Physics
ys cs 132:
3 Lecture
ectu e 22
Elements of Physics II
A
Agenda
d for
f T
Today
d


Lenz’ Law
 Emf opposes change in flux
Faraday’s Law
 Induced EMF in a conducting loop
Physics 202: Lecture 10, Pg 1
Lenz’s Law
Physics 202: Lecture 10, Pg 2
Lenz’s Law

Pushing the bar magnet
into the loop causes the
magnetic flux to increase in
th d
the
downward
d di
direction.
ti

To oppose the change in
flux which is what Lenz’s
flux,
Lenz s
law requires, the loop
itself needs to generate
an upward-pointing
upward pointing
magnetic field.

The induced current ceases
as soon as the magnet
stops moving.
Physics 202: Lecture 10, Pg 3
Lenz’s Law
Reasoning Strategy
1.
What direction is the magnetic flux that penetrates the coil.
2.
Determine whether the magnetic flux that penetrates the coil is
increasing or decreasing.
 Increasing: induced b-field opposes magnetic flux
 Decreasing: induced b-field alligned with magnetic flux
3.
Use RHR-2 to determine the direction of the induced current.
Physics 202: Lecture 10, Pg 4
Lenz’s Law
Physics 202: Lecture 10, Pg 5
Give it a try:
y
The current in the straight wire
is decreasing. Which is true?
A.
B
B.
C.
There is a clockwise
induced current in the loop.
There is a counterclockwise induced
current in the loop.
There is no induced current
in the loop
loop.
Physics 202: Lecture 10, Pg 6
Lenz’s Law
Physics 202: Lecture 10, Pg 7
Lenz’s
Lenz
s Law
Physics 202: Lecture 10, Pg 8
Lenz’s Law
Physics 202: Lecture 10, Pg 9
Lenz’s
Lenz
s Law
Physics 202: Lecture 10, Pg 10
Lenz’s Law
Physics 202: Lecture 10, Pg 11
Lenz’s Law
Physics 202: Lecture 10, Pg 12
Faraday’s Law

An emf is induced in a conducting loop if the
magnetic flux through the loop changes
changes.

The magnitude of the emf is:

The direction of the emf is such as to drive an
induced current in the direction given by Lenz’s
law.
Physics 202: Lecture 10, Pg 13
Faraday’s Law (Magnitude)
Emf = Change in magnetic Flux/Time
  f   i
 

tf  ti
t
Since = B A cos() 3 things can change
1. Area of loop
2. Magnetic field B
3. Angle
g between A and B,, 
Lenz’ Law (Direction)
E f opposes change
Emf
h
iin flflux
Physics 202: Lecture 10, Pg 14
Using Faraday’s Law

If we slide a conducting
wire along a U-shaped
conducting rail, we can
complete a circuit and
drive an electric current.

We can find the induced
emf and current by using
F d ’ llaw and
Faraday’s
d Oh
Ohm’s
’
law:
Physics 202: Lecture 10, Pg 15
Give it a try:
Th induced
The
i d
d emff around
d thi
this lloop iis
A.
200 V.
V
B.
50 V.
C.
2 V.
V
D.
0.5 V.
E.
0 02 V.
0.02
V
Physics 202: Lecture 10, Pg 16
Give it a try:
A flat
at coil
co o
of wire
e has
as a resistance
es sta ce R=10
0 . Att time
t e
t=0, it is oriented so the area vector makes an
angle 0=30o w.r.t. a constant magnetic field of 0.12
T. The loop is rotated to an angle of 0o in 0.5
seconds. Calculate the induced emf.
(a)
(b)
(c)
(d)
(e)
2.36
2
36 x 10-33 V
5.35 x 10-3 V
1.92 x 10-3 V
9.36 x 10-3 V
8.33 x 10-3 V
Physics 202: Lecture 10, Pg 17
Change 
A flat coil of wire has a resistance R=10 .
 At time t=0,
t=0 it is
oriented so the area vector makes an angle 0=30o w.r.t. a
constant magnetic field of 0.12 T. The loop is rotated to an
angle of 0o in 0
0.5
5 seconds
seconds. Calculate the induced emf.
emf
i = B A cos(30)
 
f = B A cos(0)
  f   i BA (cos( 0)  cos(30))


0 .5
t
tf  ti
 = 1.93 x 10-3 Volts
Physics 202: Lecture 10, Pg 18
Give it a try:
A flat
at coil
co o
of wire
e has
as a resistance
es sta ce R=10
0 . Att time
t e
t=0, it is oriented so the normal makes an angle
0=30o w.r.t. a constant magnetic field of 0.12 T.
The loop is rotated to an angle of 0o in 0.5 seconds.
What direction will current flow?
At the instant shown, an induced current in the loop
will
(a) flow clockwise.
(b) flow counterclockwise.
(c) not flow.
Physics 202: Lecture 10, Pg 19