Lesson 9 Lesson 9Lesson 9
Faraday’s LawFaraday’s Law
Faraday’s Law of InductionFaraday’s Law of InductionMotional EMFMotional EMFLenz’s LawLenz’s LawInduced EMF’s and Induced Electric FieldsInduced EMF’s and Induced Electric FieldsEddy CurrentsEddy Currents
Torque on LoopCurrent in loop in a magnetic
field produces torque on a loop
In general the torque on a current loop in magnetic field is
= M B
M IA, where A is the area vector of the loop,
with the orientation given by the current flow.
Induced CurrentDoes torque on loop in a magnetic field produces current in a loop ?
YESYES
Picture
current depends on the torquethus on rotational frequency
II
B
Change of Flux Picture
Current depends on speed of magnetThus rate of change of magnetic Field
Change of Flux Picture Equations
Common factors, change of area, change of magnetic field
Iind dBdt
Iind dA
dtA area perpendicular to magnetic Field
Iind dB
dtB A B
Induced Current in Wire
I
B v
FB
moving wire in field B
produces current I if there is a
conduction path
Induced emf
ji
k
z2)y1(y,
z1)(y,
Equations Iv vj
B Bi
FB Qv B QvBj i QvBk
Equations IIWork done per unit charge by F B
in moving charges from z1 to z2
vBl
where l z2 z1No work is done in moving charges in
other sections of path ( ignore Hall effect )
Work done per unit charge dW
dQ= emf
Thus
vBl
Equations IIIArea of loop in magnetic field
A t y t y1
lTotal magnetic flux through loop
t Rate of change of magnetic flux
d dt
-Bdydtl Bvl
1ytyBt AB
Faraday s Law of Induction for N loops
}{ AB ddt
dN
dt
d
This defines an Induced Electric Field
by
Faradays Law of Electromagnetic Induction
The work done per unit charge by magnetic force
moving charge from z1 to z2
dW
dQ 1
QF B d s
z 1
z2
1
QF B d s
loop E ind d s
loop
thus
N d
dt E ind d s
loop
An induced EMF is a measure An induced EMF is a measure ofof
An induced Electric FieldAn induced Electric Field If charge is in this region and If charge is in this region and there there is a conduction path it is a conduction path it will feel a will feel a force from the force from the induced Electric induced Electric Field and flow Field and flow
An induced EMF is a measure An induced EMF is a measure ofof
An induced Electric FieldAn induced Electric Field If charge is in this region and If charge is in this region and there there is a conduction path it is a conduction path it will feel a will feel a force from the force from the induced Electric induced Electric Field and flow Field and flow
Induced Electric Field
Equations
Remember for a static electric field E stat
Vab Estat d s
a
b
and
Estat d s 0 as Estat is conservative
But for an induced electric field E ind
Eind d s 0
thus
Eind is not conservative
Magnetic Flux and Induced Electric Field
Changing Magnetic Flux produces an
Induced Electric Field
Mechanical Work to Electrical work I
I Fappl
v
l
B
Blv
Pulling at constant velocity v
k
ji
y
Mechanical Work to Electrical work II
wire l with current I flowing in it
moving in a magnetic field B
feels a force given by
F Il B
F IlB k i IlB j
This force opposes the applied force F appl
and must be equal and opposite if the
velocity is to remain constant
F Fappl IlB
Mechanical Work to Electrical work III
I Fappl
v
l
B
Blv
F
Mechanical Power to Electrical Power IPower produced in circuit
I IBvlwhich is the same as the power produced by
the applied force
F appl v Fapplv IBlv
Mechanical Power to Electrical Power II
I Fappl
v
l
B
Blv
Pulling at constant velocity v
F
Magnetic Field produced by Changing Current
Circulating current produces an induced magnetic field
I
Bind
That opposes the external magnetic field B
That produces the current
Current produced by Changing Magnetic Field
(a) Change of External Magnetic Field Produces Current
(b) Current Produces Induced Magnetic Field
Lenz's Law
Lenz’s Law
Polarity of is such that it opposes the change that
caused it
Direction of Eis such that it opposes the change that
caused it
Direction of induced current is such that
it opposes the change that caused it
Conservation of Energy
Conservation of Energy
AC GeneratorAC Generator
AC Potential
t ddt
ddt
BA
ddtBACos BA sin t
if rotational speed is constant
t BAsin t maxsin t
max
BA
d
dt
t
DC GeneratorDC Generator
Eddy Currents
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