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 QuickTime™ and a decompressor are needed to see this picture.
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 appear s 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 2 loop 1
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 Loop One QuickTime™ and a Cinepak decompressor are needed to see this picture.
Induces a Current in Loop Two — Lighting Has a 60 Hz the Bulb!
Alternating Current
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Faraday’s Law: What? The Flux!
• A time varying magnetic FLUX creates an induced
d
r
A
B
EMF • Definition of magnetic flux is similar to definition of electric flux
B
r
B
d
r
A
S
E
EMF
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.
Is it …clockwise or …counterclockwise?
Example
• A closed loop of wire encloses an area of A = 1 m 2 in which in a uniform magnetic field exists at 30 0 The magnetic field is DECREASING at a rate of dB/dt = 1T/s. The resistance of the wire is 10 W .
60°
B
d
r
A
r
B
d
r
A
30 0
BA
cos(60
0
)
BA
/2
E
d
B dt
A
2
dB dt i
E
R
A
2
R dB dt i
(1m 2 ) 2(10 W ) (1T/s) 0.05
A
B
Example
• 3 loops are shown.
• B = 0 everywhere except in the circular region I where B is uniform, pointing out of the page and is
increasing at a steady rate.
• Rank the 3 loops in order of increasing induced EMF.
– (a) III < II < I ?
– (b) III < II = I ?
– (c) III = II = I ?
I B
II III
• III encloses no flux so EMF=0 • I and II enclose same flux so EMF same.
• Are Currents in Loops I & II Clockwise or Counterclockwise?
Example
• An infinitely long wire carries a constant current
i
as shown • A square loop of side
L
is moving towards the wire with a constant velocity
v
.
• What is the EMF induced in the loop when it is a distance R from the loop?
B
2 0
i
r
dR/dt=v L L R x
i r=R+x Choose a “strip” of width
dx
located as shown.
Flux thru this “strip”
B
L
0 2 0
iLdx
(
R
x
)
d
BLdx
2 0
iLdx
(
R
x
) 2 0
iL
ln(
R
2 0
iL x
) 0
L
ln
R R L
E
d
B
0
Li
2
dt d dt
ln 1
L R
E
d
B dt
2 0
Li d dt
ln 1
L R
2 0
Li dR dt
R R
L
L R
2 0
i
2
v
(
R L
2
L
)
R
Example
dR/dt=v L R x
i 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
f
t
2 a uniform magnetic field
B
shown.
as
L B
• Describe the EMF induced in the loop.
B
E
BL
2 r
B
d
r
A S
cos(
d
B
dt
)
BL
2
d
sin( )
dt
BL
2
B
sin( 2
ft
)
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!)
N S
Pendulum had kinetic energy What happened to it?
Isn’t energy conserved?? Energy is Dissipated by Resistance: P=i 2 R. This acts like friction!!
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