Download Magnetic Flux and Faraday`s Law of Induction

8.2 Magnetic Flux and Faraday’s Law of
Induction
Magnetic Flux
Magnetic flux, ϕ, is defined as the product of the component of the magnetic field, B,
perpendicular to the plane of the coil and the area, A, of the coil.
Magnetic Flux ϕ = B A = BA cos Ɵ
T
Units: 1 T•m2 = Wb (Weber)
Michael Faraday determined that the amount of induced emf for a single coil depends on the
rate at which the magnetic flux changes with respect to time:
Ɛ=
Δϕ
Δt
Where:
Δϕ = ϕ2 - ϕ1
p. 311
8.2 Magnetic Flux and Faraday’s Law of
Induction
Faraday’s Law of Induction
For a wire with multiple number of loops, N, the equation for induced emf or potential
difference becomes:
Ɛ = -N
Δϕ
Δt
When a changing magnetic flux causes an emf to be induced, the induced emf in turn
produces an induced current. The induced current causes a magnetic field to be induced
around it. This induced magnetic field opposes the original magnetic flux that produced the
induced emf in the first place. This was first stated by Heinrich Lenz and is really another
example of the Conservation of Energy Law.
Lenz’s Law:
The polarity of the induced emf will always be such that it will produce a current
whose magnetic field opposes the changing flux that produced the original emf.
p. 313
8.2 Magnetic Flux and Faraday’s Law of
Induction
Counter EMF (Back EMF) in a Motor
A motor and a generator essentially have the same parts. A motor converts electrical
energy into kinetic energy and a generator converts kinetic energy into electrical energy.
When a current exists in a motor’s armature, the armature turning in a magnetic field
produces an induced emf that opposes the voltage of the source making the motor turn.
This is known as counter or back emf and is an example of Lenz’s Law in action.
The Counter or Back emf equation is derived form Kirchhoff’s Law:
Ɛb = VAB - IR
Where VAB is the terminal voltage
of the source.
p. 315
8.2 Magnetic Flux and Faraday’s Law of
Induction
Transformers (part 1)
A transformer is a device specifically designed to alter the voltage in an altering current
(AC) circuit. The “adapter” used to charge a cell phone is example of a transformer.
The transformer is very efficient at doing what is does do to the lack of moving parts
(hence very little friction). It is indispensible when transporting electrical energy over long
distances.
A transformer has two coils, primary or input coil, and
secondary or output coil wrapped around laminated soft
iron core as shown in the diagram
If AC voltage is applied to the primary coil of the
transformer, the AC current will induce a changing magnetic
field and therefore a changing magnetic flux.
Since the changing flux also acts on the secondary coil, an
induced AC current and therefore an induced AC Voltage will
be produced on the secondary coil. The time for the changing
voltages (primary and secondary) on both coils is the same.
p. 316
8.2 Magnetic Flux and Faraday’s Law of
Induction
Transformers (part 2)
From Faraday’s Laws
Ɛp = -Np
Δϕ
Δt
Ɛs = -Ns
Δϕ
Δt
The same change in flux, Δϕ, occurs in both coils over the same time period.
Therefore:
Ɛs
Ns
=
Ɛp
Np
If you want to step-up the voltage (higher voltage on the output side) then you will
need to have more coils on the secondary than on the primary coil.
If you want to step-down the voltage (lower voltage on the output side) then you
will need to have fewer coils on the secondary than on the primary coil.
p. 316
8.2 Magnetic Flux and Faraday’s Law of
Induction
Transformers (part 3)
Ideal transformers are 100% efficient and real transformers are almost as efficient (99% or
better) which means:
(Since same time for both sides and P = Et)
Ein = Eout
Pin = Pout
(Remember: P = VI)
ƐpI p = ƐsI s
Ɛs
Ɛp
Ip
=
Is
Ns
=
Np
Note:
Current, I and, Number of
turns, N, are inverted.
p. 316
8.2 Magnetic Flux and Faraday’s Law of
Induction
Transformers (part 3)
Ideal transformers are 100% efficient and real transformers are almost as efficient (99& or
better) which means:
(Since same time for both sides and P = Et)
Ein = Eout
Pin = Pout
Remember: P = VI)
ƐpI p = ƐsI s
Ɛs
Ɛp
Ip
=
Is
Ns
=
Np
Note:
Current, I and, Number of turns are inverted.
p. 316
8.2 Magnetic Flux and Faraday’s Law of
Induction
Long Distance Transmission of Electricity (part 1)
Transformers are essential to long-distance transmission of power. The power loss in a
conductor depends on the current in the wire and the resistance of the wire (PLoss = I2R)
The resistance of the wire used in power transmission is set by the type of material used
(usually aluminum), cross-sectional area of the wire, and the length of the wire. This is
very difficult to change once the transmission wire is set up.
The current, however, can be changed due to P = VI. For example the same power
would occur whether you have high-voltage, low-current or low-voltage, high-current.
For transmission of power it is essential that you use high-voltage, low-current
combination. A sample calculation show why this on the next page.
p. 316
8.2 Magnetic Flux and Faraday’s Law of
Induction
Long Distance Transmission of Electricity (part 2)
High-Voltage, Low Current
(P = 1000000 W, R = 5 Ω)
Low-Voltage, High Current
(P = 1000000 W, R = 5 Ω)
Ɛ = 100000 V, I = 10 A
Ɛ = 1000 V, I = 1000 A
Psource = 100000 x 10 = 1000000 W
(same power at source)
Psource = 1000 x 1000 = 1000000 W
(same power at source)
Ploss = I2R = 102 x 5 = 500 W
Ploss = I2R = 10002 x 5 = 5000000 W
Pdelivered = Psource - Ploss
= 1000000 - 500
= 9999500 W (99.5 %)
Pdelivered = Psource - Ploss
= 1000000 - 5000000
= 0 (No powered delivered!)
As can be seen in the sample calculations, high voltage must be used and transformers are the key to changing to
high voltages for transmission and then back to low voltages for household use.
p. 317
8.2 Magnetic Flux and Faraday’s Law of Induction
Key Questions
In this section, you should understand how to solve the following key questions.
Page 314 – Practice Problems 8.2.1 #2
Page 315 – Quick Check #1
Page 315 – Quick Check #1, & 3
Page 321 – 322 – Review 8.2 #2,4,5,6 & 8