Physics 212 Lecture 16, Slide 1

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Physics 212 Lecture 16
2
Music

• Who is the Artist?
• Diana Krall
• Randy Crawford
• Aretha Franklin
• Jane Monheit
• Ella Fitzgerald

CD
I guess this week is a salute to wonderful female
voices Im embarrassed to admit I only
discovered Randy this year Shes been around
quite awhile.. My thanks to XM Radio for playing
her
3
Holy Smokes thatsallatta stuff
4
Things you identified as difficult
What exactly is emf? And what is flux? How do
they apply to the bar and/or the loop of current,
like how can you visualize them? I don't get how
you use Faraday's law in calculations it looks
like Gauss's law a little but I'm not really sure
what to do with it. I seriously watched this
thing 3 times now, and I still don't understand
basically anything.
5
Faradays Law
Looks scary but its not its amazing and
beautiful !
A changing magnetic flux produces an electric
field.
Electricity and magnetism are on intimate terms
6
Faradays Law
In Practical Words 1) When the flux FB through
a loop changes, an emf is induced in the loop.
B
There are many ways to change this
7
Faradays Law
In Practical Words 1) When the flux FB through
a loop changes, an emf is induced in the loop.
B
Change the B field
8
Faradays Law
In Practical Words 1) When the flux FB through
a loop changes, an emf is induced in the loop.
B
Move loop to a place where the B field is
different
9
Faradays Law
In Practical Words 1) When the flux FB through
a loop changes, an emf is induced in the loop.
B
Rotate the loop
10
Faradays Law
In Practical Words 1) When the flux FB through
a loop changes, an emf is induced in the loop.
B
A
Rotate the loop
11
Faradays Law
In Practical Words 1) When the flux FB through
a loop changes, an emf is induced in the loop.
B
A
Rotate the loop
12
Faradays Law
In Practical Words 1) When the flux FB through
a loop changes, an emf is induced in the loop.
2) The emf will make a current flow if it can
(like a battery).
I
Demo
13
Faradays Law
In Practical Words 1) When the flux FB through
a loop changes, an emf is induced in the loop.
2) The emf will make a current flow if it can
(like a battery). 3) The current that flows
induces a new magnetic field.
I
14
Faradays Law
In Practical Words 1) When the flux FB through
a loop changes, an emf is induced in the loop.
2) The emf will make a current flow if it can
(like a battery). 3) The current that flows
induces a new magnetic field. 4) The new magnetic
field opposes the change in the original magnetic
field.
B
15
Faradays Law
In Practical Words 1) When the flux FB through
a loop changes, an emf is induced in the loop.
2) The emf will make a current flow if it can
(like a battery). 3) The current that flows
induces a new magnetic field. 4) The new magnetic
field opposes the change in the original magnetic
field.
B
Demo
16
Faradays Law
Same idea in our other examples
B
Move loop to a place where the B field is
different
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Faradays Law
Executive Summary
emf?current?field a) induced only when flux is
changing b)
opposes the change
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1) A wire loop travels to the right at a constant
velocity. Which plot best represents the induced
current in the loop as it travels from left of
the region of magnetic field, through the
magnetic field, and then entirely out of the
field on the right side.
CD
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2) A copper loop is placed in a uniform magnetic
field as shown. You are looking from the right.
CD
Suppose the loop is moving to the right. The
current induced in the loop is A  zero
B  clockwise C  counter-clockwise
since the field is constant the flux through the
loop is not changing with time and no emf is
induced so there is no current
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4) A copper loop is placed in a uniform magnetic
field as shown. You are looking from the right.
CD
Now suppose the that loop is stationary and that
the magnetic field is decreasing in time. The
current induced in the loop is A   zero
B   clockwise C   counter-clockwise
Using the right had rule, since the change in
flux with respect to time is negative, then the
thumb would point towards B, showing the result
of a clockwise induced current.
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6) Now suppose that the loop is spun around a
vertical axis as shown, and that it makes one
complete revolution every second.
The current induced in the loop A   is zero
B   changes direction once per second
C   changes direction twice per second
the flux changes direction twice each second so
the current does also
22
8) A copper loop is placed in a non-uniform
magnetic field as shown. The magnetic field does
not change in time. You are looking from the
right.
Initially the loop is stationary. The current
induced in the loop is A  zero B  clockwise
C  counter-clockwise
There is no change in magnetic flux.
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10) A copper loop is placed in a non-uniform
magnetic field as shown. The magnetic field does
not change in time. You are looking from the
right.
CD
Now the loop starts moving to the left. The
current induced in the loop is A  zero
B  clockwise C  counter-clockwise
Less B will be going through the loop. Therefore,
the current will try to increase B.
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12) A conducting bar (green) rests on two
frictionless wires connected by a resistor as
shown. The entire apparatus is placed in a
uniform magnetic field pointing out of the
screen, and the bar is given an initial velocity
to the right.




The motion of the green bar creates a current
through the bar A  going up B  going down
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As the bar travels to the right, it is increasing
the area of the loop, thus increasing the
magnetic flux through the loop out of the screen.
The current will flow in order to cause a
magnetic flux into the screen resulting in it
flowing clockwise.
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13) A conducting bar (green) rests on two
frictionless wires connected by a resistor as
shown. The entire apparatus is placed in a
uniform magnetic field pointing out of the
screen, and the bar is given an initial velocity
to the right.

v
 The current through this bar results in a force
on the bar A  down B  up C  right D  left
E  into the screen X  out of the screen
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15) A horizontal copper ring is dropped from rest
directly above the north pole of a permanent
magnet.
Will the acceleration a of the falling ring in
the presence of the magnet be any different than
it would have been under the influence of just
gravity (i.e. g)? A   a g B   a g C   a g
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15) A horizontal copper ring is dropped from rest
directly above the north pole of a permanent
magnet.
The flux through the loop increases as it falls,
so a current is induced which creates a flux to
oppose the change. The loop then has a magnetic
dipole moment which points downward, meaning it
is like a magnet whose north pole is pointing
downward. Like poles repel, so the loop falls
with less acceleration than it would if under
only gravity's influence.
Demos
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Calculation
y
A rectangular loop (sides a,b, resistance R,
mass m) coasts with a constant velocity v0 in
x direction as shown. At t 0, the loop enters a
region of constant magnetic field B directed in
the z direction. What is the velocity of the
loop when half of it is in the field?
B
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
b
v0
a
x

• Conceptual Analysis
• Once loop enters B field region, flux will be
  changing in time
• Faradays Law then says emf will be induced

• Strategic Analysis
• Velocity will remain the same unless a force acts
  on the loop
• Determine whether induced emf will lead to a
  force acting on loop
• If so, calculate acceleration of loop
• If not, acceleration will be zero

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Calculation
y
A rectangular loop (sides a,b, resistance R,
mass m) coasts with a constant velocity v0 in
x direction as shown. At t 0, the loop enters a
region of constant magnetic field B directed in
the z direction. What is the velocity of the
loop when half of it is in the field?
B
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
b
v0
a
x
31
Calculation
y
A rectangular loop (sides a,b, resistance R,
mass m) coasts with a constant velocity v0 in
x direction as shown. At t 0, the loop enters a
region of constant magnetic field B directed in
the z direction. What is the velocity of the
loop when half of it is in the field?
B
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
b
v0
a
x
e Bav0
emf is induced in direction to oppose the change
in flux that produced it
Flux is increasing into the screen
32
Calculation
y
A rectangular loop (sides a,b, resistance R,
mass m) coasts with a constant velocity v0 in
x direction as shown. At t 0, the loop enters a
region of constant magnetic field B directed in
the z direction. What is the velocity of the
loop when half of it is in the field?
B
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
b
v0
a
x
e Bav0

• Force on top and bottom segments cancel (red
  arrows)
• Force on right segment is directed in x
  direction.