Download Magnetic Field due to a Current

Faraday’s Law of Induction
AP Physics C
Mrs. Coyle
What do these have in common?
Write 2 possible answers (hold your
thoughts).
Hoover Dam, CA
Michael Faraday
• 1791- 1867
• England
• Initially worked as a
bookbinder
• Son of a blacksmith
•
Thomas Phillips oil on canvas, 1841-1842
http://en.wikipedia.org/wiki/Michael_Faraday
http://ruralblacksmith.blogspot.com/2011_
01_01_archive.html
Faraday’s worked as a bookbinder…..
-From the PBS Series: Einstein’s Big Idea
-Downloaded using clipconverter.cc
Faraday got his big break when he became the assistant of
Humphry Davy (Professor at the Royal Institution):
-From the PBS Series: Einstein’s Big Idea
-Downloaded using clipconverter.cc
• Magnetic fields are caused by currents.
• Hans Christian Oersted in 1820’s showed
that a current carrying wire deflects a
compass.
Current in the Wire
No Current in the
Wire
(Ampere’s Law is the mathematical way to find B)
Since it was established by Oersted that an electric
field causes a magnetic field around it,
Faraday wanted to see if the reverse is true.
Write down a possible hypothesis that Faraday may
have formulated.
How can current be induced in a
wire?
• Michael Faraday
• A current is induced
in a wire, when the
magnetic field that is
“felt” by the wire is
changed.
Induced Current and Induced EMF
• An induced current is produced by a
changing magnetic field
• A current can be produced without a
battery present in the circuit
Faraday’s Law of Induction
• The emf, E induced in a circuit is directly
proportional to the time rate of change of
the magnetic flux through the circuit”
dB
ε
dt
Note
• If the circuit consists of N loops, all of the
same area, and if B is the flux through
one loop, an emf is induced in every loop
dB
ε  N
dt
Magnetic Flux
θ
Magnetic Flux, : The number of magnetic (flux) field lines
which pass through a given cross-sectional area A
   B  dA
For constant B and A:
  BA cos 
Units:
 webers
B Tesla
A area m2
 angle formed between B and the normal to the loop
(area vector A)
The area vector A is perpendicular to the surface A and
has a magnitude equal to the area A.
Example
• The magnetic flux
through the loop is
B = BA cos 
dB
ε
dt
• The induced emf is
e = - d/dt (BA cos )
   B  dA
The magnetic flux can be
For constant B and A:
changed by:
  BA cos 
1. Changing the orientation of the wire
loop in which the current is to be
induced (movement).
2. Changing the strength of the
magnetic field (change current of wire
that causes the field).
3. Changing the area of the coil.
1. Movement
• When a wire is moved in a constant
magnetic field, the wire “feels” a
changed magnetic field and current is
induced.
1. Change Caused by Movement
-Sliding Conducting Bar (Motional EMF)
L
emf = - B Lv sin
L: length of the wire
: angle between v and B
Sliding Conducting Bar
dB
dx
 B
 B v
• Induced emf : ε  
dt
dt
• Induced Current:
ε Bv
I 
R
R
Sliding Conducting Bar
• A bar moving through a uniform field and the
equivalent circuit diagram
• Assume the bar has zero resistance
• The work done by the applied force appears as
internal energy in the resistor R
Sliding Conducting Bar and Energy
• The applied force does work on the conducting bar to
move charges through a magnetic field
• The change in energy of the system during some time
interval must be equal to the transfer of energy into the
system by work
• The power input is equal to the rate at which energy is
delivered to the resistor
ε2
P  Fappv   I B  v 
R
Generator
http://www.walterfendt.de/ph14e/generator_e.htm
Generators at Hoover Dam
http://nrgfuture.org/Hoover_Dam_generators.jpg
3 minute video on Hoover Dam
• http://www.teachersdomain.org/resource/p
hy03.sci.phys.energy.hooverelec/
2.
Electromagnetic Induction
by changing the current causing the
B-field (thus changing the B-field).
• http://higheredbcs.wiley.com/legacy/colleg
e/halliday/0471320005/simulations6e/inde
x.htm?newwindow=true
Changing Magnetic Field
Faraday’s Experiment
• A primary coil is connected to
a switch and a battery
• The wire is wrapped around
an iron ring
• A secondary coil is also
wrapped around the iron ring
• There is no battery present in
the secondary coil
• The secondary coil is not
directly connected to the
primary coil
Faraday’s Experiment
• At the instant the switch is closed, the
galvanometer (ammeter) needle deflects in one
direction and then returns to zero
• When the switch is opened, the galvanometer
needle deflects in the opposite direction and
then returns to zero
• The galvanometer reads zero when there is a
steady current or when there is no current in the
primary circuit
Faraday’s Experiment
• An electric current can be induced in the
secondary circuit by changing the magnetic
field
• The induced current exists only while the
magnetic field is changing
• Note: the flux must be changing
The Flying Ring
• http://teachertube.com/viewVideo.php?vid
eo_id=125587
Question
• In the “flying ring” demo, how was the
magnetic field “felt” by the copper ring
changed?
• Answer: AC current
3.
When B is constant and A (area) is
changing.
Ways of Inducing an emf
• The magnitude of B can change with time
• The area enclosed by the loop can change
with time
• The angle  between B and the normal to
the loop can change with time
• Any combination of the above can occur
Applications of Faraday’s Law
-GFI (Ground Fault Interuptor)
• A GFI protects users of
electrical appliances against
electric shock by triggering a
circuit breaker
• When the currents in the
wires are in opposite
directions, the flux is zero
• When the return current in
wire 2 changes, the flux is no
longer zero
• An emf results which can be
trigger a circuit breaker.
Applications of Faraday’s Law
– Pickup Coil of an Electric Guitar
• The coil is placed near the
vibrating string and causes a
portion of the string to become
magnetized
• When the string vibrates at the
same frequency, the
magnetized segment produces
a changing flux through the coil
• The induced emf is fed to an
amplifier