Download Lenz and Inductors

Lenz’s Lab
Dr. Lenz strikes again.
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We looked at induced currents
We indirectly covered Lenz’s Law
Today we will explore induction further and
learn about a new circuit element.
Friday we will have a quiz. (Remember my
threat … it might happen! Or not.)
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We looked at currents and magnetic fields
induced by changing magnetic fields.
We defined magnetic flux.
We can now state Lenz’s Law in the following
way:
◦ If you try to change the magnetic FLUX through a
closed surface, the induced current will be in such
a direction as to OPPOSE the change that you are
trying to make!
◦ Or – “The toast will always fall buttered side down!”
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You said that there is a conducting loop.
You said that there is therefore a current
induced around the loop if the flux through
the loop changes.
But the beginning and end point of the loop
are the same so how can there be a voltage
difference around the loop?
Or a current???
‘tis a puzzlement!
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Induction
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DID I LIE??
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
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Electric fields that are created by static
charges must start on a (+) charge and end
on a (–) charge as I said previously.
Electric Fields created by changing magnetic
fields can actually be shaped in loops.
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Because you said
that an emf is a
voltage so if I put a
voltmeter from one
point on the loop
around to the same
point, I will get ZERO
volts, won’t I? How
can there be a
current??
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Induction
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Is the WORK that an external agent has to do
to move a unit charge from one point to
another.
But we also have (neglecting the sign):
V   Es
s
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emf   Es  E  s
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emf  2RE  zero
E
Conductor
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E
A
B
C
The emf
Zero
Can’t tell

A
Conductor
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emf  
MINUS????
Through
the loop
t
Michael Faraday
(1791-1867)
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A: The way that you don’t want it to
point! (Lenz’s Law).
Lenz’s Law Explains the (-) sign!
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In this case, 2 coils, each have
the SAME emf so we add..
Ohm’s Law still works, so

emf  N
t
emf
i
Rcoil
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Induction
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N B
L
i
If the FLUX changes a bit during a short
time t, then the current will change by a
small amount i.
Li  N B
Faraday says
this is the emf!
 B
i
N
L
t
t
This is actually a
calculus equation
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i
E= emf  L
t
There should be
a (-) sign but we
use Lenz’s Law
instead!
The UNIT of “Inductance – L” of a coil is the henry.
SYMBOL:
Induction
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Induction
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Switch is open .. no
current flows for
obvious reasons.
Switch closed for a
long time:
◦ Steady current, voltage
across the inductor is
zero. All voltage (E) is
across the resistor.
◦ i=E/R
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When the switch opens, current change is high and back emf from L is maximu
i
E/R
t
As the current increases, more voltage is across R, the rate of change of I decrea
and as the current increases, it increases more slowly.
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
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When L=0, the
current rises
very rapidly
(almost
instantly)
As L increases, it
takes longer for
the current to
get to its
maximum.
Induction
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i
emf  iR  L  0
i
Solution
E
i  (1  e ( R / L ) t )
R
E
i  (1  e t / )
R
L
  (time constant)
R
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 1
1    0.63
 e
}
63% of
maximum
e= 2.71828…
Induction
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
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Magnetic field
begins to
collapse, sending
its energy into
driving the
current.
The energy is
dissipated in the
resistor.
i begins at
maximum (E/R)
and decays.
Induction
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E t / 
i  (e )
R
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