Induction

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Transcript Induction

Induction
Consider a conductor moving in a
magnetic field….
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The conductor is filled with mobile charges (by definition).
Each charge is a moving charge in a magnetic field,
and will therefore have a force exerted on it. (RHR#3)
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This causes, (induces) a current to flow.
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The conductor is filled with mobile
charges (by definition).
We call this
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phenomena
Electromagnetic
Induction
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An electromotive force (emf) is produced in a conductor
whenever it cuts across magnetic field lines. No emf
arises from motion parallel to a magnetic field.
Coil moves
Up
Coil moves
Down
Magnetic
Field
Lines
Calculating EMF
EMF = BLvsinq
EMF = Electromotive Force (Volts)
B = Magnetic Field (T)
L = Length of the wire (m)
v = velocity of wire that is moving in the field (m/s)
q = angle between wire and magnetic field
Lenz’s Law:
The direction of an induced current is
always such that its own magnetic field
opposes the magnetic field responsible for
producing it.
Lenz’s law is a statement of the
Law of Conservation of Energy
Drop a magnet through a conducting ring.
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A current will be
induced in the ring.
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Consider a
charge Q in
the ring
Drop a magnetic through a conducting ring.
The
secondary
magnetic
lines of force
always
oppose the
creating lines
of force.
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As the loop is pulled out of the
field, a current will be induced in
the loop.
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pull
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Induced force
opposes original
force
Consider the force on
this leg of the loop
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pull
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Alternating Current (AC)
• Usually it isn’t a single straight wire that
is moving in a external magnetic field.
• Usually it is a coil of wires (like what
you saw with the motor) that are
rotating in the magnetic field.
Remember, a coil is just a solenoid with one
loop & a solenoid creates a magnetic field just
like a magnet
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T
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Alternating Current (AC)
• This is how the electric
company generates the
electricity we use.
• Mechanical energy
(spinning the coil) turns into
electrical energy (EMF)
• The catch is figuring out
what will spin the coil in the
external magnetic field.
Effective Current & Effective Voltage
2
I eff =
I max = 0.707I max
2
Veff =
Units: Amps
Ieff = effective current
(average current)
Imax = maximum current
Units: Volts
2
Vmax = 0.707Vmax Veff = effective voltage
(average voltage)
2
Vmax = maximum
voltage
In the USA,
Veff = 120 V
Example: A generator is created by moving a
0.20 m long wire in an external magnetic field of
2.0 T at a speed of 15 m/s.
(A) What EMF is produced by the generator?
EMF = BLvsinq
EMF = (2.0 T)(0.20 m)(15 m/s)sin90o
EMF = 6.0 V
(B) If the 6.0V is the maximum voltage
produced by the generator, what is the
effective emf?
2
Veff =
Vmax = 0.707Vmax
2
Veff = 0.707 (6.0 V)
Veff = 4.2 V
(C) If the generator is hooked up to a light
bulb with a resistance of 2.5 W, what is
the effective power of the the bulb?
Remember: P = IV = I2R = V2/R
Peff = (Veff)2/R
Peff = (4.2)2/2.5
Peff = 7.1 W
Mutual Inductance
• Mutual inductance is a measure of the
ability of one circuit carrying a changing
current to induce an emf in a nearby
circuit.
• The coil carrying the current initially is
called the primary coil.
• The coil in which the current is induced
is called the secondary coil.
Transformers
• Transformers are devices that change one
AC potential difference to a different AC
potential difference.
• Real transformers are not perfectly efficient.
– Efficiencies of real transformers typically range
from 90% to 99%.
• For this class, we will assume 100%
efficiency. (We like living in an ideal world) :)
Residential Power Poles usually have 3 levels of
wires.
High Voltage
120 –240 Volts
Telephone-Cable TV
Transformer
There are two types of
transformers:
1. Step up
and
2. Step down
Step up vs Step down:
Think of a staircase
• Step up: Start with
a low voltage, end
with a higher
voltage
• Step down: Start
with a high voltage,
end with a lower
one.
Vs
Vp
Vp
Vs
Transformers
primary volts
secondary volts

# primary coils # secondary coils
Volts x amps = Volts x amps
in
out
Transformer Equation
Vs N s

Vp N p
Where
V = potential difference (voltage)
N = # of turns in coil
Subscript p refers to primary coil
Subscript s refers to secondary coil
Example: A step up transformer is used on a 120 V
line to provide a potential difference of 2400 V. If the
primary has 75 turns, how many turns must the
secondary have?
Vs N s

Vp = 120 V
Vp N p
Vs = 2400 V
2400 N s

120
75
Ns = 1500 turns
Np = 75 turns
Ns = ?
Power for a transformer
• The power into a transformer equal the
power out of a transformer
Pp = Ps
P = IV
I pVp = I sVs
Vs N s I p


Vs I p
Vp N p I s

Vp I s