Chapter 2: Faraday`s Law

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Transcript Chapter 2: Faraday`s Law

Chapter 3: Faraday’s
Law
2.1 Induced EMF and magnetic
Faraday’s experiment
flux



Picture © Molecular Expressions

Two circuits are not
connected: no current?
However, closing the
switch we see that the
compass’ needle moves
and then goes back to its
previous position
Nothing happens when the
current in the primary coil
is steady
But same thing happens
when the switch is opened,
except for the needle going
in the opposite direction…
What is going on?
2.2 Faraday’s law of induction
Induced current
I
v
S
N
2.2 Faraday’s law of induction
I
v
B
S
I
N
B
I
v
A current is set up in the circuit as long as
there is relative motion between the magnet
and the loop.
Does there have to be motion?
I
(induced) I
-
+
AC Delco
1 volt
Does there have to be motion?
I
-
+
AC Delco
1 volt
Does there have to be motion?
I
(induced)
-
+
AC Delco
1 volt
NO!!
Does there have to be motion?
-
+
AC Delco
1 volt
Maybe the B-field needs to
change…..
B
v
Maybe the B-field needs to
change…..
I
B
v
Maybe the B-field needs to
change…..
I
I
v
B
I
Faraday’s law of magnetic
induction


In all of those experiment induced EMF is
caused by a change in the number of field
lines through a loop. In other words,
The instantaneous EMF induced in a
circuit equals the rate of change of
magnetic flux through the circuit.
Lenz’s Law: The polarity of the induced
emf is such that it produces a current
whose magnetic field opposes the change
in magnetic flux through the loop. That is,
the induced current tends to maintain the
original flux through the circuit.
Lenz’s law
E
N

The number of loops matters
Applications:
Ground fault
interrupter
 Electric guitar
 SIDS monitor
 Metal detector
…

Example 1: EMF in a loop
A wire loop of radius 0.30m lies so that an external magnetic field
of strength +0.30T is perpendicular to the loop. The field changes
to -0.20T in 1.5s. (The plus and minus signs here refer to opposite
directions through the loop.) Find the magnitude of the average
induced emf in the loop during this time.
B
Example 2: EMF of a flexible
loop
The flexible loop in figure below has a radius of 12cm and is in a magnetic
field of strength 0.15T. The loop is grasped at points A and B and stretched
until it closes. If it takes 0.20s to close the loop, find the magnitude of the
average induced emf in it during this time.
X
X
X
A
X
X
X
X
X
X
X
X
X
X
X
X
X
B
2.3 Motional EMF
l
B
v
F
Let's consider a conducting bar moving perpendicular to a uniform
magnetic field with constant velocity v.
F  qvB sin 
This force will act on free charges in the conductor. It will tend to
move negative charge to one end, and leave the other end of the bar
with a net positive charge.
Motional EMF
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
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The separated charges will create an electric field
which will tend to pull the charges back together.
When equilibrium exists, the magnetic force,
F=qvB, will balance the electric force, F=qE, such
that a free charge in the bar will feel no net
force.
Thus, at equilibrium, E = vB. The potential
difference across the ends of the bar is given by
V=El or
V  El  Blv

A potential difference is maintained across the
conductor as long as there is motion through the
field. If the motion is reversed, the polarity of the
potential difference is also reversed.
Motional EMF – conducting rails
R
x
B
v
We can apply Faraday's law to the complete loop. The change of flux through
the loop is proportional to the change of area from the motion of the bar:
  BA  Blx
current
I
or (Faraday’s law)
E Blv

R
R
E

x
 Bl
 Blv
t
t
Motional EMF
Example: wire in the magnetic
field
Over a region where the vertical component of the Earth's magnetic field is
40.0µT directed downward, a 5.00 m length of wire is held in an east-west
direction and moved horizontally to the north with a speed of 10.0 m/s.
Calculate the potential difference between the ends of the wire, and
determine which end is positive.
2.4 Lenz’s law revisited
Application of Lenz's law will tell
us the direction of induced
currents, the direction of
applied or produced forces,
and the polarity of induced
emf's.
 Lenz's law says that the induced current will
produce magnetic flux opposing this change. To
oppose an increase into the page, it generates
magnetic field which points out of the page, at
least in the interior of the loop. Such a
magnetic field is produced by a
counterclockwise current (use the right hand
rule to verify).
Lenz’s law: energy conservation


We arrive at the same conclusion
from energy conservation point of
view
The preceding analysis found that
the current is moving ccw. Suppose
that this is not so.
– If the current I is cw, the
direction of the magnetic force,
BlI, on the sliding bar would be
right.
– This would accelerate the bar to
the right, increasing the area of
the loop even more.
– This would produce even greater
force and so on.
– In effect, this would generate
Our original
assertion that the
current is cw is
not right, so the
current is ccw!
S
S
v
The induced
flux seeks to
counteract
the change.
N
change
change
S
S
N v
N
Example: direction of the
current
Find the direction of the current induced in
the resistor at the instant the switch is
closed.
Applications of Magnetic Induction

Tape / Hard Drive / ZIP Readout
– Tiny coil responds to change in flux as the magnetic domains
(encoding 0’s or 1’s) go by.
Question: How can your VCR display an image while paused?

Credit Card Reader
– Must swipe card
 generates changing flux
– Faster swipe  bigger signal