Download - FARADAY's Law.ppt
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Faradays Law
Faradays Law of Induction
Lenzs Law
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Faradays Law of Induction
The emf induced in a circuit is directly proportional
to the time rate of change of the magnetic flux
through the circuit.
dt
d B=E
For N loops,dt
dN
B=E
where,
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Lenzs LawThe polarity of the induced emf is such that it tends to produce
a current that creates a magnetic flux to oppose the change in
magnetic flux through the area enclosed !y the current loop.
#s the !ar is slid to the right,the flux through the loop
increases.
This induces an emf that will
result in an opposing flux.
$ince the external field is into
the screen, the induced field has
to !e out of the screen.
%hich means a
countercloc&wise current
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Induced EMF
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Determine if the magnetic eld (B) isincreasing
1) 2)
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The area of the coil is increasing.Determine the direction of theinduced current.
3) 4)
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Induced EMF1) 2)
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Induced EMF(change inarea)Increasing #rea of the circle
clockwise
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Induced EMF(change inarea)
clockwise
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Induced EMF (solenoid)
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Induced EMF
# current flows through
the loop when a magnet
is mo"ed near it, without
any !atteries'
The needle deflects
momentarily when the
switch is closed
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Electric uitar
To #mplifier
(ic&up )oil
*agnet
+uitar$tring
N $$N
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END
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Motional EMF
BvF =qB
#s the wire mo"es,
%hich sets the charges in motion in the
direction of Fand lea"es positi"e charges!ehind.
#s they accumulate on the !ottom, an electric
field is set up inside.
In euili!rium,
qEqvB
FFEB
==
vBE=
BlvElV ==
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Motional EMF in a !ircuit
BlxBAB ==
( )dt
dxBlBlx
dt
d
dt
d B ==
=E
Blv=ER
Blv
RI ==
E
If the !ar is mo"ed with constant "elocity,
IlBFF Bapp ==
( )RR
vlBvIlBvFapp
2222E
P ====
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Magnetic Force on a "lidingBar
The !ar has a mass, m, and
an initial "elocity vi
IlBFB =
IlBdt
dvmmaFx ===
R
BlvI=
dtmR
lB
v
dv
vR
lB
dt
dvm
=
=
22
22
122
=
mR
lB
t
ievv =
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Lenzs LawThe polarity of the induced emf is such that it tends to produce
a current that creates a magnetic flux to oppose the change in
magnetic flux through the area enclosed !y the current loop.
#s the !ar is slid to the right,the flux through the loop
increases.
This induces an emf that will
result in an opposing flux.
$ince the external field is into
the screen, the induced field has
to !e out of the screen.
%hich means a
countercloc&wise current
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Energy !onsiderations
$uppose, instead of flowing countercloc&wise, the induced current flows
cloc&wise-
Then the force will !e towards the right
which will accelerate the !ar to the right
which will increase the magnetic flux
which will cause more induced current to flow
which will increase the force on the !ar
and so on
#ll this is inconsistent with the conser"ation of energy
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Mo#ing Magnet and "tationary!oil
/ight mo"ing magnet
increases flux through
the loop. It induces a current that
creates it own magnetic
field to oppose the flux
increase.
Left mo"ing magnet
decreases flux through
the loop. It induces a current that
creates it own magnetic
field to oppose the flux
decrease.
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$%%lication of Lenzs Law
%hen the switch is closed, the flux goes
from zero to a finite "alue in the direction
shown.
To counteract this flux, the induced current in
the ring has to create a field in the opposite
direction.
#fter a few seconds, since there is no change in the flux, no current flows.
%hen the switch is opened again, this time flux decreases, so a current
in the opposite direction will !e induced to counter act this decrease.
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Loo% Mo#ing &hrough aMagnetic Field
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Induced EMF and ElectricFields
)hanging *agnetic Flux 0*F Electric Field Inside aConductor
This induced electric field is non1conser"ati"e and time1"arying
dt
d B
=E
( )rFqW E 2== E
( )rqEq 2=E
rE
2
E=
( )
dtdBrE
Brdt
d
rdt
d
rE B
2
2
1
2
1 2
=
=
=
dt
dd B
= sE.
+eneral Form of
Faradays Law
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Electric Field Induced 'y a !hangingMagnetic Field in a "olenoid
dt
dd B= sE.
( )dt
dBRRB
dt
dd
22. == sE
tItI cos)( max=
( ) dt
dB
RrE
2
2 =
tnItB
nIB
cos)( max0
0
==
( ) tnIRrE sin2 max02=
tr
RnIE
sin
2
2
max0= r2/
2rB
B =
( ) tnIrdt
dBrrE sin2
max0
22 ==
tr
nI
E
sin2
max0
= r3/
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enerators and Motors
tBABAB coscos ==
( )
NAB
tNABtdt
dNAB
dt
dN B
=
==
=
max
sincos
E
E
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Mawells Euations
dt
dd B
= sE.
dt
dId E
+= 000. sB
0. = AB d
0
.
Qd = AE Gauss Law
Gauss Law for Magnetism no magnetic mono!oles
Farada"s Law
#m!$re%Ma&well Law
BvEF += qq Lorent' Force Law