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Electromagnetic Induction
Electric Fields
• Electric fields are created bycharges
force
+
• A charge in an electric field always has a
force on it
Magnetic Field
Magnetic fields are
created by moving charges
This can happen in
magnets or
current carrying wires.
Magnetic Fields only affect moving charges
velocity
+
FORCE is… ZERO
+
FORCE is…
towards you
strong
field
weak
field
strong
field
weak
field
z
y
S
N
x
electron
beam
electron
gun
What direction is the magnetic field?
z
Wire's
velocity
S
N
y
x
wire
Magnetic Flux
• Magnetic flux is the amount of
magnetic field.
• It depends on the field strength and
the area
There is a large flux through this loop
And a smaller flux through this loop
S
N
Even smaller flux through this loop
Magnetic field lines
Which ring has
the strongest
magnetic field
strength in it?
Which ring has
the biggest
magnetic flux
in it?
Which ring has the largest
magnetic flux in it?
Magnetic = Magnetic
X
Flux
Field Strength
  B  A
Webers = Tesla x m2
Area
• Magnetic field strength is also called
flux density.
  B  A

B
A
Which ring has
the biggest
magnetic flux ?
Area is same
Field strength is same
Which ring has the
biggest magnetic
flux ?
• Year 12:
A wire cutting across a magnetic field has an
induced EMF (or voltage)
Faraday’s Law
When the magnetic flux through a loop changes,
there is an induced EMF (voltage)
The faster the change, the bigger the EMF


t
Changing the Flux
• You can change the flux by changing the
field strength or the area perpendicular
  B  A
Changing the field strength
S
N
Changing the area
S
N
Changing the area perpendicular
S
N
Flux Change in a Generator
• faraday-mx.swf
• So for many loops,
becomes,


t
N 

t
Changing the Area
Changing the actual area
Changing the angle
Flux change in a moving loop
flux
time
Induced EMF in a moving loop


t
voltage
time
flux
time
voltage
time
N
N
Close switch… current increases …field increases
Flux change through 2nd coil
Induced EMF in 2nd coil
Creates current in 2nd coil
Creates magnetic field that opposes the cause.
Lenz’s Law
Electron flow
Force on roller
1: electrons in roller are moving
2: causing them to be pushed
3: electrons in roller are now flowing
4: causing them (and roller) to be pushed
• Faraday: A flux change causes an induced
EMF (voltage)

 
t
• Lenz’s Law states that the induced voltage
opposes the flux change that caused it.
Falling magnet creates a flux
change in the pipe.
This creates induced EMF
This creates induced current
This creates induced
magnetic field
magnetic field opposes flux
change
N
So how does your electric
toothbrush charge up?
Increasing current in Primary
Causes flux change in core
Causes flux change in Sec
S
Causes induced EMF in Sec
Causes induced current in Sec
P
This is called Mutual Induction
AC Generator
• http://www.walterfendt.de/ph11e/generator_e.htm
B
A
C
D
Coil position
(End on)
Flux
Angle
Voltage
Angle
Flux
Angle
Voltage
Angle
• ..\faraday.jar
Transformers
• A transformer is used to increase or
decrease the voltage.
• Mains voltage in NZ is 240 V AC.
• Your cellphone charger needs about
4.0 V. It uses a transformer to reduce
the voltage.
Increasing current in P
Causes flux change in P
Causes flux change in S
P
S
Causes induced EMF in S
Causes induced current in S
This is called Mutual Induction
• transformer.jar
Primary current
Magnetic flux in core
Induced EMF in Secondary
The AC current in the primary coil is
changing sinusoidaly
So the magnetic flux is changing
sinusoidally
So the induced EMF is sinusoidal
• The output voltage (Vs) depends on:
the input voltage
the ratio of turns
Iron core
Vp
Vs
secondary
primary
Np
Ns
Vs  Vp 
Np
Ns
Np
or
Ns

Vp
Vs
Mutual Induction
• This is when a changing current in one
coil induces a voltage (EMF) in a
second coil.
Small Mutual Inductance between coils
Iron cores produce stronger, more
concentrated magnetic field
 larger
Mutual Inductance
Toroidal core produces even larger
Mutual Inductance
I P
EMF in secondary coil  M
t
M is the mutual inductance, measured
in Henries (H)
• Using transformers to save energy
You’ve seen these around the streets. What do they do?
Transformers are very important for
power transmission.
• The power transmitted along wires is
given by:
Power = V x I
• The power wasted as heat in the wire is
given by :
Power = I2 x R
• To minimise the power lost as heat,
the wire’s resistance and the current
must be a small as possible.
Power lost = I2 x R
• To transmit the same power, the
voltage must be very large.
Power transmitted = V x I
Power station generators produce
electricity at about 4000 V
Transformers increase it to about
400 000 V. (and reduce the current)
Transmission lines then carry
the electricity at 400 000 V
Transformers in Auckland reduce
the voltage to about 4000 V
This is then reduced to 240 V in
local transformers around the
streets
4000 V
400 000 V
4000 V
240 V
Your cellphone charger changes the
240 V current to about 4 V
• http://phet.colorado.edu/webpages/simulations-base.html
Inductors
An inductor is a wire coil usually wrapped
around an iron core
Self Inductance
A coil can induce a voltage in itself !!!??
A
Predict what happens when the switch
closes.
What does happen when the switch
closes?
A
What happens when the switch opens?
A
An inductor is designed to oppose a
changing current
This is because it can induce an EMF in
itself. This is called Self Inductance.
Increasing current
Current Increasing
Causes increasing magnetic field
There is a flux change through coil
Causes induced EMF
Increasing current
Direction of EMF
opposes current change
Induced EMF
Self Inductance
• A coil can induce a voltage in itself.
I P
EMF in coil   L
t
• L is called the self inductance
Self Inductance (L) is measured in Henries (H)
• This induced EMF (or back EMF) opposes
the increase in current, so the current
rises…
SLOWLY
This is called Self Inductance
(The coil induces an EMF in itself)
current
I = V/R
R is the ohmic resistance
of the inductor
L

R
Close switch
time
current
Close switch
Back
EMF
Recall:
I P
EMF in coil   L
t
Imax
0.63 Imax
Close
switch
L

R

time
Recall the meaning of time constant for a capacitor
and resistor?
It means the same for an inductor and resistor.
Larger inductance, longer time
to reach maximum current
L

R
Larger resistance, smaller
current so shorter time to
reach maximum current
How would the graph change if:
Inductor had higher inductance?
Inductor had higher resistance (careful)
current
Close switch
Decreasing current
Current Decreasing
Causes decreasing magnetic field
This is a flux change
Causes induced EMF
Direction of EMF
opposes current change.
• This induced EMF (or back EMF)
opposes the decrease in current, so
the current drops…
SLOWLY
This is called Self Inductance
When the switch opens, the current drops to
zero rapidly
This causes a large flux change
This induces a very large EMF
This causes a spark across the switch
Mutual Inductance
http://phet.colorado.edu/webpages/simulations-base.html
Extension: LC oscillation
http://www.walterfendt.de/ph11e/osccirc.htm