d⇥m
dI
VL =
=L
dt
dt
We choose same sign convention as
in resistors...voltage decreases in
direction of current flow.
13
Clicker Question #2
Which current is changing more rapidly?
!
A. Current I1.
B. Current I2.
C. They are changing at the same rate.
D. Not enough information to tell.
14
Clicker Question #2
Which current is changing more rapidly?
!
A. Current I1.
B. Current I2.
C. They are changing at the same rate.
D. Not enough information to tell.
14
Inductors
15
Inductors
How much energy is stored in the magnetic field of an inductor?
16
LC Circuits
A circuit with an inductor and capacitor arranged in series is called a
LC circuit. The current in this circuit will oscillate in time.
17
LC Circuits
18
LR Circuits
A circuit with an inductor and resistor arranged in series is called a
LR circuit.
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Reminders
!
•HW #10 due on Tuesday.!
•Exam #3 next Thursday.
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