Transcript Magnetic Induction

Magnetic Induction
Your new puzzle Pieces
d B
  N
dt
  NAB sin( t   )
Induction
• What is it?
• Recall how a current in a wire can cause a
magnetic field, well it’s only fair then that a
magnetic field can cause (induce) a
current in a wire.
• Two Laws to quantify the effect:
– Faraday’s
– Lenz’s
Applications
•
•
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•
Electric Power generation
Electric Guitar
Radio and TV broadcast/reception
You’ll think of many others for sure by the
end of the day!
Let’s get right to it!
• If F = ma is the “mother of all” mechanics
Eqn’s
• Then F = qv x B could be the mother of all
magnetism eqn’s
qv x B helps explain many
electromagnetic effects
• Motion of charged particle in a magnetic field.
• Force on a current carrying wire in a magnetic
field.
• If you move a conductor in a magnetic field, the
“free” electrons experience a Force of F=qv x B,
they tend to move, that’s a current!
• Voltage induced in a conductor moving through
a magnetic field
• Current induced in a conducting loop
Faraday’s Law
• The electromotive force, emf, (think voltage)
induced in a circuit equals the time rate of
change of the magnetic flux through the
circuit.
d B
  N
dt
Lenz’s Law
• The polarity of the emf opposes the
change in magnetic flux, it tends to
maintain the flux present before the
change, think inertia .
Magnetic Flux B
• So what’s with Flux?
– Magnetic field times area, how much
magnetism passes through an area,
– Think through a conducting loop
B = BAcosq
B is field Strength, A is area q is angle
between field and normal to the plane of the
coil.
B
A
q
B
 B = BAcosq
Component of B that goes through the loop.
Problem#1
• A square loop of copper with area =0.5m2
is perpendicular to a magnetic field of
1.2T. It is pulled out of the field in 2.4 sec.
What is average emf induced in the loop?
Dt=2.4sec
A=0.5m2
B=1.2T
Problem #2a
What is the emf induced in the bar?
vbar=3000m/s
d=20cm
B= 1.25T
R= 100W
Problem #2b
What is direction of the induced current in the “loop”
(clockwise or counter clockwise)?
vbar
B
R
Point right thumb in direction OPPOSING increasing
flux.
Flux increases into page here, so thumb point out of
page.
Fingers wrap counterclockwise, so that is the direction
of induced current.
• Pulling out a hoop is cool at
the circus, but it’s a bit more
practical to spin the loop…if
you want to make electricity.
Calculus is great!
• Faraday said the
dB
  N
induced emf is the
dt
time rate of change in
 B = BAcosq
magnetic flux
If B and A are constants…and
qt...
dBAcosq
  N
dt
  NAB sin(t   )
Problem # 3
• Let’s spin the 0.5 m2 loop at 100 rad/s in a
1.2 T magnetic field and find the induced
voltage.
A=0.5m2
B=1.2T
Induced current
• Generators
V  IR
NAB

I


sin(t   )
R
R
Alternating current
Problem # 4
• Now my 0.5m2 loop has 100 turns,
resistance of the device attached is 10
ohms, and the induced current is 0.10
Amps. What must be the rate of change
of the magnetic field?
B, dB/dt
Self-Inductance
• OK so an electrical current can cause a
magnetic field.
• A changing magnetic field can cause an
induced current…
• Can an electrical circuit induce a magnetic
field that induces a current in the circuit
that caused the magnetic field?
• YES!
Self-Inductance
• Once a current is established in a circuit,
self inductance will tend to keep the
current going even after the circuit is
turned off…
• No it isn't perpetual motion.
• The current will decay to zero in a short
time, but not instantly.
Solenoid
• A solenoid is a coil of
wire such as is used
to change voltage.
Think transformer.
• It has an inductance
given by:
L
0 N 2 A
l
Lenz’s Law
• So the emf opposes the change in
magnetic flux, that amounts to the induced
voltage and current being directed
opposite the applied voltage
dB
  N
dt
Check this out…What if we
disconnect the voltage, that’s
decreasing the flux, so the
solenoid will tend to keep the
current going in the same
direction it was before!!!
Problem # 5
Let’s design a generator. I want to generate 120 volts. My loop can only be
0.10 meters in diameter. I can only turn it at 3000 rpms. We can only wrap
400 turns around the rotor. How strong must the magnetic field be?
B

Your new puzzle Pieces
d B
  N
dt
  NAB sin( t   )
Problem # 5
Let’s design a generator. I want to generate 120 volts. My loop can only be
0.10 meters in diameter. I can only turn it at 3000 rpms. We can only wrap
400 turns around the rotor. How strong must the magnetic field be?
B
