Download EM PPT4

Faraday’s Law of Electromagnetic Induction
induced voltage, , in a coil is proportional to
the product of the number of loops, N, and the
rate at which the magnetic flux changes within
those loops, Φ/t .
► Faraday’s Law of Electromagnetic Induction:
► The
►
= N(Φ/t)
► Remember,
if not ┴ then need to use:
► Φ = BA (cos)
► Φ = magnetic flux
law states that an emf  is generated if
the magnetic flux changes for any reason. Since
Φ = BA (cos), magnetic flux can change b/c
either B, A, or  change.
► Faraday’s
A flat coil of wire has an area of 0.020 m2 and consists of 50 turns. At t=0s,
the coil is oriented so the normal to its surface is parallel (angle = 0o) to a
constant magnetic field of magnitude 0.18 T. The coil is then rotated through
an angle of 30.0o in a time of 0.10 s. Determine the average induced emf.
►
= N(Φ/t)
► In the time of 0.10 seconds, the only variable
changing is the angle between the normal to the
surface of the coil and the magnetic field; 
►  = N(BA)(cos)/t
►  = (50)(0.18T)(0.020m2)(cos30.0o – cos 0o)/0.10s
►  = -0.24 V
► The negative just implies a certain direction of
current. If the coil of wire were rotated in the
opposite direction, then the emf would be + and
the current would flow opposite.
► An
Lenz’s Law
induced electromotive force  generates
a current that induces a counter magnetic
field that opposes the change in magnetic field
generating the current.
► http://www.micro.magnet.fsu.edu/electrom
ag/java/lenzlaw/index.html
► An
induced emf drives current around a circuit just
as the emf of a battery does.
► With a battery, conventional current is directed
out of the positive terminal, through the attached
device, and into the negative terminal.
► The same is true for an induced emf, but the
location of the positive and negative terminals is
not as obvious.
►
►
►
►
To determine the location of the positive and
negative terminals (i.e., the direction of current), it is
important to remember that there are two
magnetic fields in these situations:
The original magnetic field, and
The induced magnetic field created by the
induced current.
Lenz’s Law: polarity from the induced emf is
found first by knowing…
1.
The induced magnetic field opposes the original flux
2.
Using the RHR#2: if fingers point in direction of induced
magnetic field in coil, then thumb points in direction of
induced current.
Current flows from positive to negative in any circuit.
3.
change
EMF
produced by
a moving
magnet:
1.
The induced magnetic field opposes the original flux
2.
Using the RHR#2: if fingers point in direction of induced
magnetic field in coil, then thumb points in direction of
induced current.
Current flows from positive to negative in any circuit.
3.
change
►
►
►
►
Lenz’s Law
When an emf is generated by a change in magnetic flux
according to Faraday’s Law, the polarity of the induced emf is
such that it produces a current whose magnetic field opposes
the change which produces it.
The induced magnetic field inside any loop of wire always acts
to keep the magnetic flux in the loop constant.
In the examples below, if the magnetic field B is increasing, the
induced magnetic field B acts in opposition to that increase.
If the magnetic field B is decreasing, the induced field B acts in
the direction of the applied field to try to keep it constant.
A copper ring passes through a rectangular region where a
constant magnetic field is directed into the page. The picture
shows that a current is induced in the ring at locations 2 and 4.
1.
2.
3.
4.
5.
No current b/c no flux since no
magnetic field, B=0.
Flux increases. External B
points into page, so I must
move to create a B that offsets
this flux increase. I moves ccw
to counter increase in flux.
Flux is not changing (B is
constant, A is constant, angle is
constant), so I is NOT induced.
Flux decreases. External B
points into page, so I must
move to create a B that offsets
this flux decrease. I moves cw
to counter decrease in flux.
B=0, so no magnetic flux. No
current.
Eddy Currents
► As
the copper plate is
pulled to the right
there are circular
currents induced in the
plate.
► If you use the RHR and
point thumb in the
direction of current in
the center of the plate
what is the direction of
magnetic force?
Eddy currents in bike.
Electric Generators: supply electrical energy
by producing an induced emf according to
Faraday’s law of electromagnetic induction
http://ga.water.usgs.gov/edu/hyhowworks.html
http://www.wvic.com/hydro-works.htm
http://www.wvic.com/how-gen-works.htm
http://people.howstuffworks.com/hydropowerplant2.htm
►A
motor converts
electrical energy into
mechanical energy.
► A generator converts
mechanical energy
into electrical energy.
► In a motor, an input
electric current causes
a coil to rotate,
thereby doing
mechanical work on
any object attached to
the shaft of the motor.
► In
a generator, the shaft is rotated by some
mechanical means, such as an engine or turbine, and
an emf is induced in a coil.
► If the generator is connected to an external circuit, an
electric current is the output of the generator.
►
►
►
►
►
If one end of a magnet is plunged in and out of a coil of wire, the induced
voltage alternates in direction. As the magnetic field strength inside the coil
is increased (magnet entering), the induced voltage in the coil is directed in
one way. When the magnetic field strength diminishes (magnet leaving),
the voltage is induced in the opposite direction.
When the voltage changes direction, so does the current.
Lenz’s law basically states that the moving magnetic field will
induce a current that produces its own magnetic field opposite in
direction to the change in magnetic flux.
The greater the frequency of field change, the greater the induced voltage
(move the magnet fastergreater emf).
The frequency of the induced alternating voltage equals the frequency of
the changing magnetic field within the loop.
► Rather
than moving the
magnet, it is more
practical to move the coil.
► This is best accomplished
by rotating the coil in a
stationary magnetic field.
► This arrangement is
called a generator.
► A generator converts
mechanical energy into
electric energy.
The theory is to build a dam on a large river that has a large drop in elevation (there are not many
hydroelectric plants in Kansas or Florida). The dam stores lots of water behind it in the reservoir.
Near the bottom of the dam wall there is the water intake. Gravity causes it to fall through the
penstock inside the dam. At the end of the penstock there is a turbine propeller, which is turned by
the moving water. The shaft from the turbine goes up into the generator, which produces the
power. Power lines are connected to the generator that carry electricity to your home and mine.
The water continues past the propeller through the tailrace into the river past the dam. By the way,
it is not a good idea to be playing in the water right below a dam when water is released!