Download PowerPoint-Electromagnetic Induction File

Electromagnetic Induction
Magnetic Flux
• The magnetic flux is important in understanding electromagnetic
induction.
• The magnetic flux (Φ) is a measure of the number of field lines
passing through a region.
• The unit of magnetic flux is the weber (W)
• It is a vector quantity
A
A uniform
magnetic
field has a
constant
density of
field lines
throughout
B
In a uniform field the
number of field lines
passing through the
larger region B is
greater than through
the smaller region A.
Therefore we can say
that there is a greater
flux through B than A
Magnetic Flux
Here the magnetic flux is the
same in region A and B.
Sometimes a measure of
magnetic flux can be
misleading.
Magnetic Flux
• Below the magnetic flux through region A
is greater than through B because the
density of the field lines is greater.
A
B
The relationship between B and Φ
B
A
If the magnetic field is perpendicular to a region with area A, and the flux
density is B, Then the flux Φ in that region is given by:
Φ = AB
Moving a conducting wire in a
magnetic field
• If a wire is moved in a magnetic field such that field lines
are cut an emf is induced between the ends of the wire
An emf is induced between the ends of
the wire
An emf is NOT induced between the
ends of the wire
N
N
S
S
The direction of the induced emf
S
N
Direction of induced
emf
field
emf
motion
Induced e.m.f and moving
electrons
Motion of the bar
A
Magnetic field
Force tends to move
electrons in this direction
C
As we saw with free electrons moving in a field, they experience a force
as show in the diagram
+++
A
++
-----C
Here we see that conventional current will be driven from C to A if the
circuit is complete. i.e. the direction of the emf is from C to A.
The direction of the induced emf
S
N
With a closed
conducting loop, the emf
induced drives a current
through the loop
Here a current is induced in the single turn coil
in the same way.
N
If a current flows it always produces a field which opposes the motion of
the coil. In this case a north pole is induced on the face of the coil being
pulled towards the magnet.
This is a consequence of the law of conservation of energy. It always
applies. It is known as Lenz’s law.
Again as a consequence of Lenz’s law
When the coil is withdrawn a south pole is produced to oppose the motion
of the coil.
N
Note that if a North pole had been produced instead, the coil would
be repelled and the current due to induction increased. This would
cause further repulsion. We would have built a perpetual motion
machine! We would get energy for nothing in contravention of the
law of conservation of energy.
Coils With More Turns
Where the coil has more than one turn, the
magnetic flux through the turns of the coil is
called the flux linkage.
N
When a magnet moves through the coil, each
turn of the coil cuts the magnetic field by the
same amount.
So the flux linkage is just the
sum of flux through each turn.
If the magnet is moved with the same speed.
2 turns, → 2 x emf
3 turns → 3 x emf etc.
A
S
N
North pole induced at the
top of the coil on approach
A
G
North pole induced at the
bottom of the coil on leaving
S
Induced
emf/V
N
A
V
Time/s
The direction of the emf is reversed as the induced poles of the coil are
reversed. The bar magnet is accelerating so the rate of flux cutting is higher as
the magnet leaves the coil, hence the larger amplitude of emf for a shorter
time.
Faraday’s Law of Electromagnetic
Induction
1. The e.m.f. induced
in a coil depends on
the rate of change
of flux through the
coil.
N
The faster the flux changes the
greater the e.m.f. induced
Ε
Φ
t
Faraday’s law of electromagnetic
induction
• The e.m.f. induced is
proportional to the
number of turns in the
coil
N
N
ΕN
Faraday’s law of electromagnetic
induction
ΔΦ
ΕN
Ε
Δt
So combining these relationships
ΔΦ
ΕN
Δt
The units of the SI system combine in such a way that
the constant of proportionality is 1

ΕN

t
The expression to the right of the = sign is just the
rate of change of flux linkage
Faraday’s Law

ΕN
t
E is the e.m.f. Induced (V)
N is the number of turns on the coil
∆Φ is the change in flux though each turn of the coil. (Wb)
∆t is the time taken for the flux change.(s)
Note that in this equation the total change in flux linkage in the coil is N∆Φ.
Sometimes you may see this written as ∆NΦ.
It follows that 1 weber is the flux linkage in a coil if an emf of 1V falls
evenly to zero in 1 second
Using Faraday’s Law
A coil of 200 turns and 3cm in radius lies perpendicular to a uniform
magnetic field with a flux density of 2 x10-2 T. The field falls evenly to 0T in
1s. Calculate the emf generated:.
1. Calculate the flux
through 1 turn of the coil
  BA
  .02T  .003m2  6 104Wb
2 Now apply Faraday’s law
V

ΕN
t
(610 4 )
Ε  200
 0.12V
1
Some effects of induction
The effect of a changing field on an
aluminium ring
d.c. supply to coil
When the d.c. supply is
switched on, there is a
change in flux through the
aluminium ring. An emf is
induced in the ring with a
field opposed to the coil.
The ring is repelled and
rises. As soon as the
current is steady though
the coil there is no further
change in flux and the ring
falls back.
When the circuit is broken, the flux changes again through the ring and
the ring is repelled again in accordance with Lenz’s law.
The effect of a changing field on an
aluminium ring
ac. supply to coil
When the a.c. supply is
switched on, there is a
continuous change in flux
through the aluminium ring.
An emf is induced in the
ring with a field opposed to
the coil. This field reverses
every time the field in the
coil reverses.The ring
continues to be repelled.
Electromagnetic damping
Electromagnetic damping
Electromagnetic damping
Electromagnetic damping
BACK EMF
When the coil L is connected in series with the cell V it produces an increasing
magnetic field as the current through the coil rises. This induces a “back emf” in
the reverse direction to the emf produced by the cell.
The magnetic field stores energy transferred from V
When S is moved so that L is in series with R only, the back emf
drives a current through R dissipating the energy stored.