Transcript CHAPTER 20 Induced Voltages and Inductance

CHAPTER 20
Induced Voltages and Inductance
An electric current produces a magnetic field.
o I
B=
2r
Scientists in the 19th century saw that electricity (a relatively
new discovery) and magnetism (a relatively old discovery)
were related.
They hypothesized:
“If electricity (current) produces a magnetic field,
then a magnetic field should be able to produce
electricity.”
As with many initial hypotheses, this one was close to
correct…but not exactly.
Michael Faraday (as in Farad) 1791-1867
Faraday discovered the correct relationship between
electricity and magnetism. The relationship came as a
surprise to him and was discovered somewhat accidentally.
- The iron in the illustration is not a magnet.
- With the switch open, it contains no magnetic field.
-When the switch is closed, the primary coil will have
current flowing and a B-field is established.
Use one of the 2 RHR’s to determine the direction of the
B-field lines established in the iron.
B
- Notice the B-field extends all the way around the inside of
the iron.
- A current in the secondary coil wire develops only
momentarily when the switch is closed (indicated by the
Galvanometer) and then returns to zero.
- A current in the secondary coil also develops (in the
opposite direction) momentarily when the switch is opened.
Faraday: It is the change in a magnetic field that can
produce current, not the magnetic field itself.
The change in B-field strength produces an emf (voltage) in
the wire that then causes current.
Application:
Current produced by a battery producing current
elsewhere seems at first like an interesting novelty, but of
little practical value.
However, a magnet alone moving through a coil of wire
produces the same effect (current) for the same reason.
This is essentially how electricity has been produced for
most of the past 150 years and how it is still produced
today.
Demo: magnets, coil, galvanometer
Faraday’s Law of Magnetic Induction

 = - N t
 = emf = voltage
N = number of turns of wire in the loop
 = change in flux (Webers)
t = change in time
Lenz’s Law: “the no free lunch law”
The direction of the induced emf (voltage) is such
that it produces a current whose magnetic field
opposes the change in magnetic flux through the
loop. That is, the induced current tends to maintain
the original flux through the loop.
Example #1
A Conducting Bar Moving Perpendicular to a Uniform
Magnetic Field
Size of loop increases
as the bar is pulled
right at a velocity v.
 Magnitude

 = t
B A
 = t
 = B tLx
=BLv
Direction of Current
Downward B-field lines being added
Current creates a B-field with
upward pointing B-field lines
Current goes up on right side
of loop and down through
resistor on left. (CCW)
Lenz Law Examples
Example #2
Square Loop of Wire Pulled at Constant Velocity into a
Magnetic Field
Field Strength = B (down)
L
v
x
t
A = Area exposed to B-field = x  L
 = B x  L
 = B x  L

t
t
t =  = B v L
What will be the direction of current? Counter Clockwise
B’-field lines pointed up canceling out the
increase in B-field lines pointing down.
v=
NOTE: Current stops once loop is entirely in field.
Example #3
Stationary Loop I a Spacially Uniform Magnetic Field
Whose Magnitude is Changing at a Constant Rate
Bo
B
A
t=0
A
t=t
=BA
o = B o A
 = (B – Bo) A
 = B  A

B
t =  = t  A
Find Direction of Current
Decreasing B
Increasing B
Current produced B ‘ tends
Current produced B ‘ tends to
to restore B-field lines lost.
oppose B-field lines gained.
( )
I = Clockwise
I = Counter Clockwise
Example #4
Loop of Wire Rotates at a Constant Rate about an Axis
Perpendicular to a Uniform Magnetic Field


v
Rotation
I
sin  = 1
Right half of loop
= 2 B l v = 2 B l v sin
2 in formula because
2 wires of length l (left
and right side of loop)
Remember:
If loop is horizontal
and moving up (or
down) the velocity
component of
movement  to the Bfield is at a maximum.
Magnetic Flux ():
A measure of the B-field lines
that actually pass through a loop
of given area (A)
Flux Example (Perpendicular Situation)
Wb
Wb (Weber) can be thought
B = 20 T = 20
of as magnetic field lines.
m2
A = .25m2
If B-field lines are perpendicular to the area of the loop,
then the magnetic flux through the loop is:
B
=BA
Wb
2
 = 20
x
.25m
m2
 = 5 Wb
A
Flux Example (Angled Situation)
Caution:  = B A cos only when
B 
A
certain angles are referenced
 = B A sin 
Think!

Area remains equal to .25 meters2, but is at an angle of
 (30) with the horizontal while B (20T) is perpendicular
() to the horizontal.
The B-field only “sees” an area of A cos
• If  = 90
Area exposed to B-field view is 0.
(cos(90)=0)
• If  = 0
Area exposed to B-field view is A.
(cos(0)=1)
=BA
Notice: As loop rotated in a
stationary B-field, the  changed
 = B A cos 
from 5.0Wb to 4.3Wb. This  will
induce emf and current in the wire
Wb
2
 = (20 2 )(.25m )(cos30) (as long as the loops is rotating
m
and the flux through it is
changing.)
 = 4.3 Wb
Faraday’s Law of Magnetic Induction
 = emf = voltage

 = - N t
N = number of turns of wire in the loop
 = change in flux (Webers)
t = change in time
Lenz’s Law: “the no free lunch law”
The direction of the induced emf (voltage) is such
that it produces a current whose magnetic field
opposes the change in magnetic flux through the
loop. That is, the induced current tends to maintain
the original flux through the loop.
B
A
I
FB

As loop rotates CCW,  gets smaller
(less B-field lines intersect the opening).
The current sets up additional B-field
lines going down through the loop.
Find direction of current.
Find direction of Force on the current
carrying wire in a magnetic field.