Transcript Physics 2102 Spring 2002 Lecture 15

Physics 2102
Spring 2007
Jonathan Dowling
Lecture 25: MON 16 MAR
Ch30.1–4
Induction and Inductance
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Fender Stratocaster
Solenoid Pickup
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Faraday's Experiments
In a series of experiments, Michael Faraday in England
and Joseph Henry in the U.S. were able to generate
electric currents without the use of batteries.
The circuit shown in the figure consists of a wire loop connected to a sensitive
ammeter (known as a "galvanometer"). If we approach the loop with a permanent
magnet we see a current being registered by the galvanometer.
1. A current appears only if there is relative motion between the magnet and the loop.
2. Faster motion results in a larger current.
3. If we reverse the direction of motion or the polarity of the magnet, the current
reverses sign and flows in the opposite direction.
The current generated is known as "induced current"; the emf that appears
is known as "induced emf"; the whole effect is called "induction."
Changing B-Field Induces a Current in a Wire Loop
Note Current Changes Sign With Direction
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No Current When Magnet Stops
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loop 1
loop 2
In the figure we show a second type of experiment
in which current is induced in loop 2 when the
switch S in loop 1 is either closed or opened. When
the current in loop 1 is constant no induced current
is observed in loop 2. The conclusion is that the
magnetic field in an induction experiment can be
generated either by a permanent magnet or by an
electric current in a coil.
Faraday summarized the results of his experiments in what is known as
"Faraday's law of induction."
An emf is induced in a loop when the number of magnetic field lines that
pass through the loop is changing.
Loop Two is Connected
To A Light Bulb.
The Current in Loop
One Produces a
Rapidly Changing
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Induces a Current in
Loop One
Loop Two — Lighting
Has a 60 Hz
the Bulb!
Alternating Current
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•
Faraday’s Law: What? The Flux!
r
A time varying magnetic
dA
B
FLUX creates an induced
EMF
• Definition of magnetic flux is
similar to definition of electric
flux
r r
B   B  dA
S
EEMF
dB

dt

dA
• Take note of the MINUS sign!!
• The induced EMF acts in
such a way that it OPPOSES
the change in magnetic flux
(“Lenz’s Law”).
Lenz’s Law
• The Loop Current Produces a B Field
that Opposes the CHANGE in the bar
magnet field.
• Upper Drawing: B Field from Magnet
is INCREASING so Loop Current is
Clockwise and Produces an Opposing
B Field that Tries to CANCEL the
INCREASING Magnet Field
• Lower Drawing: B Field from Magnet
is DECREASING so Loop Current is
Counterclockwise and Tries to BOOST
the Decreasing Magnet Field.
Example
• A closed loop of wire encloses
an area of A = 1 m2 in which in
a uniform magnetic field exists
at 300 to the PLANE of the loop.
The magnetic field is
DECREASING at a rate of
dB/dt = 1T/s. The resistance of
the wire is 10 W.
r
dA
B
300
60°
r r
 B   B  dA
• What is the induced current?


Is it

…clockwise or
…counterclockwise?

 BA cos(60 0 )  BA /2
dB A dB
E

dt
2 dt
E
A dB
i

R 2R dt
(1m2 )
i
(1T /s)  0.05A
2(10W)
Example
• 3 loops are shown.
B
II
• B = 0 everywhere except in
III
I
the circular region I where B
is uniform, pointing out of
the page and is increasing
at a steady rate.
• III encloses no flux so EMF=0
• Rank the 3 loops in order of • I and II enclose same flux so
EMF same.
increasing induced EMF.
• Are Currents in Loops I & II
– (a) III < II < I ?
Clockwise or Counterclockwise?
– (b) III < II = I ?
– (c) III = II = I ?
Example
B
0i
2r
i
• An infinitely long wire carries a constant
current i as shown
R
r=R+x
• A square loop of side L is moving
x
L
 dR/dt=v
towards the wire with a constant velocity
L
v.
• What is the EMF induced in the loop
Choose a “strip” of width dx
when it is a distance R from the loop?
located as shown.
Flux thru this “strip”
B 
L

0
0iLdx
2 (R  x)
0iLdx
d  BLdx 
2 (R  x)
  0iL


ln( R  x ) 
 2
0
L
 0iL  R  L 

ln 

2
 R 

dB
E 
dt
0 Li d  

ln1
2 dt  
L 


R 
Example
dB
E 
dt
0 Li d   L  

ln 1   
2 dt   R  
0 Li dR  R  L

2 dt  R  L  R 2
 0i  L2 

v

2  ( R  L) R 
i
R
dR/dt=v
L
x
What is the DIRECTION of the
induced current?
• Magnetic field due to wire points
INTO page and gets stronger as
you get closer to wire
• So, flux into page is
INCREASING
• Hence, current induced must be
counter clockwise to oppose this
increase in flux = CCW
B
Example : The Generator
• A square loop of wire of side L
is rotated at a uniform
frequency f in the presence of
a uniform magnetic field B as
shown.
• Describe the EMF induced in
the loop.
r r
B   B  dA
S
  t
f  2
L
B

B

 BL cos( )
dB
2 d
E 
 BL
sin( )  BL2 2f sin(2ft )
dt
dt
2
Example: Eddy Currents
• A non-magnetic (e.g. copper,
aluminum) ring is placed near a
solenoid.
• What happens if:
– There is a steady current in the
solenoid?
– The current in the solenoid is
suddenly changed?
– The ring has a “cut” in it?
– The ring is extremely cold?
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Another Experimental
Observation
• Drop a non-magnetic pendulum
(copper or aluminum) through an
inhomogeneous magnetic field
• What do you observe? Why? (Think
about energy conservation!)
Pendulum had kinetic energy
What happened to it?
Isn’t energy conserved??
N
S
Energy is Dissipated by
Resistance: P=i2R. This acts
like friction!!
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