Teaching Notes for Unit 9.3 Motors and Generators Topic of NSW HSC Physics Course

1. Topic 9.3
3.2.1 Electromagnetic Induction

2. Inducing an EMF
● In the 1830s when Michael Faraday moved a
wire through a magnetic field just to see what
happened, he discovered that a small pulse of
current was generated.
● He hypothesised that the magnetic field created
a force on the electrons causing them to move
along the wire.
● He dubbed this force an electromotive force
● i.e. a force that causes the movement of electrons.
● This often abbreviated as emf

3. Inducing an EMF
● He knew that electrons could flow (a current)
only if there was a potential difference (a
voltage) present.
● He reasoned that the emf caused an imbalance
of charge
● i.e. one end of the rod was more negative than the
other.
● Hence an induced voltage along the length of
the wire.

4. Inducing an EMF
● He found that an emf was only created when
the wire was moved.
● If it was held stationary then no emf was created.
● When the wire was moved in the opposite
direction, the emf was generated in the
opposite direction.
● If he used stronger magnets a larger emf was
generated.
● emf is dependent on magnetic field

5. Inducing an EMF
● If he moved the wire faster a larger emf was
generated.
● emf is dependent on velocity
● If he moved a coil of wire a larger emf was
generated.
● emf is dependent on the number of coils.
● If he moved the magnet instead of the wire there
was no change in the results.
● Emf is dependent on relative motion between the
wire and magnetic field.

6. Induced EMF
● The direction of the
induced current is given
by Flemming’s right
hand rule.
● First finger = Field
● seCond finger = Current
● Thumb = Thrust (force & motion)
● NOTE this is the opposite of the motor
(gun) rule.

7. Deriving induced EMF
(Beyond HSC Syllabus)
● Consider a wire moving in a
magnetic field
● The electrons in the wire will
experience a force on them as the
wire moves.
● The electrons will move along the
wire creating an imbalance and
hence an electric field.
● When the E field and the B-field are
equal the electrons stop moving.
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + +
I
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + B +
v
FB=BIl=B(Qt
)l=BQ( l
t )=Bqv
FE=qE
FB=FE
q ⃗B×⃗v
=q ⃗E
⃗B×⃗v
=⃗E

8. Deriving induced EMF
(Beyond HSC Syllabus)
● When the E field and the
B-field are equal the
electrons stop moving.
● This also shows that an
electric field is created by
a moving (changing)
magnetic field.
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + +
I
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + B +
v
FB=FE
q ⃗B×⃗v
=q ⃗E
⃗B×⃗v
=⃗E

9. Deriving induced EMF
(Beyond HSC Syllabus)
● If the electric field along the
wire is considered to be
uniform then.
● Where ε is the induced emf.
● Therefore by substitution this
becomes.
● Or if the wire is a coil on n
turns.
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + +
I
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + B +
v
E=
Vl
=εl
ε=l ⃗B×⃗v
ε=n l ⃗B×⃗v

10. Induced EMF
● Faraday was working with large coils of wire and
found that this simple derivation did not work perfectly.
● He found that coils with bigger areas induced bigger
emf’s.
● He reasoned that because the EMF was dependent
on both the magnetic field strength and the area as
well as the velocity, the emf was really dependent on
the rate of cutting of magnetic flux lines.
● This is known as Faraday’s law.

11. Magnetic Field and Flux
● A magnetic flux line is an imaginary line which determines the
direction in which a north monopole magnet (if one could exist)
would move if placed in a field.
● As already defined, the magnetic field strength B is the density of
the magnetic flux lines.
● The total magnetic flux penetrating an area (a surface) near a
magnetic field source is given by:
Φ=⃗B A
● Magnetic flux Φ is a scalar quantity while flux density is a vector.
● Magnetic flux is measured in Tesla-square-metres (Tm2) or
Webers (Wb)

12. Faraday’s Law
● As the wire moves up
through the field it sweeps
out an area per second of
At
=ldt
● But because the speed of
the wire is v, this becomes
At
=l (⃗v)
● Therefore the induced
emf is.
ε=n ⃗Bl ⃗v=n Δ ⃗B A
Δt
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + +
I
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + B +
v
I
v

13. Faraday’s Law
● The magnetic flux density
multiplied by area gives
the total magnetic flux.
Φ=BA
● Therefore the induced
emf is given by:
ε=n Δ Φ
Δt
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + +
I
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + B +
v
I
v

14. Lenz’s Law
● Heinrich Lenz observed that the direction of an
induced emf always acts to provide a resistive
force and not an accelerating force.
● This is also required when considering the law
of conservation of energy.
● Lenz's law states that
● The induced emf is such that the induced current
creates a magnetic field that opposes the the
change producing it.

15. Faraday's Law
● Faraday's law when combined with Lenz's law
gives us the induction formula:
ε=−n ΔΦ
Δt
● Note the negative sign which indicates the
reversed direction of the induced emf.

16. Motors and emf
● A motor works on the principle of a current in a
coil of wire placed in a magnetic field
generating a torque.
● However, when a coil is turned in a magnetic
field it also generates an emf.
● Which rule is true for a motor?
● Both! The turning motor produces a back emf
which tries to resist the turning torque.

17. Back emf in Motors
● A motor can be
(simply) modelled as a
resistor.
● Technically there
should also be an
inductor but this is not
relevant if we assume
slow speeds.
Motor
R
Vs

18. Back emf in Motors
● When the motor is
turned on it acts as if
there is an additional
battery inside the
motor.
● This is the back emf.
● Notice that the back
emf opposes the
supply emf.
Motor
R
Vs
Vback

19. Back emf in Motors
● The back emf causes
the motor current to
fall when the motor is
spinning.
● Using Ohm's law:
Motor
R
Vs
Vback
I=
V
R

20. Back emf in Motors
● When the motor starts, the
back emf is zero (as the coil
is not turning) so the current
is:
I Vback max=
● When the motor is running at
a steady speed, the back emf
is not zero so the current is:
Motor
R
Vs
V s
R
I run=
V s−V back
R
Time
Current

21. Eddy Currents
● When a conductor is near a
changing magnetic field, Lenz's law
states that
● an emf will be induced that
● Induces a current that
● Induces a magnetic field that
● Opposes the changing field.
● These small circular currents in the
conductor are known as Eddy
currents

22. Eddy Currents
● If the conductor swings
through a fixed magnetic
field,
● Eddy currents are
produced which
● produce a magnetic
braking force and
● the pendulum stops
swinging

23. Eddy Currents
● If the conductor has slots in
it then:
● the eddy currents are
smaller and they produce
● A smaller magnetic field
which produces
● a smaller magnetic braking
force and
● the pendulum stops
swinging more slowly.

24. Electromagnetic Braking
● Eddy currents are commonly used as a
fail safe braking system on roller
coasters.
● Magnets are placed at the side of the
track and large metal plates are placed
on the bottom of the cars to pass
between them.
● Eddy currents are formed in the brakes
● A force is induced
● The roller coaster comes to a gentle
stop.
● The faster the coaster is going the
bigger the current and the higher the
stopping force.

25. Electromagnetic Braking
● Electromagnets could also be used to
provide the external field.
● This allows electromagnetic braking to
be used on large vehicles such as
trains and on high performance
vehicles like racing cars.
● Being non contact brakes they tend to
last longer than friction brakes as well
as being smoother acting.