Transcript Electromagnetic Induction_ch25 - bba-npreiser

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Electromagnetic Induction
and Electromagetism
Chapter 25 and 26
• Electric currents produce magnetic fields (Oersted’s
experiments)
• “While performing his electric demonstration,
Oersted noted to his surprise that every time the
electric current was switched on, the compass
needle moved. He kept quiet and finished the
demonstrations, but in the months that followed
worked hard trying to make sense out of the new
phenomenon.”
• Is the opposite true: can magnetic fields
create electric currents?
Faraday’s experiments
• Faraday discover the answer…..
• On August 29, 1831, Faraday wound
a thick iron ring on one side with
insulated wire that was connected
to a battery. He then wound the
opposite side with wire connected
to a galvanometer.
• He closed the primary circuit and,
to his delight and satisfaction, saw
the galvanometer needle jump.
• When he opened the circuit,
however, he was astonished to see
the galvanometer jump in the
opposite direction.
• In the fall of 1831 Faraday
attempted to determine just how
an induced current was produced.
Faraday’s experiments
Faraday is
thought of as
one of the
greatest
experimentalist
of all time. He
developed many
important
devices
including the
Faraday cage,
the first dc
generator and
the first ac
generator
Induced current
• When a magnet approaches a coil of wire, the magnetic field
becomes stronger, and it is this changing field that produces
the current.
• The current in the coil is called induced current because it is
brought about by a changing magnetic field.
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Induced EMF
• Since a source of emf is always need to produce a current, the
coil itself behaves as if it were a source of emf. This emf is
known as an induced emf.
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B
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I
B
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N
A current is set up in the circuit as
long as there is relative motion
between the magnet and the loop.
Back to Faraday’s two coils of wire
I
If you have a current
flowing through one coil
and no current in a
second coil which is not
touching the first,
then………
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AC Delco
1 volt
Back to Faraday’s two coils of wire
I
(induced)
A current will also be induced
(in the other direction) when
the switch is closed again.
open the the switch
(stop the current in the
first), an induced
current is brought about
in the second coil. The
coils do not need to
touch or move relative
to each other.
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AC Delco
1 volt
Back to Faraday’s two coils of wire
• In Faraday’s experiment, the current (moving charge)
produces a magnetic field.
• When the current is turned off, the magnetic field changes
and a current is induced in the other coil.
• The changing magnetic field brings about an induced current.
• In the experiment shown below, again the changing magnetic
field brings about an induced current and induced emf.
Motional EMF
• As the hand pushes the conducting rod, in a constant
magnetic field, an induced current causes the light bulb to
come on.
• In this case, the magnetic field is not changing, but there is
still an induced current. Why?
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Motional EMF
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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
• 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.
• So, 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 and forces
L
Magnetic force to the left resists push to the right by the hand
If the rod moves at a constant speed, F = IBL, equals the magnetic force
and the force on the hand, where I is the current, B is the magnetic field
and L is the length of the conducting rod. (This force is the force on a
current carrying wire in a magnetic field discussed in the magnetic fields
power point presentation.)
Faraday’s Law
• Faraday was able to explain
all three experiments with his
law.
• Faraday’s Law: The
instantaneous EMF
induced in a circuit
equals the rate of change
of magnetic flux through
the circuit.
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 = BA
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The number of loops matters
  BA cos 
Magnetic flux
• Place a loop in the B-field. The
flux, , is defined as the
product of the field magnitude
by the area crossed by the
field lines.
• Units: T·m2 or Webers (Wb)
• The value of magnetic flux is
proportional to the total
number of magnetic field lines
passing through the loop.
• Faraday said the induced emf
depends on the rate of change
of the flux, so a change in B or
Area or a change in both can
cause a flux change.
  B A  BA cos 
B is the component of B perpendicular to the
loop,  is the angle between B and the normal
to the loop and A is the area of the loop.
Faraday’s Law - Example
This time,  changes because
the B-field changes.
 = (B)A
---------------------------------Example: B0 = 0.04 T
B = 0.07 T
B = 0.03 T
A = 0.004 m2
t = 0.005 s
 = (0.03)(0.004)
= 1.2 x 10-3 T-m2
Induced emf =  /t
= 1.2 x 10-3 /0.005
= 0.24 V
Faraday’s Law - Example
 = BA
 = B (A)
Magnetic field doesn't
change; area changes.
Induced emf = N /t
(Omitting negative sign)
The more quickly the
loop is stretched, the
smaller will be t and
the larger will be the
transient emf.
Motional EMF-Faraday’s Law
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
or (Faraday’s law)
E Blv
I 
R
R
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E

x
 Bl
 Blv
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Motional EMF
Lenz’s Law
• Lenz’s Law allows for the determination of the
direction of the induced current, clockwise or
counter clockwise
• 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.
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Lenz’s law
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Lenz’s Law - examples
(A)
(B)
• 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. In diagram A, to oppose
an increase into the page, a magnetic field which points out of
the page is generated, 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 energy
out of nothing violating the law of
conservation of energy.
Our original
assertion that the
current is cw is not
right, so the current
is ccw!
Lenz’s Law – more examples
Cause: More B-arrows puncture plane
Effect: Induced electromagnet creates
its own B-field arrows pointing
in the opposite direction, partially
cancelling the increase.
Cause: Fewer B-arrows puncture plane
Effect: Induced electromagnet creates
its own B-field arrows pointing in the
same direction as the bar magnet's field,
partially cancelling the loss of B arrows
Generators
• A generator is a
device that that
converts
mechanical
energy into
electrical
energy
• A coil is rotated
in a magnetic
field, as a result
the coil has an
alternating emf
induced in it.
Simple Generator
The First Generator
Simple A.C. Generator
• Consider a coil of wire rotating in a uniform magnetic field, B, as shown in
diagram A below.
• When the coil is in the position shown in diagram A, side 2 is moving down
and side 1 is moving up and end q will (at that instant) be the positive
terminal of the generator.
• When the coil has rotated through half a turn, end p will be the positive
terminal.
• Therefore, a coil of wire rotating in a magnetic field has an alternating emf
induced in it.
• To connect the coil to a light bulb (or any other component) brushes made of
carbon make contact with slip rings made of brass, as shown in diagram B.
(A)
(B)
Generators
Graph of induced
emf against time
• In a hydroelectric
plant the coil in the
generator is turned by
the waterfall.
• As the coil turns the
induced emf changes
as shown in the graph
above.
AC
• AC stands for alternating current. Alternating Current (AC)
flows one way, then the other way, continually reversing
direction.
• An AC voltage is continually changing between positive (+)
and negative (-).
• Electric generators used in power plants produce AC current,
• so AC current is the type of current that is in your home.
DC
• DC stands for direct current. Direct Current (DC)
always flows in the same direction, but it may
increase and decrease.
• A DC voltage is always positive (or always negative),
but it may increase and decrease
• Cells, batteries and regulated power supplies provide
steady DC which is ideal for electronic circuits
Transformer
• A transformer is an
electrical device used to
convert AC power at a
certain voltage level to
AC power at a different
voltage, but at the same
frequency.
There are two kinds of
transformers: step down
and step up. Step up
transformers increase
the voltage where step
down transformers
decrease the voltage.
The First Generator
Step-up and Step-down Transformers
• A transformer consists of
a primary coil and a
secondary coil both
wound on an iron core.
• The changing magnetic
flux produced by the
current in the primary coil
induces an emf in the
secondary coil.
• Step-up example (pictured above): A picture tube in a TV needs about
15000 V to accelerate the electron beam that is needed for the picture,
and a step-up transformer is used to obtain this high voltage from the 120
V wall socket.
• Step-down example: Only 3 – 9 V are needed to energize batteries. A
step-down transformer is used to reduce the 120 ac voltage from the wall
to a much smaller value.
Electromagnetic Waves
• Faraday’s law states: An electric field is created in any region of space in
which a magnetic field is changing with time. The magnitude of the
induced electric field is proportional to the rate at which the magnetic
field changes. The direction of the induced electric field is at right angles
to the changing magnetic field.
• James Clerk Maxwell states: A magnetic field is created in any region of
space in which an electric field is changing with time. The magnitude of
the magnetic field is proportional to the rate at which the magnetic field
changes. The direction of the induced magnetic field is at right angles to
the changing electric field.
• The vibrating electric and magnetic fields in the diagram above regenerate
each other to make up an electromagnetic wave (light), which emanates
from a vibrating charge.
James Clerk Maxwell's Equations
• James Clerk Maxwell.James
Clerk Maxwell is considered
one of the most important
physicists of the 19th century
and of all time.
• His best-known discoveries
concern the relationship
between electricity and
magnetism and are
summarized in what has
become known as Maxwell’s
Equations, which have
become a major underpinning
of modern physics.
Maxwell’s four equations by
themselves, define the entire
field of electricity and magnetism
Electromagnetic Waves: Radio waves
• http://phet.colorado.edu/simulations/sims.php?sim=R
adio_Waves_and_Electromagnetic_Fields
• If charges oscillate back and forth in the wire, you get
a changing electric fields.
• If charges oscillate back and forth, you get changing
magnetic fields too.
• If the fields are perpendicular, you have
electromagnetic radiation.
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Electromagnetic Waves: X-rays
• X-ray production occurs whenever electrons of high energy strike a heavy
metal target, like tungsten or copper. When electrons hit this material,
some of the electrons will approach the nucleus of the metal atoms where
they are deflected because of their opposite charges (electrons are
negative and the nucleus is positive, so the electrons are attracted to the
nucleus). This deflection causes the energy of the electron to decrease,
and this decrease in energy then results in forming an x ray.
Sources
• http://sol.sci.uop.edu/~jfalward/electromagn
eticinduction/electromagneticinduction
• http://www.physics.wayne.edu/~apetrov/PHY
2140/#lectures
• Physics by Zitzewitz