Physics 212 Lecture 16, Slide 1

1
Physics 212 Lecture 17
What the flux?!?! (sorry, I couldn't resist) )
Faradays Law
i dont understand why the prelecture guy was so
excited, it seemed pretty boring to me, but that
might be because i didnt understand the stuff too
well
2
Comments
Is this some kind of mistake?
Why am I doing this twice?
When do we get to completely interconnect, and
relate EM together?
I'm just really extremely confused by all the new
things presented in the past four or five
lectures.
3
Faradays Law
How do we deal with all these derivatives and
integrals??
Looks scary but its not its amazing and
beautiful !
A changing magnetic flux produces an electric
field.
Electricity and magnetism are on intimate terms
for the love of god please help me understand
this material
4
Faradays Law
What is flux?
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
5
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
6
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
7
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
8
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
9
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
10
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
11
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
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). 3) The current that flows
induces a new magnetic field. 4) The new magnetic
field opposes the change in the original magnetic
field.
B
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. 4) The new magnetic
field opposes the change in the original magnetic
field.
B
Demo
14
Faradays Law
Same idea in our other examples
As I pull loop down, which direction will the
induced current create a B field? A) Left B)
Right
B
Move loop to a place where the B field is
different
CD
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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.
emf is defined as the change in flux in the loop,
so as the loop enters the constant field, the
flux increases, so the flux changes, however once
it fully enters the field, it does not change any
longer, so the emf becomes zero, similarly when
it leaves, it has an EMF in the opposite
direction because flux is Decreasing now.
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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
HELP!!! i'm lostttt how can you even know
whether the current is counter clockwise or
clockwise??? and what does it mean???
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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
It changes direction every time the loop becomes
perpendicular with the B field
19
A horizontal copper ring is dropped from rest
directly above the north pole of a permanent
magnet.
(copper is not ferromagnetic)
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 gt g B   a g C   a lt
g
Please discuss the previous question (loop
falling and magnetic flux thru it increasing
leading to a clockwise current....) How does that
affect the acceleration??!!?? Thanks dude!
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A horizontal copper ring is dropped from rest
directly above the north pole of a permanent
magnet.
There will be an induced current in the loop
which will create a magnetic field which opposes
the existing one. Therefore, our new induced
magnetic field points down. It will create a
situation whereby the loop will experience and
upward force, slowing its rate of descent.
Demos
21
Calculation
y
A rectangular loop (height a, length 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 direction and the magnitude of the force on
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
a
v0
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
• Find the emf
• Find the current in the loop
• Find the force on the current

22
Calculation
A rectangular loop (height a, length 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 magnitude of the emf induced in the
loop just after it enters the field?
(A) e Babv02 (B) e ½ Bav0 (C) e ½
Bbv0 (D) e Bav0 (E) e Bbv0
In a time dtit moves by v0dt
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Calculation
A rectangular loop (height a, length 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 magnitude of the emf induced in the
loop just after it enters the field?
(A) e Babv02 (B) e ½ Bav0 (C) e ½
Bbv0 (D) e Bav0 (E) e Bbv0
a
The area in field changes by dA v0dt a
In a time dtit moves by v0dt
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Calculation
y
A rectangular loop (height a, length 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.
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
a
v0
x
emf is induced in direction to oppose the change
in flux that produced it
Flux is increasing into the screen
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Calculation
y
A rectangular loop (height a, length 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.
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
a
v0
x
What is the direction of the net force on the
loop just after it enters the field?
(A) y (B) -y (C) x
(D) -x

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

x
26
Calculation
y
A rectangular loop (height a, length 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.
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
a
v0
x
What is the magnitude of the net force on the
loop just after it enters the field?
e Bav0
(A) (B)
(C) (D)