Transcript 12: Electromagnetic Induction

12: Electromagnetic
Induction
12.1 Induced Electromotive Force
Induced EMF
Revision of magnetism:
• Magnetic flux: The amount of field or number of field
lines passing through a certain area. Measured in
Webers (Wb).
• Magnetic flux density: The amount of magnetic flux per
unit cross sectional area perpendicular to a field.
Measured in Tesla (T).
• Force on a current carrying conductor in a magnetic
field:
F = BIL
• Force on a single moving charge in a magnetic field:
F = Bqv
(from the above, if v = L / t)
Moving a conductor through a B field
Consider a conductor of length L moving through a
magnetic field (strength B) at speed v.
x
x
B
x
x
v
x
x
e
x
x
L
The electron is moving ‘down’ (so it effectively forms
a current moving ‘up’).
Fleming’s LHR tells us that the force on the electron
is to the left. As a result of movement of electrons,
opposite charges build up at either end of the
conductor.
The charges in turn create a p.d. across the wire
and thus an electric field. The field will exert electric
force on remaining free electrons, balancing out the
magnetic force, so they don’t move.
so...
FB = FE
but we know...
FB = Bqv = Bev
and also...
E = (-) ΔV = V  FE = Eq = eV
Δx
L
L
Equating gives...
Bev = eV
L
Rearrange to give...
V = (-) BLv
(e = electron charge)
This voltage supplies an EMF
(ε) to an external circuit. So...
ε = BLv
ε = EMF generated across wire (V)
B = magnetic flux density (Tesla)
L = length of conductor in field (m)
v = velocity of moving conductor
(ms-1)
This gives the EMF induced across a single wire moving
perpendicular to a uniform magnetic field.
However if the motion is at an angle of less than 90° to
the field then we only use the component of the field
perpendicular to the motion...
θ
ε = B sinθ Lv
v
B
Magnetic Flux and Magnetic Flux Linkage
In simple terms a ‘single flux’ can be thought of as a
single magnetic field line.
If magnetic flux density (B) is the flux (ϕ) per unit
cross sectional area perpendicular to the field
then...
Magnetic flux density = Magnetic flux
Area
B = ϕ
A
ϕ = BA
ϕ = Magnetic flux (Wb or Tm2)
B = Magnetic flux density (T)
A = Area (m2)
If a single flux passes through a coil, the coil is
‘linked’ to the flux (or ‘threaded’ by the flux). We
could say there is magnetic flux linkage of 1. If the
coil is linked (‘threaded’) by two flux then the flux
linkage is 2 and so on. Increasing the number of
coils also increases the flux linkage.
E.g. If a solenoid has three coils linked by two flux
then the flux linkage is six.
Total magnetic flux linkage = Nϕ
Note: Even a straight wire has flux linkage although
this is less easy to define. N=1 for a straight wire.
E.g.
A small circular coil of area 7.5 x 10–3 m2 contains
400 turns of wire. If it is linked by a perpendicular
magnetic field of flux density 5.0 x 10-2 T, determine
the magnetic flux linkage through the coil.
Answer:
Flux linkage = N ϕ and ϕ = BA
So... Flux linkage = NBA
= 400 x (5.0 x 10-2) x (7.5 x 10–3)
= 0.15 Wb
Faraday’s law
Michael Faraday discovered electromagnetic
induction in 1831.
Faraday’s law states...
The induced EMF in a circuit is equal to the rate
of change of flux linkage in a circuit.
so...
ε = - dNϕ
dt
Note: Negative sign is a result of Lenz’s law.
Lenz’s Law
Demo:
A north pole moving into a coil creates north pole,
resisting its motion.
A north pole moving out of a coil creates a south
pole, resisting its motion.
The magnitude of an induced EMF is given by
Faraday’s Law. However the direction of an
induced current can be determined by applying
Lenz’s law which states...
The direction of an induced current is always
such as to oppose the change that causes it.
In the previous example, if the currents were
induced in the opposite direction the magnet would
be repelled – free energy! Impossible. So Lenz’s
Law is an application of the principle of conservation
of energy.
Demo:
- Neodymium magnet in copper tube.
- Swinging aluminium vane in magnetic field.
Demonstrating Lenz’s Law
Conclusion: Explain the shape of this graph in as
much detail as possible.
- Flux through coil is changing so EMF induced.
- Rate of change of flux is increasing as magnet
speeds up so EMF is increasing.
- When magnet in central position there is no
change in flux so EMF is zero for an instant.
- As magnet exits, Lenz’s law tells us that the
current must flow in the opposite direction so as to
oppose motion.  reversed EMF
- Max induced EMF occurs on exit because magnet
is moving fastest.
- t2 is smaller due to greater speed.
Electromagnetic Induction Braking
Induced currents are used in electromagnetic
induction braking in vehicles:
- An electromagnet is switched on next to the
rotating non-magnetic metal disk.
- The disk cuts through the B field, inducing EMFs
and currents within the disk.
- Currents flow between the edge and centre of
disk. Energy is then lost as heat or the EMF can be
used to charge batteries.
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