Faradays Law

1
Faradays Law
Physics 102 Lecture 10
Changing Magnetic Fields create Electric Fields

• Exam 1 tonight
• Be sure to bring your ID and go to correct room
• All you need is a 2 pencil and calculator
• No cell phones
• No I-pods, laptops, etc.

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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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Today Faradays Law

• The principle that unifies electricity and
  magnetism
• Key to EVERYTHING in EM
• Generating electricity
• Microphones, speakers and tape decks
• Amplifiers
• Computer disks and card readers
• Ground Fault Interrupters (GFI)

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First a preliminary Magnetic Flux

• Count number of field lines through loop.

B
Uniform magnetic field, B, passes through a plane
surface of area A.
Magnetic flux F B A
Magnetic flux F ? B A cos(f)
f is angle between normal and B
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5
Preflight 10.7
B
n
n
more lines pass through its surface in that
position.
b
a
FA B A cos(0) BA
FB B A cos(90) 0

• Compare the flux through loops a and b.
• 1) FagtFb 2) Falt Fb

68
32
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Faradays Law of InductionThis is new physics
and not simply an application of stuff you
already know

• induced emf rate of change of magnetic flux

• Since F B A cos(f), 3 things can change F
• Area of loop
• Magnetic field B
• Angle f between A and B

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Lenzs Law (EMF Direction)
Induced emf opposes 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

EMF does NOT oppose B field, or flux! EMF opposes
the CHANGE in flux
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demo 1093
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ACT Change Area
3
W
2
1
v
L
v
v
Which loop has the greatest induced EMF at the
instant shown above?
1 moves right - gets 4 more field lines. 2 moves
down - gets 0 more field lines. 3 moves down -
only gets 2 more lines.
1 is gaining flux fastest!
E 3 BvW
E1 BvL
E 2 0
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Example Change Area
W
V
L
I
t0 F0BLW
t FtBL(Wvt)
F B A cos(q)
EMF Magnitude
EMF Direction B is out of page and F is
increasing so EMF creates B field (inside loop)
going into page.
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10
Motional EMF circuit
Moving bar acts like battery e vBL
B
-

• Magnitude of current

V
I e/R
vBL/R

• Direction of Current

Clockwise ( charges go down thru bar, up thru
bulb)

• Direction of force (FILB sin(q)) on bar due to
  magnetic field

What changes if B points into page?
To left, slows down
DEMO 371
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Motional EMF circuit
Moving bar acts like battery e vBL
B
x x x x x x x x x x x x x
x x x x
-

• Magnitude of current

x x x x x x x x x x x x x
x x x x
V
x x x x x x x x x x x x x
x x x x
I e/R vBL/R
x x x x x x x x x x x x x
x x x x

• Direction of Current

x x x x x x x x x x x x x
x x x x
Counter-Clockwise ( charges go up thru bar, down
thru bulb)

• Direction of force (FILB sin(q)) on bar due to
  magnetic field

Still to left, slows down
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Preflight 10.4
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

• Increase
• Stay the Same
• Decrease

32 52 16
FILB sin(q))
B and v still perpendicular (q90), so FILB just
like before!
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Preflight 10.5
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.

• True
• False

51 49
Current flows in the opposite direction, so force
from the B field remains the same!
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ACT Change B
SN

• As current is increasing in the solenoid, what
  direction will current be induced in ring?

• Same as solenoid
• Opposite of solenoid
• No current

• ? Solenoid current (counter-clockwise)
• ? B-field (upwards) gt ? Flux thru loop
• EMF will create opposite B-field (downwards)
• Induced loop current must be clockwise

Demo 157
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ACT Change B II

• Which way is the magnet moving if it is inducing
  a current in the loop as shown?
• Up
• Down

S N
Flux from magnet is down. Induced current
creates flux up - opposite original. So flux from
magnet must be increasing. Magnet must be
falling down
Demo 371
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ACT Change B II (contd)

• If I reduce the resistance in the wire, the
  magnet will fall
• faster
• slower
• at the same speed

S N
N
S
Decreasing R, increases I. Increases opposing
field, which makes magnet fall slower.
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Change f

• A flat coil of wire has A0.2 m2 and R10W. At
  time t0, it is oriented so the normal makes an
  angle f00 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.

Example
Fi B A cos(0)
Ff B A cos(30)
e 6.43x10-3 Volts
What direction is the current induced?
F upwards and decreasing. New field will be in
same direction (opposes change). Current must be
counter clockwise.
Demo 68, 371
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Magnetic Flux Examples
Example
A conducting loop is inside a solenoid (BmonI).
What happens to the flux through the loop when
you
Increase area of solenoid?
Nothing
Increase area of loop?
Increases
Increase current in solenoid?
Increases
F ? B A cos(f)
Rotate loop slightly?
Decreases
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Magnetic Flux II
Example
A solenoid (BmonI) is inside a conducting loop.
What happens to the flux through the loop when
you
Increase area of solenoid
Increases
Increase area of loop
Nothing
Increase current in solenoid
Increases
F ? B A cos(f)
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Good Luck Tonight!
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Motional EMF, Preflight 10.1
B
Moving charge feels force downwards

• F q v B sin(q)

v

F
B
Moving charge still feels force downwards
Potential Difference F L/q EMF q v B sin(q)
L/q v B L
Only 22 got this correct on the preflight!!
10
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Preflight 10.2

• Which bar has the larger motional emf?

v
a
b
v
E v B L sin(q)
q is angle between v and B
Case a q 0, so E 0
Case b q 90, so E v B L
52 got this correct.
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