AP Physics C Faradays Discovery Electromagnetic Induction is the process of using magnetic fields to produce voltage and in a complete circuit a current Michael Faraday first discovered it in 1831 using some of the works of Hans Christian ID: 604610
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Slide1
Electromagnetic Induction
AP Physics CSlide2
Faraday’s Discovery
Electromagnetic Induction is the process of using magnetic fields to produce voltage, and in a complete circuit, a current.
Michael Faraday first discovered it in 1831, using some of the works of Hans Christian
Oersted
.
He started by using different combinations of wires and magnetic strengths and currents, but it wasn't until he tried moving the wires that he got any success.
It turns out that electromagnetic induction is created by just that - the moving of a conductive substance through a magnetic field.Slide3
Magnetic Flux
The magnetic flux measures the amount of magnetic field passing through a loop of area A if the loop is tilted at an angle
θ
f
rom the field.
We represent magnetic flux with a dot product, just like with electric flux.The unit for magnetic flux is a Webber.
Slide4
Magnetic Flux for Non-Uniform Magnetic Fields
If you have a non-uniform magnetic field through a loop, you have to integrate to find the total flux.
This often involves a change of variable.Slide5
Faraday and Lenz’s Laws
Faraday realized that changing the magnetic flux in any way induced a voltage (and therefor a current) in a circuit.
Faradays law gives the magnitude of the induced voltage.
Lenz’s law (the negative sign) indicates the direction of the induced current.
Lenz’s law states that inductors resist changes in magnetic flux.
Slide6
Lenz’s LawSlide7
Example
The current in the straight wire is decreasing. Which is true?
A. There is a clockwise induced current in the loop.
B. There is a counterclockwise induced current in the loop.
C. There is no induced current in the loop.Slide8
Example
The magnetic field is confined to the region inside the dashed lines; it is zero outside. The metal loop is being pulled out of the magnetic field. Which is true?
A. There is a clockwise induced current in the loop.
B. There is a counterclockwise induced current in the loop.
C. There is no induced current in the loop.Slide9
Eddy Currents
Consider pulling a
sheet
of metal through a magnetic field.
Two “whirlpools” of current begin to circulate in the solid metal, called
eddy currents.The magnetic force on the eddy currents is a retarding force.
This is a form of magnetic braking.Slide10
Motional EMF
Motional EMF is voltage generated by a conductive bar moving through a magnetic field.
The picture to the right shows a current being generated by motional EMF.Slide11
Example
An airplane with a wing span of 30.0 m flies parallel to the Earth’s surface at a location where the downward component of the Earth’s magnetic field is 0.60 x10
-4
T. Find the difference in potential between the wing tips is the speed of the plane is 250 m/s.Slide12
AC Generators
AC generators convert mechanical energy into electrical energy.
The change in magnetic flux through the loop induces a current, which then goes to powering various devices.
This is the basic principle behind wind power and hydroelectric power.Slide13
Transformers
A transformer sends an alternating
emf
V1 through the primary coil.This causes an oscillating magnetic
flux through the secondary coil and, hence, an induced emf V
2.The induced emf of the secondary coil is delivered to the load:Slide14
Transformers
A
step-up transformer
, with
N
2 >> N
1, can boost the voltage of a generator up to several hundred thousand volts.Delivering power with smaller currents at higher voltages reduces losses due to the resistance of the wires.High-voltage transmission lines carry electric power to urban areas, where step-down transformers (
N
2
<<
N
1
) lower the voltage to 120 V.Slide15
The Induced Electric Field
Faraday’s law and Lenz’s law may be combined by noting that the
emf
must oppose the change in
Φm.
Mathematically, emf must have the opposite sign of dB/
dt.Faraday’s law may be written as:Slide16
The Induced Magnetic Field
As we know, changing the magnetic field induces a circular electric field.
Symmetrically, changing the electric field induces a circular magnetic field.
The
induced magnetic field was first suggested as a possibility by James Clerk Maxwell in 1855.Slide17
Maxwell’s Equations
We have now been introduced to the four most important equations in all of electromagnetic field theory. These formulas are known as Maxwell’s equations, named after James Clerk Maxwell.Slide18
Electromagnetic Waves
A changing electric field creates a magnetic field, which then changes in just the right way to recreate the electric field, which then changes in just the right way to again recreate the magnetic field, and so on.
This is an electromagnetic wave (a light wave).Slide19
Inductors
A coil of wire, or solenoid, can be used in a circuit to store energy in the magnetic field.
We define the
inductance
of a solenoid having
N
turns, length l and cross-section area A
as:
The
SI unit of inductance is the henry, defined as:
1 henry = 1 H = 1
Wb
/A = 1 T m2/A
A coil of wire used in a circuit for the purpose of inductance is called an
inductor.
If you divide both sides by time we get:Slide20
Inductors in Circuits
When an inductor is placed in a circuit, it may experience either a rise or a drop in voltage.
If the current is increasing in the inductor, the voltage decreases.
If the current is decreasing in the inductor, the voltage increases.
This is a consequence of energy being stored in the inductor’s magnetic field.Slide21
Energy in an Inductor
We can find the total energy stored in an inductor by integrating:
P
elec
is negative because the current is losing energy.
That energy is being transferred to the inductor, which is
storing energy
U
L
at the rate:
As current passes through an inductor, the electric power is:Slide22
LC Circuits
The figure shows a capacitor with initial charge
Q
0
, an inductor, and a switch.The switch has been open for a long time, so there is no current in the circuit.
At t
0, the switch is closed.How does the circuit respond?The charge and current oscillate in a way that is analogous to a mass on a spring.Slide23
LC CircuitsSlide24
LC Circuits
An
LC
circuit is an
electric oscillator.
The letters on the graph correspond to the four steps in the previous slides.
The charge on the upper plate is Q
Q
0
cosω
t
and the current through the inductor is
I
I
max
sin
ω
t
,
where:Slide25
LR Circuits
LR circuits involve inductors and resistors.
When the switch is closed, the inductor resists changes in magnetic flux, and therefor resists current.
As time goes on, the current through the inductor reaches a steady state.
The current through the inductor is modeled as logarithmic growth, while the voltage across the inductor is modeled as exponential decay.Slide26
LR Circuits
If the battery is removed from an LR circuit, the circuit no longer receives
emf
from the battery, however there is still current for a short period of time.
The sudden change in the magnetic flux through the inductor induces an
emf
whose current can be modeled with an exponentially decaying function.
L/R is often represented as
τ
, which is the time constant for an LR circuit.Slide27
Example
What is the battery current immediately after the switch has closed?
What is the battery current immediately after the switch has been closed for a very long time?