102: Physics Lecture 10
Faradays Law
Changing Magnetic Fields create Electric Fields
Physics 102: Lecture 10, Slide 1
Last Two Lectures
Magnetic fields
Forces on moving charges and currents
Torques on current loops
Magnetic field due to
Long straight wire
Solenoid
Physics 102: Lecture 10, Slide 2
Motional EMF
A metal bar slides with velocity v on a track in a uniform B field
I
q+
V
Fq
Moving + charges in bar experience force down (RHR1)
Electrical current driven clockwise!
Moving bar acts like a battery (i.e. generates EMF)!!
Physics 102: Lecture 10, Slide 3
(Recall that e- actually move,
opposite current)
Faradays Law of Induction:
induced EMF = rate of change of magnetic flux
f i
=
=
The principle that unifies electricity and magnetism
Key to many things in E&M
Generating electricity
Microphones, speakers, guitar pickups
Amplifiers
Computer disks and card readers
Physics 102: Lecture 10, Slide 4
First a preliminary: Magnetic Flux
Counts number of field lines through loop.
B
A
Uniform magnetic field, B, passes
through a plane surface of area A.
Magnetic flux = B A
(Units Tm2 = Wb)
B
rm
no
Magnetic flux B A cos()
al
A
is angle between normal and B
Note: The flux can be negative
(if field lines go thru loop in opposite direction)
Physics 102: Lecture 10, Slide 5
Preflight 10.7
nB
n
a
b
more lines pass through
its surface in that
position.
A = B A cos(0) = BA
B = B A cos(90) = 0
Compare the flux through loops a and b.
1) a>b
2) a< b
Physics 102: Lecture 10, Slide 6
Faradays Law of Induction:
induced EMF = rate of change of magnetic flux
f i
=
=
Since = B A cos(), 3 things can change
1. Area of loop
2. Magnetic field B
3. Angle between normal and B
Physics 102: Lecture 10, Slide 7
ACT: Change Area
W
L
1
3
v
2
v
v
Which loop has the greatest induced EMF at the
instant shown above?
Physics 102: Lecture 10, Slide 8
Faraday: Change Area
vt
W
W
V
V
L
t=0
0=BLW
t
t=BL(W+vt)
= B A cos()
f i ( + )
=
=
EMF Magnitude: =
=
0
0
What about the sign of the EMF?
Physics 102: Lecture 10, Slide 9
Lenzs Law (EMF direction)
I
V
Bind
Flux is increasing
Induced current is clockwise
Current loop generates induced B field
from RHR2, into page, opposite external B field!
What happens if the velocity is reversed?
Physics 102: Lecture 10, Slide 10
V
Lenzs Law (EMF direction)
I
V
V
Bind
Flux is decreasing
Induced current is counterclockwise
Current loop generates induced B field
from RHR2, out of the page, along external B field!
Induced EMF opposes change in flux
Physics 102: Lecture 10, Slide 11
Lenzs Law (EMF Direction)
Induced emf opposes change in flux
f i
=
=
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
Physics 102: Lecture 10, Slide 12
Motional EMF circuit
Magnitude of current
I
q+
I = /R = vBL/R
Fbar
V
Fq
Direction of Current
Clockwise (+ charges go down thru bar, up thru bulb)
B field generates force on current-carrying = bar
Fbar ILB sin(), to left (RHR1)
Fbar opposes v!
Careful! There are two forces:
Fbar = force on bar from induced current
Fq = force on + charges in bar driving induced current
Physics 102: Lecture 10, Slide 13
Motional EMF circuit
What happens if field is reversed? (TRY IT AT HOME)
Magnitude of current
I = /R = vBL/R
Direction of Current
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
xxxxxxxxxxxxx
xxxxxxxxxxxxx
V
xxxxxxxxxxxxx
xxxxxxxxxxxxx
xxxxxxxxxxxxx
Counter-Clockwise (+ charges go up thru bar, down thru bulb)
Direction of force (F=ILB sin()) on bar due to
magnetic field
F always opposes v, bar slows down
Still to left, opposite v
Physics 102: Lecture 10, Slide 14
Must apply external force to keep bar
moving
Preflight 10.4
To keep the bar moving at the same speed, the force supplied
by the hand will have to:
Increase
Stay the Same
Decrease
Physics 102: Lecture 10, Slide 15
F=ILB sin()
Preflight 10.5
To keep the bar moving to the right, the hand will have to
supply a force in the opposite direction.
True
False
Physics 102: Lecture 10, Slide 16
Faradays Law of Induction:
induced EMF = rate of change of magnetic flux
f i
=
=
Since = B A cos(), 3 things can change
1.
Area of loop
2. Magnetic field B
3. Angle between normal and B
Physics 102: Lecture 10, Slide 17
ACT: Induction cannon (Demo)
A solenoid is driven by an increasing current. A loop of wire is placed
around it
As current increases in the solenoid, what direction
will induced current be in ring?
1) Same as solenoid
2) Opposite of solenoid
3) No current
Physics 102: Lecture 10, Slide 18
Bsol
Induction cannon (Demo)
A solenoid is driven by an increasing current. A loop of wire is placed
around it
Recall: current loop behaves like bar magnet
Opposite currents => opposite polarities
Like poles repel! Loop shoots up
What happens when loop has less resistance?
What happens if the loop is broken?
Physics 102: Lecture 10, Slide 19
ACT: Change B (Demo)
Which way is the magnet moving if it is
inducing a current in the loop as shown?
1) Up
2) Down
Physics 102: Lecture 10, Slide 20
Demo 371
ACT: Change B II (contd)
If I reduce the resistance in the wire, the
magnet will fall
1) faster
2) slower
3) at the same speed
Physics 102: Lecture 10, Slide 21
N
S
Magnetic Flux Examples
A conducting loop is inside a solenoid (B= onI).
What happens to the flux through the loop when you
Increase area of solenoid?
Increase area of loop?
Increases
Increase current in solenoid?
Rotate loop slightly?
Physics 102: Lecture 10, Slide 22
Nothing
Increases
B A cos()
Decreases
Magnetic Flux II
A solenoid (B= onI) is inside a conducting loop.
What happens to the flux through the loop when you
Increase area of solenoid
Increase area of loop
Increases
Nothing
Increase current in solenoid
Increases
B A cos()
Physics 102: Lecture 10, Slide 23
Faradays and Lenzs Law
Faraday: Induced emf = rate of change of magnetic flux
f i
=
=
Lenz: Induced emf opposes change in flux
Since = B A cos(), 3 things can change
1.
2.
Area of loop
Magnetic field B
Next lecture 3. Angle between normal and B
Physics 102: Lecture 10, Slide 24