Transcript Physics 2054 Lecture Notes

If we can get magnetism out of
electricity, why can’t we get electricity
from magnetism?
The
answer………………..
Electromagnetic
induction
Transformers
 This is how first experiment
by Faraday was done
 He only got a deflection of
the galvanometer when the
switch is opened or closed
 Steady current does not
make induced emf.
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Experimental Observation of Induction
This effect can be quantified by Faraday’s Law
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Electromagnetic Induction
Faraday
discovered that a changing magnetic flux leads to
a voltage in a wire loop
 Induced
voltage (emf) causes a current to flow !!
Symmetry:
 electric
electricity
current
 magnetic
field
magnetism
magnetic field
electric current
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What does Faraday’s law say?
Faraday’s
law says that
 a)
an emf is induced in a loop when it moves through an electric
field
 b) the induced emf produces a current whose magnetic field
opposes the original change
 c) the induced emf is proportional to the rate of change of
magnetic flux
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Faraday’s Law of Induction

 B
 N
t
rate of change
of flux with time
induced
emf
number
of loops


The faster the change, the larger the induced emf
The induced emf is a voltage
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TYPES OF INDUCED EMF
Statically

induced emf
Conductor remains stationary and flux linked with it is changed
(the current which creates the flux changes i.e increases or
decreases)
TYPES
Self induced
 Mutually induced
Dynamically
induced emf
 Field
is stationary and conductors cut across it
 Either the coil or the magnet moves.
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Can we get emf induced
in
a motionless circuit?
An
induced emf produced in a
motionless circuit is due to
 1)
 2)
 3)
 4)
 5)
a static (steady) magnetic field
a changing magnetic field
a strong magnetic field
the Earth’s magnetic field
a zero magnetic field
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Induction in Stationary Circuit
Switch
closed (or opened)
 Current
Steady
 No
induced in coil B
state current in coil A
current induced in coil B
A
B
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How does a magnetic field change?

The
 B
 N
t
field can itself be changing in nature
Either
the magnet itself should move or the
conductor should move with respect to each
other
Hence
there should be a relative motion
between magnet and the conductor
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Electric Generators
Rotate
a loop of wire in a uniform magnetic field:
  changing flux  induced emf
= B A cos  = B A cos(t)
 changing
 B
Rotation: 
= t
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Faraday’s Law
 How
to change the flux?
 Recall
that flux is:
B  B A cos
B or A or  will
change the flux.
 Changing
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Faraday’s Law of Induction

 B
 N
t
rate of change
of flux with time
induced
emf
number
of loops


Minus sign from Lenz’s Law:
Induced current produces a magnetic field
which opposes the original change in flux
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Comment on Lenz’s Law
Why
does the induced current oppose the change in flux?
Consider
the alternative
 If
the induced current reinforced the change, then the change
would get bigger, which would then induce a larger current, and
then the change would get even bigger, and so on . . .
 This
leads to a clear violation of conservation of energy!!
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Direction of Induced Current
Bar magnet moves through coil
 Current induced in coil
S
N
N
S
S
N
N
S
v
Reverse pole
 Induced current changes sign
v
Coil moves past fixed bar magnet

Current induced in coil
Bar magnet stationary inside coil
 No current induced in coil
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ConcepTest: Lenz’s Law
If
a N pole moves towards the loop from above the page,
in what direction is the induced current?
 (a)
clockwise
 (b) counter-clockwise
 (c) no induced current
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SELF
INDUCTANCE AND MUTUAL INDUCTANCE
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Self - Inductance
Consider
a single isolated coil:
 Current
(red) starts to flow clockwise due to the battery
 But the buildup of current leads to changing flux in loop
 Induced emf (green) opposes the change
This is a self-induced emf (also called “back” emf)
   N ddt   L dIdt
L is the self-inductance
units = “Henry (H)”=N2/R
induced
emf
PROPERTY OF A COIL DUE TO WHICH
IT OPPOSES THE CHANGE OF
CURRENT OR FLUX THROUGH IT
SELF INDUCTANCE
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Mutual Inductance
Consider
 if
two neighboring coils:
current changes in coil #1, an emf is induced in coil #2

2
 N
d 1
dt

B
 B  I1
 rewrite as:

2
 M
dI1
dt
M is the “mutual inductance”
units = Henry (H)
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MUTUAL INDUCTANCE
Principle
of operation of Transformer
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