Transcript Electromagnetic Induction and Power Transmission

Electromagnetic Induction
and Power Transmission
Physics
Montwood High School
R. Casao
Electromagnetic induction is the process of generating
an electric current by varying the magnetic field that
passes through a circuit.
Oersted’s discovery that an electric current creates a
magnetic field resulted in experimentation that led to
Faraday’s discovery of induced currents.
Faraday was experimenting with two coils of wire wrapped
around an iron ring. He hoped that the magnetic field
generated in the coil on
the left would induce a
magnetic field in the
iron and that the
magnetic field in the
iron might create a
current in the circuit
on the right.
The technique failed to generate a
current.
Faraday noticed that the needle of
the current meter jumped slightly
at the instant when he closed the
switch in the circuit on the left.
After the switch was closed, the
needle immediately returned to
zero.
The needle again jumped when he
later opened the switch, but this
time in the opposite direction.
Faraday recognized that the
motion of the needle indicated a
very slight current in the circuit on
the right.
The effect happened only during the brief interval when
the current on the left was starting or stopping, not
while the current was steady.
Faraday’s observation that the current meter needle
jumped only when the switch was opened and closed
suggested that a current was generated only when the
magnetic field was changing as it passed through the
coil.
Faraday’s law: there is a current in a coil of wire if and
only if the magnetic field passing through the coil is
changing.
The strength of the magnetic field can be changed.
The area of the coil through which the magnetic field
lines pass can be changed.
The EMF that accompanies the current induced in a coil
of wire is given by:
d B A
EMF  N 


dt
N is the number of coils
The negative sign appears because the EMF that is generated in
the wire is in a direction that opposes the change in the number
of magnetic field lines that pass through the area of the coil (this is
called Lenz’s law).
If the magnetic field strength changes over time:
EMF  N  A 
d B 
dt
 N  A 
B f  Bi
t f  ti
If the area of the coil changes over time:
EMF  N  B 
d A
dt
 N  B 
A f  Ai
t f  ti
Electromagnetic Induction
(a) When there is no relative motion between the magnet and the wire
loop, the number of field lines through the loop (in this case, 7) is constant,
and the galvanometer shows no deflection.
(b) Moving the magnet toward the loop increases the number of field lines
passing through the loop (now 12), and an induced current is detected.
(c) Moving the magnet away from the loop decreases the number of field
lines passing through the loop (to 5). The induced current is now in the
opposite direction. (Note the needle deflection.)
It makes no difference what causes the magnetic field to
change:
current stopping or starting in a nearby circuit;
moving a magnet through the coil; or
moving the coil in and out of a magnet.
In all cases the effect is the same; there is no current if
the field through the coil is not changing.
It is not the magnetic field itself that is responsible for
the current, but the changing of the magnetic field.
Relative motion and no induction: when a loop is moved parallel to a uniform
magnetic field, there is no change in the number of field lines passing through the
loop, and there is no induced current
The current in a circuit due to a changing magnetic field
is called an induced current.
Opening the switch or moving the magnet induces a current
in a nearby circuit.
An induced current is not caused by a battery.
Application: magnetic data storage encodes
information in a pattern of alternating magnetic fields.
When the fields move past a small pick-up coil, the changing
magnetic field creates an induced
current in the coil.
The current is amplified into a
sequence of voltage pulses that
represent the 0’s and 1’s of digital
data.
Motional EMF
An induced current is created in two different ways:
1. By changing the size or orientation of a circuit in a
stationary magnetic field.
2. By changing the magnetic field through a stationary circuit.
Consider a conductor of length l that moves with
velocity v through a uniform
magnetic field B.
The charge carriers inside the
wire also move with velocity
v, so they experience a
magnetic force FB = q·v·B.
This causes the charge carriers to move, separating the
positive and negative charges.
The separated charges then create an electric field inside the
conductor.
The charge carriers continue to move until the electric
force FE = q·E exactly balances the magnetic force FB.
This happens when the electric field strength is E = v·B.
The magnetic force on the charge carriers in a moving
conductor creates an electric field E = v·B inside the
conductor.
The electric field creates an electric potential difference
between the two ends of the moving conductor.
Equation: EMF = v·l·B
The motion of the wire through
a magnetic field induces a
potential difference EMF = v·l·B
between the ends of the
conductor.
The potential difference depends
on the strength of the magnetic
field and on the speed of the wire
through the field.
The EMF of a battery refers to the
work done per charge to separate
the charges. A battery, where the
charges are separated by chemical
reactions is a source of chemical
EMF.
A moving conductor develops a
potential difference because of the
work done by magnetic forces to
separate the charges.
You can think of the moving
conductor as a battery that stays
charged only as long as it keeps
moving but runs down if it stops.
The EMF of the conductor is due to
its motion and is called motional
EMF.
The motional EMF of a conductor moving with velocity v
perpendicular to a magnetic field B is: EMF = v·l·B
The moving conductor has an EMF, but it cannot sustain
a current because the charges have nowhere to go.
It’s like a battery that is
disconnected from a circuit.
Consider a wire sliding with
speed v along a U-shaped
conducting rail. The rail is
fixed and cannot move.
The wire and the rail together
form a closed conducting loop –
a circuit.
Suppose a magnetic field B is
perpendicular to the plane of the
circuit.
Charges in the moving wire will
be pushed to the ends of the wire
by the magnetic force, but now
the charges can continue to flow
around the circuit.
The moving wire acts like a
battery in a circuit.
The current in the circuit is an
induced current.
The induced current is
counterclockwise in the example.
If the resistance of the circuit is R, the induced current is
given by Ohm’s law:
EMF v  l  B
I 

R
R
The induced current is
due to magnetic forces on
moving charges.
A continuous pulling force
Fpull is required to keep the
wire moving along the rail at
constant speed.
The moving wire, which now
carries induced current I is in
a magnetic field and the
magnetic field exerts a force
F = I·l·B on the wire.
According to the right-hand rule, the magnetic force
Fmag on the moving wire points to the left.
This magnetic drag will cause the wire to slow down and
stop unless we exert an equal and opposite pulling force
Fpull to keep the wire
moving.
The force required to pull the
wire with a constant speed v
is:
F pull  Fmag  I  l  B
EMF v  l  B
I 

R
R
v l B
F pull  Fmag 
l B
R
F pull  Fmag 
v l
2
R
 B2
Energy Considerations
Work must be done on the wire to pull it.
Power is the rate at which work is done on the wire.
The power exerted by a force pushing or pulling an
object with velocity v is P = F·v
The power provided to the circuit by pulling on the wire
is:
v  l 2  B2
v2  l 2  B2
Pinput  Fpull  v 
v 
R
R
The circuit also dissipates energy by transforming
electric energy into the thermal energy of the wires and
the components, heating them up.
The power dissipated by current I as it passes through
resistance R is P = I2·R
Power dissipated by the circuit is:
2
Pdissipated
2
2
2
v

l

B
v

l

B


 I2 R  
R 

R
 R 
The rate at which work is done on the circuit exactly
balances the rate at which energy is dissipated.
Energy is conserved.
Summary
1. Pulling or pushing the wire through the magnetic field
at speed v creates a motional EMF in the wire and
induces a current
EMF in the circuit.
I 
R
2. To keep the wire moving at constant speed, a pulling
or pushing force must balance the magnetic force on
the wire. This force does work on the circuit.
3. The work done by the pulling or pushing force
exactly balances the energy dissipated by the
current as it passes through the resistance of the
circuit.
There are two different ways to induce a current
in a conducting loop:
1. The loop can move or rotate or change size, creating
a motional EMF.
2. The magnetic field strength B can be changed.
Generators
A slide wire pulled through a magnetic field on a Ushaped track is a simple generator because it transforms
mechanical energy into electric energy.
In a more practical generator, a coil of wire is rotated in
a magnetic field.
Both the magnetic field and the area of the loop are
constant, but the number of magnetic field lines passing
through the area of the loop changes continuously as the
loop rotates.
Changing the number of magnetic field lines passing
through the area of the loop changes the strength of
the magnetic field through the loop.
The induced current is moved from the rotating loop by
brushes that press up against slip rings.
The EMF generated by the change in the number of
magnetic field lines that passes through the rotating
loop is given by:
EMF    A  B  N  sin   t 
ω is the angular frequency (ω = 2·π·f) with which the coil
rotates
A is the area of the coil
B is the strength of the magnetic field
N is the number of turns or windings in the coil
The sign of the EMF alternates between positive and
negative as the angle  = ω·t changes (remember that
the sin  is positive in quadrants I and II and negative in
quadrants III and IV).
Maximum EMF: EMF = ω ·N·A·B
Because the EMF alternates in sign, the current through
the resistor R alternates back and forth in direction.
The generator is an alternating-current generator
producing an AC voltage.
AC Outlet
Receptacles have three holes each
Lower (rounded) hole is the
ground
connected to pipes, etc.
green wire
Larger slot is “neutral”
for current “return”
never far from ground
white wire
Smaller slot is “hot”
swings to +170 V and
170 V
black wire
dangerous one
Transformers
The transformer has two
coils wrapped on an iron
core.
The left coil is called the
primary coil.
The primary coil has N1
turns and is driven by an
oscillating voltage V1·cos (ω·t).
The magnetic field of the primary follows the iron core
and passes through the right coil, which has N2 turns
and is called the secondary coil.
The alternating current
through the primary coil
causes an oscillating
magnetic flux through the
secondary coil and an
induced EMF.
The induced EMF of the
secondary coil is delivered to
the load as the oscillating voltage V2·cos (ω·t).
Faraday’s law tells us that the voltage V1 across the
primary coil is equal to the number of turns N1
multiplied by the changing number of magnetic field
lines passing through the area of the
d B
primary coil:
V1  N1 
dt
ΦB is the changing number of magnetic field lines
passing through the area of the primary coil.
The number of magnetic field lines that pass through
the primary coil remain within the iron core and pass
through the secondary coil.
The voltage across the secondary is:
d
d  B V1

and
dt
N1
d  B V2

dt
N2
V2
V1

N1 N 2
V2  N 2 
B
dt
If the secondary coil has more
windings than the primary coil
(that is Ns/Np > 1), the voltage is
stepped up because Vs > Vp and
this is called a step-up transformer.
There is less current in the
secondary than in the primary.
If the secondary coil has fewer
turns than the primary does
(Ns/Np < 1), we have a step-down
transformer.
The voltage is stepped down and
the current is increased (Is < Ip).
Transformers are used to
transmitting power over long
distances.
The generator voltage is stepped up
so the current in the transmission
line is small, therefore, power losses
to Joule heating (P = I2·R) are
reduced.
Voltages are stepped up to around
230000 V at the generating station,
stepped down to about 20000 V at a
distributing station, then down to
4000 V for delivery to residential
areas, and finally to 120 V to 240 V
at the customer’s site.
Power Consumption in Wires
Reminder:
power consumption = current × voltage drop
voltage = resistance × current
power consumption = resistance × current2
So?
Wires waste power as Joule heat
Doubling current quadruples wasted power
Better not transmit high current!
Power Transmission
Power to primary coil = Power to secondary coil
Pin = Pout; Pprimary = Psecondary; Iin·Vin = Iout·Vout
Power delivered to a city is:
power delivered = current × voltage drop
Power wasted in transmission wires is:
power wasted = resistance × current2
For efficient power transmission:
Use low-resistance wires (thick, short copper)
Use low current and high voltage drop
This can be accomplish this with AC (alternating current)
power transmission.