Mon
Apr
Physics 152
Phys
152
Announcements
.23.
Monday,
April 23, 2007
• Help sessions
• W 9 - 10 pm in NSC 119
• MasteringPhysics
• WU #22 due Fri., April 27
• Hwk #5 due Fri., May 4
• No class on Wednesday
• More Faraday
• Lenzs Law
• Motional EMF
http://www.voltnet.com/ladder/
Lecture
35
= N
d
dt
t
Lecture
35
Phys
152
Ch. 33: Electromagnetic Induction
= N
d
dt
Faraday’s law tells us the average value of
the EMF over the time period t in which
the magnetic flux is changing.
Note the minus sign…The
induced EMF will attempt
to oppose the changing
magnetic flux. This result
is known as
t
t
Phys
152
Ch. 33: Electromagnetic Induction
Lecture
35
Phys
152
Ch. 33: Electromagnetic Induction
35
d
dt
Graphically, the
slope of the plot of
magnetic flux versus
time is the negative
of the instantaneous
induced EMF divided
by the number of
turns, N.
= N
Lecture
t
t
Graphically, the slope of
the line connecting the
two points in the flux vs
time plot is the negative
of the average induced
EMF divided by the
number of turns, N, over
the time interval, t.
Ch. 33: Electromagnetic Induction
Phys
152
Specifically,
Lenz’s Law
states:
The polarity of the induced EMF is such that
it produces a current whose magnetic field
opposes the change in magnetic flux through
the loop caused by the external source.
Stated another way, the induced current tries
to maintain the original flux through the circuit.
1
Lecture
Phys
152
Ch. 33: Electromagnetic Induction
35
Lecture
Phys
152
Ch. 33: Electromagnetic Induction
35
A
Worksheet Problem #1
S
N
As the bar magnet is brought toward the
loop, which way will the current flow in
through the ammeter?
From Lenz’s Law, the current will flow through
the loop in such a way that the magnetic field
it creates opposes the increasing rightward field
caused by the approaching bar magnet. So...
Lecture
Phys
152
Ch. 33: Electromagnetic Induction
35
I
S
A
Lecture
35
Loops in the presence of changing magnetic
fields pick up induced currents. The resulting
electricity in the circuit can then be used to
power appliances (resistors) or charge
capacitors.
N
As the bar magnet is brought toward the
loop, which way will the current flow in
through the ammeter?
Are we getting something for nothing?
...the current in the circuit will flow counterclockwise as viewed from the bar magnet. It
flows away from the left terminal of the
ammeter and toward the right terminal.
Lecture
35
I
S
N
So, from where is the energy coming?
Phys
152
Ch. 33: Electromagnetic Induction
Lecture
35
I
S
N
Bloop
Notice that as the bar magnet approaches the
loop, the induced magnetic field from the loop
points opposite the magnetic field of the bar
magnet.
Phys
152
Ch. 33: Electromagnetic Induction
A
Bmagnet
Phys
152
Ch. 33: Electromagnetic Induction
A
Bmagnet
Bloop
S
N
Bmagnet
Equivalent
Problem
N
S
Bloop
2
Lecture
35
Ch. 33: Electromagnetic Induction
Phys
152
Lecture
35
Phys
152
Ch. 33: Electromagnetic Induction
Worksheet Problem #2
S
S
N
N
Recall that for the case of two bar magnets,
like poles repel one another.
So WE must do mechanical work to push the
bar magnet toward the loop.
That mechanical work is what is transformed
into the electrical current (available energy)
the ammeter indicates.
Lecture
35
Ch. 33: Electromagnetic Induction
Phys
152
Lecture
35
Phys
152
Ch. 33: Electromagnetic Induction
A 100-turn coil with radius 4 cm and resistance 25 is found in a region with a
magnetic field perpendicular to the plane of
the coil. The magnetic field is decreasing at a
rate of 200 T/s. What is the induced current?
Worksheet Problem #3
B
Induced current due to changing
magnetic flux.
dB
= 200 T / s
dt
LENZ’S LAW
Lecture
35
Ch. 33: Electromagnetic Induction
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x x
xL x
x x
x x
x
x
x
x
x x x x
xv x x x
x x x x
x x x x
What happens to the charges in this
conducting bar as it moves with a
constant velocity v through a uniform
magnetic field?
The positive charges within the conductor feel
a magnetic force upwards.
The negative charges feel a downwards force.
Phys
152
Lecture
35
A
N = 100 turns
R = 25 A = (.04)2 = 5 X 10-3 m2
Phys
152
Ch. 33: Electromagnetic Induction
How long
can charge
be separated this
way?
FE = FB
x x x
x x x
F
x x+ x
x x Lx
x x x
xFx– 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
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
Until the electrostatic force balances the
magnetic force!
3
Lecture
35
How long
can charge
be separated this
way?
FE = FB
FE = qE
FB = qv B
Lecture
35
Phys
152
Ch. 33: Electromagnetic Induction
x x x
x x x
F
x x+ x
x x Lx
x x x
xFx– 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
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
Lecture
35
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
L
x x
x x
x
x
x
x
x x
x vx
x x
x x
x
x
x
x
x
x
x
x
What is the magnitude of the potential
difference between the ends of the bar
when the electrostatic and magnetic
forces are in balance?
|V | =| E | L = v B L
E =v B
Ch. 33: Electromagnetic Induction
Phys
152
Ch. 33: Electromagnetic Induction
Phys
152
Lecture
35
Worksheet Problem #4
Phys
152
Ch. 33: Electromagnetic Induction
What is the
current
induced in
this circuit?
x x
x x
R
x x
x x
x
x
x
x
x
x
x
x
x x
xL x
x x
x x
x
x
x
x
x x
xv x
x x
x x
x
x
x
x
x
x
x
x
x
x
x
x
Using Ohm’s Law: I = V / R
We saw that the induced EMF
in a bar of length L is simply:
V=BLv
I=
Note: You can get the same
answer using Faraday’s Law!!!
Lecture
35
Ch. 33: Electromagnetic Induction
What is the
current
induced in
this circuit?
x x
x x
R
x x
x x
x
x
x
x
x
x
x
x
x x
xL x
x x
x x
x
x
x
x
x x x x
xv x x x
x x x x
x x x x
Using Faraday’s Law: E = -N d/dt
= B A cos =B
A cos 0
=BA
Phys
152
x
x
x
x
Lecture
35
BLv
R
Ch. 33: Electromagnetic Induction
What is the
current
induced in
this circuit?
x x
x x
R
x x
x x
x x
x x
xx x
x x
x x
xL x
x x
x x
x
x
x
x
x x x x
xv x x x
x x x x
x x x x
Phys
152
x
x
x
x
Using Faraday’s Law: E = -N d/dt
0
dB
dA
d d
=
AB = A
+B
dt
dt
dt
dt
d( Lx)
dx
d
=B
= BL
= BLv
dt
dt
dt
( )
4
Lecture
35
What is the
current
induced in
this circuit?
d
E =
= BLv
dt
Lecture
35
Phys
152
Ch. 33: Electromagnetic Induction
x x
x x
R
x x
x x
x x
x x
xx x
x x
x x
xL x
x x
x x
I=
x
x
x
x
x x
xv x
x x
x x
x
x
x
x
x
x
x
x
x
x
x
x
Lecture
35
Ch. 33: Electromagnetic Induction
Phys
152
Worksheet Problem #5
BLv
R
Ch. 33: Electromagnetic Induction
Phys
152
Worksheet Problem #6
5