Post on 25-Jun-2015
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Magnetic Flux
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)
This year we are interested in;
Examples
1. A magnetic field of a small NIB* magnet is 0.2T and covers an area of 0.12m2. Calculate the magnetic flux.
0.024Wb2. A magnetic flux of 2.5Wb is measured in an area of
0.25m2. Calculate the flux density (magnetic field strength).
10T3. 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
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)
Faraday’s Law of Induction
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
tΔΔΦ
Bwhere;
ε =emf or voltage (V)ΔΦ=change in flux
(Wb)Δt= change in time
(s)
Changing the Magnetic Flux in a Constant Magnetic Field
Examples
1. Find the induced emf when a change in flux of 0.56Tm2 occurs in 0.02s.
28V2. A magnetic field of 0.20T forms across and area of
0.12m2 in 0.02s. Calculate the emf induced1.2V
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
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;
tΔΔΦ
B
Direction of Induced Current
induced I opposes the motion of magnet (being attracted)
induced I opposes the motion of magnet (being repelled)
Direction of Induced Current
In both cases, magnet moves against a force.Work is done during the motion & it is transferred as electrical energy.
Try these;
A bar magnet passes through a coil:
Indicate the direction of the induced I in each case. Explain briefly.
(i) (ii) (iii)
Answer(i) Indicate the direction of the induced I. Explain.
(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.
Lenz’s law
I
S N
Answer
(ii) Indicate the direction of the induced I. Explain.
(ii)
The induced I become zero
I is about to change direction.
Answer
(iii) Indicate the direction of the induced I. Explain.
(iii)
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.
I
N S
Lenz’s Law
Use the RH Grip rule for Solenoids and Lenz’s law to predict the magnetic poles formed by the coils below
Lenz’s LawPredict the poles and the current direction for each of the following;
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.
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 of N wire loops (e.g. a coil): t
N B
tB
Faraday’s Law of Inductionfor a single circuit loop:
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:
BvqF
Since force F on electrons is upward, I is downward in the wire.
An emf is induced and a current flows in the wire as long as it movesin the magnetic field. (principle of the electric generator).
BvLV (Potential difference)
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 thecurrent flowing in the loop during this motion?
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
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 LawV=Δ/ Δt =0.05512/0.1029 =0.5355V
Use any breadth for area as long as use same for distance travelled
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
0.98V2. 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?
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
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;
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
Laminated Iron Core
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
DC in Transformers
According to Faraday’s Law ;
voltage is induced only when the flux changesIn a DC circuit that is only when the current is switched on (field created) or off (field collapsed)
tN B
AC in Transformers
• Transformers are most commonly used in AC circuits because the constantly changing direction of the current means that induction is continuous
Transformers in Action
Transformers -Mathematically
• In the ideal transformer;
and
• 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
P
S
P
S
N
N
V
V
1100
energy energy output
inputEfficiency
SSPP IVIV
Examples1. 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
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
112V4. 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%
Exercises
Pg 247Activity 15B
Inductance
Inductance is the ability of an inductor to store energy in a magnetic field
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
Mutual Inductance –the Maths
• When mutual inductance occurs the flux is proportional to the current in the primary coil
• Substituted into Faraday’s law;
• Units for mutual inductance is the Henry (symbol H)
IM
t
IMV
Where; =magnetic flux
(Wb)M=mutual
inductance (H)I= Current(a)
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 1.5s0.18V
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
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
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
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)
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
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
RVV Terminal
An ideal inductor has a resistance small enough to be ignored
Self Inductance –the Maths
• When self inductance occurs the flux is proportional to the current in the inductor
• Substituted into Faraday’s law;
• Units for self-inductance is the Henry (symbol H)
IL
t
ILV
Where; =magnetic flux
(Wb)L=self-inductance
(H)I= Current(a)
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 1.2s0.14V
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
Energy stored in an Inductor
• Current in an inductor causes a magnetic field to form. Energy is stored in this field.
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
221 LIE
Exercises
1. An ideal inductor has a inductance of 0.080H. Calculate the energy stored in the inductor when the current is 4.5A.
0.81J2. Find inductance of an inductor that stores
1.8J of energy when the current is 3.8A.
0.25H
Exercises
Read Pg 249-253Do Activity 15C
Voltage and Current Graphs for Inductors
R
L
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
Volt
ag
eC
urr
en
t
Time
The shape of these curves can be controlled by a resistor in series, the higher the resistance the slower the rate of
change
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
Volt
ag
e
The shape of these curves can be controlled by a resistor in series, the higher the resistance the slower the rate of
change
Time
Cu
rre
nt
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
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)orfor VL to reach 37%
• Experts; this is because of the exponential nature of the curves;
IL
t
63.5%
VL
t
37.5%
C
1
1
C
t
C
V0.37V0.37,eas
eVVtwhen
eVVDecayFor
,
C
1
1
C
t
C
V0.63V0.37,eas
e1VVtwhen
e1VVgrowthFor
)(
)(,
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
• Remember that R will include the resistance of the inductor as well as any other resistance in the circuit
R
L
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