#### Transcript Electromagnetic Induction

```Topic 12 Electromagnetic Induction
Electromagnetic induction
• Make a coil using wire. The coil should be
wide enough to easily move a magnet
inside
Electromagnetic induction
• Put your coil in this circuit. The multimeter
should be on the μA scale.
μA
Electromagnetic induction
• MOVE a magnet in and out of the coil.
Watch the meter!
μA
Electromagnetic induction
If a magnet is
moved inside a
coil an electric
current is
induced
(produced)
Generator/dynamo
A generator
works in this way
by rotating a coil
in a magnetic
field (or rotating a
magnet in a coil)
Motor = generator
If electric energy enters a motor it is
changed into kinetic energy, but if kinetic
energy is inputted (the motor is turned)
electric energy is produced!
The Motor Effect
When a current is placed in a magnetic
field it will experience a force (provided the
current is not parallel to the field). This is
called the motor effect.
Can you
copy this
sentence
into your
books
The Motor Effect
The direction of the force on a current in a
magnetic field is given by Flemming’s left
hand rule.
Thumb = Motion
First finger = Field direction
Centre finger = Conventional Current
The Motor Effect
Can you copy
WITH
DIAGRAM!
The direction of the force on a current in a
magnetic field is given by Flemming’s left
hand rule.
Thumb = Motion
First finger = Field direction
Centre finger = Conventional Current
Sample question
In this example, which way will the wire be
pushed? (red is north on the magnets)
Sample question
In this example, which way will the wire be
pushed? (red is north on the magnets)
Current
Field
IB Level!
Electromagnetic Induction
Imagine a wire moving with velocity v in a
Wire
magnetic field B out of the page.
L
moving
with
velocity v
v
Region of
magnetic
field B out of
page
The electrons in the wire feel a force (the
motor effect) which pushes the electrons
to the right. This creates a potential
difference in the wire.
L
v
Electrons
pushed this
way (left
hand rule)
The field in the wire that produces this
potential difference is given by E = V/L
e.m.f. (voltage) across
the wire in the magnetic
field
L
+
v
The force produced by this field E = V/L
would push the electrons back again, but
this is opposed by the force on the
electrons due to the magnetic filed F = Bev
L
+
v
There exists a balance between the force
on the electrons due to the field in the wire
and the force due to the field
eE = Bev
L
v
eE = Bev
since E = V/L, V = vBL
L
v
V = vBL
This means that a conducting wire of length L moving with
speed v normally to a magnetic field B will have a e.m.f.
of vBL across its ends. This is called a motional e.m.f.
L
Wire
moving
with
velocity v
v
Region of
magnetic
field B out of
page
My hero!
Consider a magnet moving through a
rectangular plane coil of wire.
N
A
S
A current is produced in the wire only
when the magnet is moving.
N
A
S
The faster the magnet moves, the bigger
the current.
N
A
S
The stronger the magnet, the bigger the
current.
N
A
S
The more turns on the coil (same area),
the bigger the current.
N
A
S
The bigger the area of the coil, the bigger
the current.
N
A
S
If the movement is not perpendicular, the
current is less.
A
Magnetic Flux (Ф)
Imagine a loop of (plane) wire in a region
where the magnetic filed (B) is constant.
B
The magnetic flux (Ф) is defined as Ф = BAcosθ
where A is the area of the loop and θ is the
angle between the magnetic field direction and
the direction normal (perpendicular) to the plane
of the coil.
B
If the loop has N turns, the flux is given by
Ф = NBAcosθ in which case we call this the flux
B
The unit of flux is the Weber (Wb) (= 1 Tm2)
It can help to imagine the flux as the number of
lines of magnetic field going through the area of
the coil. We can increase the flux with a larger
area, larger field, and keeping the loop
perpendicular to the field.
B
As we seen, an e.m.f.
is only induced when
the field is changing.
The induced e.m.f. is
law, which uses the
idea of flux.
I built the first
electric motor and
generator too. I
refused all prizes
and awards
because that
would detract from
God’s glory.
The induced e.m.f. is
equal to the (negative)
rate of change of
magnetic flux,
E = -ΔФ/Δt
Example question
The magnetic field through a single loop of
area 0.2 m2 is changing at a rate of 4 t.s-1.
What is the induced e.m.f?
“Physics for the IB Diploma” K.A.Tsokos (Cambridge University Press)
Example question
The magnetic field (perpendicular) through a single loop of area 0.2
m2 is changing at a rate of 4 t.s-1. What is the induced e.m.f?
Ф = BAcosθ = BA
E = ΔФ = ΔBA = 4 x 0.2 = 0.8 V
Δt
Δt
Another example question!
There is a uniform magnetic filed B = 0.40 T out of the
page. A rod of length L = 0.20 m is placed on a railing
and pushed to the right at a constant speed of v = 0.60
m.s-1. What is the e.m.f. induced in the loop?
L
v
The area of the loop is decreasing, so the
flux (BAcosθ) must be changing. In time Δt
the rod will move a distance vΔt, so the
area will decrease by an area of LvΔt
L
LvΔt
v
E = ΔФ = BΔA = BLvΔt = BLv
Δt
Δt
Δt
E = 0.40 x 0.20 x 0.60 = 48 mV
L
LvΔt
v
An important
result, you may be
Lenz’s Law
The induced current will be in such a
direction as to oppose the change in
magnetic flux that created the current
(If you think about it, this has to be so…….)
Alternating current
A coil rotating in a magnetic field will
produce an e.m.f.
N
S
Alternating current
The e.m.f. produced is sinusoidal (for
constant rotation)
e.m.f.
V
Slip ring commutator
To use this e.m.f. to produce a current the
coil must be connected to an external
circuit using a split-ring commutator.
Slip-rings
lamp
Increasing the generator
frequency?
e.m.f.
V
Root mean square voltage and current
It is useful to define an “average” current
and voltage when talking about an a.c.
supply. Unfortunately the average voltage
and current is zero!
To help us we use the idea of root mean
square voltage and current.
Root mean square voltage
e.m.f.
V
Root mean square voltage
First we square the voltage to get a
quantity that is positive during a whole
cycle.
e.m.f.
V
Root mean square voltage
Then we find the average of this positive
quantity
e.m.f.
V
Root mean square voltage
We then find the square root of this
quantity.
e.m.f.
V
Root mean square voltage
We then find the square root of this
quantity.
e.m.f.
V
This value is called the
root mean square
voltage
Root mean square voltage
We then find the square root of this
quantity.
e.m.f.
V
Emax
Erms = Emax/√2
Transformers
What can you
transformers from last
year?
Transformers
Vp
Np
turns
Vs
Ns
turns
Primary coil
Iron core
“Laminated”
Secondary coil
Transformers
How do they work?
Vp
Np
turns
Vs
Ns
turns
Primary coil
Iron core
Secondary coil
An alternating current in the primary coil
produces a changing magnetic field in the
iron core.
Vp
Np
turns
Vs
Ns
turns
Primary coil
Iron core
Secondary coil
The changing magnetic field in the iron
core induces a current in the secondary
coil.
Vp
Np
turns
Vs
Ns
turns
Primary coil
Iron core
Secondary coil
It can be shown using Faraday’s law that:
Vp/Vs = Np/Ns and VpIp = VsIs
Vp
Np
turns
Vs
Ns
turns
Primary coil
Iron core
Secondary coil
Power transmission
When current passes through a wire, the
power dissipated (lost as heat) is equal to
P = VI across the wire
Since V = IR
Power dissipated = I2R
Power transmission
Power dissipated = I2R
Since the loss of power depends on the square
of the current, when transmitting energy over
large distances it is important to keep the current
as low as possible.
However, to transmit large quantities of energy
we therefore must have a very high voltage.
Power transmission
Electricity is thus transmitted at very high voltages using
step up transformers and then step down transformers.
220 V
Step-down
250,000 V
15,000 V
Step-up
15,000 V
Step-down
Dangerous?
Dangerous?
Low-frequency electromagnetic fields can
induce currents in the human body!
Dangerous?
Current evidence suggests that lowfrequency fields do not harm genetic
material. This is not fully proven or
understood.
Whew! That’s it!
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