Physics 102: Lecture 10, Slide 1 Faraday’s Law Physics 102: Lecture 10 Changing Magnetic Fields create Electric Fields Last Two Lectures • Magnetic fields • Forces on moving charges and currents • Torques on current loops • Magnetic field due to – Long straight wire – Solenoid
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Physics 102: Lecture 10, Slide 1 Faraday’s Law Physics 102: Lecture 10 Changing Magnetic Fields create Electric Fields Last Two Lectures Magnetic fields.
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Physics 102: Lecture 10, Slide 1
Faraday’s LawPhysics 102: Lecture 10
Changing Magnetic Fields create Electric Fields
Last Two Lectures
• Magnetic fields
• Forces on moving charges and currents
• Torques on current loops
• Magnetic field due to– Long straight wire– Solenoid
Physics 102: Lecture 10, Slide 2
Last Two Lectures
• Magnetic fields
• Forces on moving charges and currents
• Torques on current loops
• Magnetic field due to– Long straight wire– Solenoid
Physics 102: Lecture 10, Slide 3
Today: Faraday’s Law
• The principle that unifies electricity and magnetism
• Key to many things in E&M– Generating electricity– Microphones, speakers and tape decks– Amplifiers– Computer disks and card readers
Physics 102: Lecture 10, Slide 4
Physics 102: Lecture 10, Slide 5
First a preliminary: Magnetic Flux
• “Counts” number of field lines through loop.
Uniform magnetic field, B, passes through a plane surface of area A.AMagnetic flux = B A
Magnetic flux B A cos() is angle between normal and B
B
A
normal
B
Note: The flux can be negative(if field lines go thru loop in opposite direction)
Physics 102: Lecture 10, Slide 6
Preflight 10.7
Compare the flux through loops a and b.
1) a>b 2) a< b
ab
nn B
A =
B =
“more lines pass through its surface in that position.”
Physics 102: Lecture 10, Slide 7
Faraday’s Law of Induction:This is new physics and not simply an application of stuff you already know
“induced emf” = rate of change of magnetic flux
if
if
ttt
Since = B A cos(3 things can change
1. Area of loop
2. Magnetic field B
3. Angle between A and B
Physics 102: Lecture 10, Slide 8
Physics 102: Lecture 10, Slide 9
Lenz’s Law (EMF Direction)
Induced emf opposes change in flux
EMF does NOT oppose B field, or flux!
EMF opposes the CHANGE in flux
• If flux increases: New EMF makes new field opposite to original
field
• If flux decreases:New EMF makes new field in same direction
as original field
Physics 102: Lecture 10, Slide 10
ACT: Change Area
1v
v
3
Which loop has the greatest induced EMF at the instant shown above?
L
W
2
v
Physics 102: Lecture 10, Slide 11
Example: Change Area
V
t=00=BLW
tt=BL(W+vt)
t
BLWvtWBL
ttt
)(
00 vBL
L
W
V
W vt
EMF Direction: B is out of page and is increasing so EMF creates B field (inside loop) going into page.
I
EMF Magnitude:
= B A cos()
Physics 102: Lecture 10, Slide 12
Physics 102: Lecture 10, Slide 13
Motional EMF circuit
• Direction of Current
• Direction of force (F=ILB sin()) on bar due to magnetic field
I = /R
• Magnitude of current
Clockwise (+ charges go down thru bar, up thru bulb)
To left, slows down
Moving bar acts like battery = vBL
B
-+
V
What changes if B points into page?
= vBL/R
Physics 102: Lecture 10, Slide 14
Motional EMF circuit
I = /R = vBL/R
Still to left, slows down
Moving bar acts like battery = vBL B
+ -
V
x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
• Direction of Current
• Direction of force (F=ILB sin()) on bar due to magnetic field
• Magnitude of current
Counter-Clockwise (+ charges go up thru bar, down thru bulb)
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Physics 102: Lecture 10, Slide 15
Preflight 10.4
• Increase• Stay the Same• Decrease
Suppose the magnetic field is reversed so that it now points OUT of the page instead of IN as shown in the figure.
To keep the bar moving at the same speed, the force supplied by the hand will have to:
19
Physics 102: Lecture 10, Slide 16
Physics 102: Lecture 10, Slide 17
Preflight 10.5
• True• False
Suppose the magnetic field is reversed so that it now points OUT of the page instead of IN as shown in the figure.
To keep the bar moving to the right, the hand will have to supply a force in the opposite direction.
Physics 102: Lecture 10, Slide 18
ACT: Change BAs current is increasing in the
solenoid, what direction will current be induced in ring?
1) Same as solenoid
2) Opposite of solenoid
3) No current
SN
Physics 102: Lecture 10, Slide 19
ACT: Change B II
S
N
N
S
Which way is the magnet moving if it is inducing a current in the loop as shown?
1) Up
2) Down
Physics 102: Lecture 10, Slide 20
Physics 102: Lecture 10, Slide 22
Change A flat coil of wire has A=0.2 m2 and R=10. At time t=0, it is
oriented so the normal makes an angle 0=0 w.r.t. a constant B field of 0.12 T. The loop is rotated to an angle of =30o in 0.5 seconds. Calculate the induced EMF.
n
B
A
if
if
ttt
i = B A cos(0)
f = B A cos(30)
= 6.43x10-3 Volts
What direction is the current induced?
5.0))0cos()30(cos( BA
Physics 102: Lecture 10, Slide 23
Magnetic Flux ExamplesA conducting loop is inside a solenoid (B=onI). What happens to the flux through the loop when you…
Increase area of solenoid?
Increase area of loop?
Increase current in solenoid?
Rotate loop slightly? B A cos()
Physics 102: Lecture 10, Slide 24
Physics 102: Lecture 10, Slide 25
Magnetic Flux II
Increase area of solenoid
Increase area of loop
Increase current in solenoid
A solenoid (B=onI) is inside a conducting loop. What happens to the flux through the loop when you…