NCEA Level 3 Physics Electricity AS91526 Magnetic Flux

1. Magnetic Flux

2. This year we are interested in;
Magnetic Flux
• Magnetic Flux (symbol B ) is a measure of
the magnetic field strength present over a
given area. The units are Weber (symbol Wb)
B=BA
Last year we looked at B magnetic field strength
which is ΦB/A (that’s why B is also called flux
density)

3. Examples
1. A magnetic field of a small NIB* magnet is 0.2T and
covers an area of 0.12m2. Calculate the magnetic flux.
0.024Wb
2. A magnetic flux of 2.5Wb is measured in an area of
0.25m2. Calculate the flux density (magnetic field
strength).
10T
3. A strong electromagnet produces a field with a flux
density of 1.5T and has a flux of 0.54Wb. Calculate
the area that the field covered.
0.36m2
*NIB short for the alloy of neodymium, iron, and boron

4. Faraday’s Law of Induction
• Any change in a magnetic field will induce a
voltage and thereby a current in a circuit. The
faster this change occurs, the larger the
induced voltage
(a voltage can be induced by a magnet moving in
and out of a coil or past a conductor, a wire moving
through a magnetic field, or by the growth or
collapse of a magnetic field)

5. Faraday’s Law of Induction
ΔΦ
B   
Δt
where;
ε =emf or voltage (V)
ΔΦ=change in flux (Wb)
Δt= change in time (s)
An emf (voltage) is induced in a circuit only if ΦB changes
within the circuit, i.e.
• if the magnitude of B changes.
• if the direction of B changes
• If the position of B changes
• if the area enclosed by the circuit changes

6. Changing the Magnetic Flux in a Constant
Magnetic Field

7. Examples
1. Find the induced emf when a change in flux of
0.56Tm2 occurs in 0.02s.
28V
2. A magnetic field of 0.20T forms across and area of
0.12m2 in 0.02s. Calculate the emf induced
1.2V
3. A very strong electromagnet creates a magnetic field
of 1.5T at a frequency of 25Hz over an area of 25cm2.
Calculate the emf induced in a wire within the field.
0.94V

8. Lenz’s Law
• An induced current is always in such a direction
as to oppose the motion or change causing it
This helps explain the negative sign in
Faraday’s Law;
ΔΦ
B   
Δt

9. Direction of Induced Current
induced I opposes
the motion of
magnet (being
repelled)
induced I opposes
the motion of
magnet (being
attracted)

10. Direction of Induced Current
In both cases, magnet
moves against a force.
Work is done during
the motion & it is
transferred as electrical
energy.

11. Try these;
A bar magnet passes through a coil:
(i) (ii) (iii)
Indicate the direction of the induced I in each
case. Explain briefly.

12. Answer
(i) Indicate the direction of the induced I. Explain.
S N
(i)
When magnet’s N-pole is moving
into coil,
induced I flows in such a direction as
to produce a N-pole
to oppose the approaching of magnet.
I
Lenz’s
law

13. Answer
(ii) Indicate the direction of the induced I. Explain.
(ii)
The induced I become zero

I is about to change direction.

14. Answer
(iii) Indicate the direction of the induced I. Explain.
N S
(iii)
I
When magnet’s S-pole is leaving the coil,
induced I flows in such a direction as to
produce a N-pole to oppose the leaving of
magnet.

15. Lenz’s Law
Use the RH Grip rule for Solenoids and Lenz’s law
to predict the magnetic poles formed by the coils
below

16. Lenz’s Law
Predict the poles and the current direction for each
of the following;

17. Lenz’s Law and Energy
• Lenz’s law makes sense if we think about the
conservation of energy. The electrical energy
induced must come from work being done.
e.g. a greater force (W=Fd) must be applied to
move the magnet through a solenoid, than
through open space, as some of the mechanical
energy is being converted into electrical
energy.

18. Lenz’s Law –the Maths
• The induced emf produces a current that opposes the
change that produces it (i.e. the emf tries to keep the flux
constant or to compensate for the change in flux).
• Lenz’s law determines the direction of current flow and
accounts for the negative sign in Faraday’s Law.


For a circuit consisting ofN
wire loops (e.g. a coil): t
N B

  
t
B

   Faraday’s Law of Induction
for a single circuit loop:

19. Induced Voltage (emf)
• An emf is induced in a conductor moving in a magnetic field. A
conducting wire of length L moves perpendicularly to a uniform
magnetic field B with constant velocity v.
Force on electrons in the wire:
  
 
F qv B
Since force F on electrons is upward, I is downward in the wire.
V  BvL (Potential difference)
An emf is induced and a current flows in the wire as long as it moves
in the magnetic field. (principle of the electric generator).

20. Example
• A single rectangular loop of wire (0.230 Ω) sits in a region
of uniform magnetic field of 0.450 T. Calculate the voltage
induced in the loop as it is pulled out of the field (to the
right) at a constant velocity of 3.40 m/s.
What is the
magnitude and
direction of the
current flowing in
the loop during this
motion?

21. Working
V=BvL
=0.450×3.4×0.350
=0.5355 V
=0.536V (3sf)
I=V/R
=0.5335/0.230
=2.328A
=2.33A (3sf) anticlockwise

22. Example -rethink
This too is a Faraday’s law problem;
 =BA
=0.450×0.350×0.350
=0.05512
Time taken to move through the field (B from 0.450T to 0T)
t=d/v
=0.350/3.4
=0.1029 s
Faraday’s Law
V=Δ/ Δt
=0.05512/0.1029
=0.5355V
Use any breadth for
area as long as use
same for distance
travelled

23. Examples
1. The Airbus A380 has a wingspan of 78.6m.
Calculate the induced voltage across the wingtips
when it flies through the earth’s magnetic field
(5×10-5T) (vertically down) at 900kmh-1
0.98V
2. A coil connected to a voltmeter is moved through
a magnetic field of 0.2T at 2.4ms-1. Find the
length of the coil if the induced voltage is 1.5V.
3.1m
Why is it not possible to use the voltage in Question 1?

24. Uses of Induction
1. The Electric Generator
– using mechanical energy to turn a motor and
produce electrical energy.
2. The Transformer
– uses one coil to induce a current in another
3. The Inductor
– an electrical component that produces and
induced current and behaves like a very efficient
resistor in an AC circuit

25. The Transformer
• An electrical transformer is
an arrangement of two coils
usually around a laminated
iron core
• The primary coil induces a
voltage and therefore a
current in the secondary coil
• The ratio of the number of
turns on each coil
determines the output
voltage of the secondary
coil
• Symbol;

26. Iron Core
• The efficiency of a transformer is greatly
increased by placing an iron core between the
primary and secondary coils.
• The core greatly increases the magnetic field.
• Cores are laminated to reduce inductance within
the core itself, which can cause eddy currents
that result in energy loss through heating
(resistance).
• Each laminate is insulated from it’s neighbour
• The use of non-conducting, magnetic material
such as ferrite as a core also avoids eddy currents

27. Laminated Iron Core

28. Types of Transformers
• There are three basic types of transformer;
1.Step up Transformer
– low voltage and higher output voltage
2.Isolating Transformer
– Used to produce an “isolated” circuit that is safe for
using electrical appliances outdoors
3.Step down Transformer
– High input voltage and lower output voltage

29. DC in Transformers
According to Faraday’s Law ;

N B
t

  
voltage is induced only when the flux
changes
In a DC circuit that is only when the
current is switched on (field created)
or off (field collapsed)

30. AC in Transformers
• Transformers are most
commonly used in AC
circuits because the
constantly changing
direction of the current
means that induction is
continuous

31. Transformers in Action

32. Transformers -Mathematically
• In the ideal transformer;
and
S
P
V
S
P
N
N
V

• Transformer efficiency is never 100% as there are
always “loses” of energy e.g heat, sound? etc.
However good design has given some 99% efficiency
100
1
output energy
input
 
energy
Efficiency
P P S S V I V I

33. Examples
1. A primary coil of a transformer has primary
voltage of 12V and 36 turns. How many turns
will be needed on the secondary coil to give
an output voltage of 20V?
48 turns
2. The output voltage of a transformer is 15V.
Find the input voltage if NP=600 and Ns=75.
120V

34. Examples (con’t)
3. A step up transformer has 12V across the
primary (1) coil which carries a current of 1.4A.
Calculate the voltage of the 2 coil if the current
is 0.15A
112V
4. An isolating transformer has 240V across its 1
coil and 10A. What is the efficiency of the
transformer if the 2 coil produces 240V with a
current of 8.5A?
85%

35. Exercises
Pg 247
Activity 15B

36. Inductance
Inductance is the ability of an inductor to
store energy in a magnetic field

37. Mutual Inductance
• Transformers use the
changing current in the
primary coil to induce a
voltage in the secondary
coil this is Mutual
Inductance.
• The current in coil A can
be changed by;
– changing the resistance of
the variable resistor
– switching the circuit on
and off
– connecting it to an AC
supply

38. Mutual Inductance –the Maths
• When mutual inductance occurs the flux is
proportional to the current in the primary coil
MI
• Substituted into Faraday’s law;
M I
 

t
V

Where;
 =magnetic flux (Wb)
M=mutual inductance (H)
I= Current(a)
• Units for mutual inductance is the Henry (symbol H)

39. Exercises
1. Two coils have a mutual inductance of
0.060H. Calculate the induced emf when the
current in the 1 increases from 0 to 4.5A in
1.5s
0.18V
2. Find the mutual inductance between two
coils when the current in the 1 increases
from 0 to 2.8A in 0.5s and the induced
voltage is 80mV.
0.014H

40. Self Inductance
• When a switch is closed and current flows through a
coil it will take time (usually a very short time) for the
current to build up from 0 to a steady flow.
• As the current is increasing the magnetic flux in the coil
is changing
• This change in flux induces a voltage and therefore a
current in the coil
• This induced current is in such a direction so as to
oppose the current that created it
• This is self-inductance
• When the switch is closed the same thing happens
with the induced current in the opposite direction

41. Self Inductance in AC
• When an inductor is attached
to an AC supply the inductor
behaves like a resistor
restricting the flow of current
• The inductor is an efficient
way to restrict current as it
uses induction rather than
resistance
• The inductor stores electrical
energy in a magnetic field
then releases it as electrical
energy. The resistor converts
some electrical energy to
heat which is then “lost”
from the circuit

42. Self-inductance and Circuit Voltage
• A Neon bulb takes about 70V to
ionise the gas and light the bulb
• Closing the switch causes current
to flow and the inductor
produces a small induced
voltage briefly as the flux
changes.
• Opening the switch however
causes the lamp to light briefly
• Because of the high resistance of
the lamp, the collapse of the
field is very rapid o the induced
voltage is large (>70V)

43. Inductors
• Inductors are electrical
components that make use of
the principal described by
Lenz’s law.
• They produce a magnetic field
when current passes through
them.
• This field induces a voltage
and therefore a current that
opposes the current that
created it.
An Inductor is an electrical component that produces a voltage
when the current (and therefore the magnetic field) changes

44. Inductor Structure
• The wire coil of the inductor is usually wound
around an iron core to increase the field strength
• Because the inductor is a length of wire it has a
resistance so inductors are often drawn with a
resistor in a similar way to the internal resistance
of a battery
V  VR Terminal
An ideal inductor has a resistance small enough to be ignored

45. Self Inductance –the Maths
• When self inductance occurs the flux is proportional
to the current in the inductor
 LI
• Substituted into Faraday’s law;
L I
 

t
V

Where;
 =magnetic flux (Wb)
L=self-inductance (H)
I= Current(a)
• Units for self-inductance is the Henry (symbol H)

46. Exercises
1. An ideal inductor has a inductance of 0.060H.
Calculate the induced emf when the current
increases from 0 to 2.8A in 1.2s
0.14V
2. Find the terminal voltage of an inductor with
an inductance of 0.040H and a resistance of
0.60 when the current increases from 0 to
2.5A in 0.4s.
-1.25

47. Energy stored in an Inductor
• Current in an inductor causes a magnetic
field to form. Energy is stored in this
field.
2
E  1 LI
2
An inductor in a circuit with a bulb can
delay the lighting of the bulb as the electrical
energy is stored in the magnetic field

48. Exercises
1. An ideal inductor has a inductance of 0.080H.
Calculate the energy stored in the inductor
when the current is 4.5A.
0.81J
2. Find inductance of an inductor that stores
1.8J of energy when the current is 3.8A.
0.25H

49. Exercises
Read Pg 249-253
Do Activity 15C

51. Voltage and Current Graphs for
Inductors
L
R
 

52. Voltage and Current of Inductors
• When a switch is closed it takes
time for the current to reach a
steady flow
• The change in current through
the inductor induces an emf
• The induced current opposes the
current that created it (slowing
down the rate of change –slope of
graph)
• The greatest induced voltage is
when ΔI is greatest (Faraday’s
law)
• As ΔI decreases so does VL
Time
Voltage Current
Time
The shape of these curves can be controlled by a resistor in series, the
higher the resistance the slower the rate of change

53. Voltage and Current of Inductors
• When a switch is opened it takes
time for the current to decrease
to 0
• The change in current through
the inductor induces an emf
• The induced current opposes the
current that created it (slowing
down the rate of change –slope of
graph)
• The greatest induced voltage is
when ΔI is greatest (Faraday’s
law)
• As ΔI decreases so does VL
Time
Time
Current
Voltage
The shape of these curves can be controlled by a resistor in series, the
higher the resistance the slower the rate of change

54. Voltage and Current of Inductors
• Being able to describe the
changes in V and I of
inductors is important
• Consider the switch
positions in the circuit
and the graphs

55. Time Constant ( )
• One time constant is the time
taken for IL or VL to change by
63%
i.e. the time for current to reach
63% of IL
(or 36.5% when switched off)
or
for VL to reach 37%
• Experts; this is because of the exponential
nature of the curves;

IL
t
63.5%
VL
t
37.5%
C
For Decay V 
V e
when t V V e
1
1
C
t
C
 

as e 
 0.37, V  0.37 
V


 ,
, ( )
C
For growth V  V 1 
e
when t V V 1 e
1
1
  
C
t
C
as e 
 0.37, V  0.63 
V


( )



56. Time Constant ( 
) -the maths
• The shape of the I/t and V/t curves is
controlled by a resistance (R) of the circuit and
the self-inductance (L) of the inductor
L
R
 
• Remember that R will include the resistance of
the inductor as well as any other resistance in
the circuit

57. Examples
1. A circuit with a resistance of 28  has a 0.75
H inductor in it. Calculate the Time constant
of the inductor.
2. Find the resistance of a circuit where a 0.50H
inductor has a time constant of 1.8s