Transcript PPT

Physics 102: Lecture 10
Faraday’s Law
Changing Magnetic Fields create Electric Fields
• Exam 1 tonight
• Be sure to bring your ID and go to correct room
• All you need is a #2 pencil and calculator
– No cell phones
– No I-pods, laptops, etc.
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
Summary of Right-Hand Rules
RHR 1
RHR 2
Force on moving q
Alternate
B field from current I
Straight wire
I
B
r
I
Solenoid
B
I
Physics 102: Lecture 10, Slide 3
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 4
(Recall that e- actually move,
opposite current)
Faraday’s Law of Induction:
“induced EMF” = rate of change of magnetic flux
∆Φ
Φf − Φi
𝜀=−
=−
Δ𝑡
𝑡𝑓 − 𝑡𝑖
• 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 5
First a preliminary: Magnetic Flux
• “Counts” number of field lines through loop.
B
Uniform magnetic field, B, passes
through a plane surface of area A.
Magnetic flux F = B A
(Units Tm2 = Wb)
B
f
Magnetic flux F  B A cos(f)
f 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 6
Preflight 10.7
n B
n
a
b
“more lines pass through
its surface in that
position.”
FA = B A cos(0) = BA
FB = B A cos(90) = 0
Compare the flux through loops a and b.
1) Fa>Fb
2) Fa< Fb
68%
Physics 102: Lecture 10, Slide 7
32%
Faraday’s Law of Induction:
“induced EMF” = rate of change of magnetic flux
∆Φ
Φf − Φi
𝜀=−
=−
Δ𝑡
𝑡𝑓 − 𝑡𝑖
Since F= B A cos(f), 3 things can change F
1. Area of loop
2. Magnetic field B
3. Angle f between normal and B
Physics 102: Lecture 10, Slide 8
ACT: Change Area
W
L
1
3
v
2
v
v
Which loop has the greatest induced EMF at the
instant shown above?
1 moves right - gets 4 more field lines.
2 moves down - gets 0 more field lines.
3 moves down - only gets 2 more lines.
Physics 102: Lecture 10, Slide 9
Faraday: Change Area
vt
W
W
V
V
L
t=0
Fi = BLW
t
Ff = BL(W+vt)
F = B A cos(f)
∆Φ Φf − Φi 𝐵𝐿(𝑤 + 𝑣𝑡) − 𝐵𝐿𝑤
EMF Magnitude: 𝜀 =
=
= 𝐵𝐿𝑣
=
𝑡−0
Δ𝑡
𝑡−0
What about the sign of the EMF?
Physics 102: Lecture 10, Slide 10
Lenz’s 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 11
V
Lenz’s 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 12
Lenz’s Law (EMF Direction)
Induced emf opposes change in flux
∆Φ
Φf − Φi
𝜀=−
=−
Δ𝑡
𝑡𝑓 − 𝑡𝑖
• 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 13
Motional EMF circuit
• Magnitude of current
I
I = e/R = vBL/R
q +
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(q), 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 14
Motional EMF circuit
What happens if field is reversed? (TRY IT AT HOME)
x x x x x x x x x x x x x x x x x
• Magnitude of current
I = e/R = vBL/R
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
• Direction of Current
x x x x x x x x x x x x x x x x x
Counter-Clockwise (+ charges go up thru bar, down thru bulb)
• Direction of force (F=ILB sin(q)) on bar due to
magnetic field
F always opposes v, bar slows down
Still to left, opposite v
Physics 102: Lecture 10, Slide 15
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:
25% •
Increase
63% • Stay the Same
12% • Decrease
F=ILB sin(q)
B and v still perpendicular (q=90),
so F=ILB just like before!
Physics 102: Lecture 10, Slide 16
Preflight 10.5
To keep the bar moving to the right, the hand will have to
supply a force in the opposite direction.
47% • True
53% • False
Current flows in the opposite direction, so force
from the B field remains the same!
Physics 102: Lecture 10, Slide 17
Faraday’s Law of Induction:
“induced EMF” = rate of change of magnetic flux
∆Φ
Φf − Φi
𝜀=−
=−
Δ𝑡
𝑡𝑓 − 𝑡𝑖
Since F= B A cos(f), 3 things can change F
1.
Area of loop
2. Magnetic field B
3. Angle f between normal and B
Physics 102: Lecture 10, Slide 18
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
•
•
•
•
Solenoid current  (counter-clockwise)
B-field  (upwards) => Flux thru loop 
EMF will create opposite B-field (downwards)
Induced loop current must be clockwise
Physics 102: Lecture 10, Slide 19
Bind
Bsol
Induction cannon (Demo)
• Recall: current loop behaves like bar magnet
• Opposite currents => opposite polarities
• Like poles repel! Loop shoots up
N
S
A solenoid is driven by an increasing current. A loop of wire is placed
around it
N
• What happens if the loop is broken?
Physics 102: Lecture 10, Slide 20
S
• What happens when loop has less resistance?
ACT: Change B (Demo)
1) Up
2) Down
N
S
Which way is the magnet moving if it is
inducing a current in the loop as shown?
N
S
Field from magnet is down. Induced current creates
field up - opposite original. So flux from magnet must
be increasing. Magnet must be falling down
Demo 371
Physics 102: Lecture 10, Slide 21
ACT: Change B II (cont’d)
1) faster
2) slower
3) at the same speed
N
S
If I reduce the resistance in the wire, the
magnet will fall
N
S
Decreasing R, increases I. Increases opposing field,
which makes magnet fall slower.
Physics 102: Lecture 10, Slide 22
Magnetic Flux Examples
A conducting loop is inside a solenoid (B=monI).
What happens to the flux through the loop when you…
Increase area of solenoid?
Nothing
Increase area of loop? Increases
Increase current in solenoid? Increases
Rotate loop slightly?
Physics 102: Lecture 10, Slide 23
F  B A cos(f)
Decreases
Magnetic Flux II
A solenoid (B=monI) is inside a conducting loop. What
happens to the flux through the loop when you…
Increase area of solenoid Increases
Increase area of loop
Nothing
Increase current in solenoid Increases
F  B A cos(f)
Physics 102: Lecture 10, Slide 24
Faraday’s and Lenz’s Law
Faraday: Induced emf = rate of change of magnetic flux
∆Φ
Φf − Φi
𝜀=−
=−
Δ𝑡
𝑡𝑓 − 𝑡𝑖
Lenz: Induced emf opposes change in flux
Since F= B A cos(f), 3 things can change F
1.
2.
Area of loop
Magnetic field B
Next lecture 3. Angle f between normal and B
Physics 102: Lecture 10, Slide 25