Engineering Electromagnetics- 1 - KOCWcontents.kocw.net/KOCW/document/2015/sungkyunkwan/... ·...
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Department of Semiconductor Systems Engineering SoYoung Kim Engineering Electromagnetics- 1 Lecture 21: Magnetic Circuit, Faraday’s Lw SoYoung Kim [email protected] Department of Semiconductor Systems Engineering College of Information and Communication Engineering Sungkyunkwan University
Transcript of Engineering Electromagnetics- 1 - KOCWcontents.kocw.net/KOCW/document/2015/sungkyunkwan/... ·...
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Department of Semiconductor Systems Engineering SoYoung Kim
Engineering Electromagnetics- 1 Lecture 21: Magnetic Circuit, Faraday’s Lw
SoYoung Kim
Department of Semiconductor Systems Engineering
College of Information and Communication Engineering
Sungkyunkwan University
mailto:[email protected]
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Department of Semiconductor Systems Engineering SoYoung Kim
Outline
Magnetic Circuit
Chapter 9
Faraday’s Law
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Department of Semiconductor Systems Engineering SoYoung Kim
Magnetic Circuits (8.10)
Mathematical analogy, physical meaning
Electric circuit problems – V, I
Magnetic circuit problems – NI,
Magnetomotive Force Electromotive Force
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Department of Semiconductor Systems Engineering SoYoung Kim
Magnetic Circuits
Magnetomotive Force
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Department of Semiconductor Systems Engineering SoYoung Kim
Example
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Department of Semiconductor Systems Engineering SoYoung Kim
Power link for wireless neural recording system
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Department of Semiconductor Systems Engineering SoYoung Kim
Chapter 9. Maxwell’s Equations
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Department of Semiconductor Systems Engineering SoYoung Kim
FARADAY'S LAW
In 1820, Oersted's experimental discovered that a steady current produces a magnetic field.
In 1831, Michael Faraday in London and Joseph Henry in New York discovered that a time-varying magnetic field would produce an electric current.
Faraday’s law : A static magnetic field produces no current flow, but a time-varying field produces an induced voltage (called electromotive force or simply emf) in a closed circuit, which causes a flow of current.
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Department of Semiconductor Systems Engineering SoYoung Kim
FARADAY'S LAW
l = NY : flux linkage, N : number of turns, Y : flux through each turn
(-) sign means that the induced voltage acts in such a way as to oppose the flux producing it Lenz’s law
It emphasizes that the direction of current flow in the circuit is such that the induced magnetic field produced by the induced current will oppose the change in original magnetic field.
dt
dN
dt
dVemf
l
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Department of Semiconductor Systems Engineering SoYoung Kim
EMF
Source of electric field
Electric charge
Electromotive force (EMF) : electric field is generated from nonelectrical energy ( generators, batteries, thermocouples, fuel cells, photovoltaic cells, etc)
Static Electric Field
+
- Electromotive Force
E l
E l E l
E l E l 0
L
f eL L
P
f eN L
d
d d
d d
nonconservative
IRddVP
Ne
P
Nfemf lElE
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Department of Semiconductor Systems Engineering SoYoung Kim
ELECTRO MOTIVE FORCE
Not force[N], but voltage [V]
An electric field is one in which electric charges experience force.
Flux lines of the static fields generated by electric charges begin and end on the charges conservative
Electric fields produced by EMF are not caused by electric charges and different form the static electric field not conservative
0
0
L
emf
emf
dlEV
IRV 0
Y
L
dlEdt
d
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Department of Semiconductor Systems Engineering SoYoung Kim
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Department of Semiconductor Systems Engineering SoYoung Kim
Review
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Department of Semiconductor Systems Engineering SoYoung Kim
3. TRANSFORMER AND MOTIONAL ELECTROMOTIVE FORCES
EMF for a Circuit with a Single Turn
S : surface area of the circuit bounded by the closed path
dl and dS : obey the right hand rule and Stokes’s theorem
The Variation of Flux with Time
a stationary loop in a time-varying B field
a time-varying loop area in a static B field
a time-varying loop area in a time-varying B field
E l B SemfL s
dΨ dV d d
dt dt
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Department of Semiconductor Systems Engineering SoYoung Kim
A. STATIONARY LOOP IN TIME-VARYING B FIELD (TRANSFORMER EMF)
A stationary conducting loop is in a time-varying magnetic B field
The time-varying E field is not conservative ! The principle of energy conservation is not violated. The work done in taking a charge around a closed
path is due to the energy from the time-varying magnetic field.
BE l S= ( E) S
BE
emfL s s
dV d d d
dt
t
one of the Maxwell's equations for time-varying fields.
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Department of Semiconductor Systems Engineering SoYoung Kim
B. MOVING LOOP IN STATIC B FIELD (MOTIONAL EMF or FLUX CUTTING EMF)
Force on a charge moving with uniform velocity u in a magnetic field B
Define motional electric field
Motional EMF in the loop
The integral is zero along the portion of the loop where u = 0.
The direction of the induced current is the same as that of Em or u XB
Ex
Who supplies the energy?
LL memf ddV lBulE )(
( )
m
emf mL L
I
B
B
d
l
V d u
E l u B
F
l
m Q F u B
m E u B
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Department of Semiconductor Systems Engineering SoYoung Kim
C. MOVING LOOP IN TIME-VARYING FIELD
Both transformer emf and motional emf are present.
LSL
emf ddt
dV lBuSB
lE )(
SL
SL
dd
dd
SBulBu
SElE
)()(
)(
)( BuB
E
t
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Department of Semiconductor Systems Engineering SoYoung Kim
Example. 1
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Department of Semiconductor Systems Engineering SoYoung Kim
Solution
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Department of Semiconductor Systems Engineering SoYoung Kim
Example 1. (a),(b)
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Department of Semiconductor Systems Engineering SoYoung Kim
Example 1 (c) Method 1
(c) Both transformer emf and motional emf are present in this case
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Department of Semiconductor Systems Engineering SoYoung Kim
Example 1.(c) Method2
Use of flux rule
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Department of Semiconductor Systems Engineering SoYoung Kim
General Faraday’s Law
