Change Area of loop Change orientation Faraday’s Law of ... · of loop Change orientation...
Transcript of Change Area of loop Change orientation Faraday’s Law of ... · of loop Change orientation...
Change Area of loop Change orientation
of loop relative to BFaraday’s Law
Notice the minus sign!!!
Putting it Together
AB
dt
d
Electricity & Magnetism Lecture 16, Slide 1
Question
Electricity & Magnetism Lecture 17, Slide 2
If I attempt to drop a magnet down an iron pipe, it will just stick to the side of the pipe.
What will happened if I attempt to drop a magnet down a copper pipe?
A) It will fall straight through B) It will stick to the side of the pipeC) It will fall very slowly through the pipeD) It will be pulled very fast down the pipe
Physics 2112
Unit 17
Today’s Concept:
Faraday’s Law
Lenz’s Law
dt
ddEemf B
Electricity & Magnetism Lecture 17, Slide 3
Your Comments
Pretty good lecture.I would really need to discuss the directions of everything defined here. How do you find the direction of the induced emf? of the change in flux? like to discuss how we decide the direction of induced currents.
I feel as though I am going to need a ton of practice with this section. It would be great if you could reiterate the directions and rotations of the induced flux and current.I think I understood this lecture for the most part none Ahhh so so. Please no more integrals. i'm still not caught up! this isn't good! Still confused on this. HOW MANY LAWS ARE THERE IN THIS CLASS! i honestly dont understand. thats too much Faraday is okay but when i see lenz's law in addition,i just skip through all the prelecture. Come on, we're emgineers, not lawyers!! this is all very confusing
Electricity & Magnetism Lecture 17, Slide 4
The Plan
• Define Magnetic Flux, B
• Introduce Faraday’s Law in terms of magnetic flux
• Do some examples to show how Faraday’s Law explains motional emf results we had last time.
Electricity & Magnetism Lecture 17, Slide 5
dt
ddEemf B
B
A
Magnetic Flux: AdBB
Electricity & Magnetism Lecture 17, Slide 6
Define B
Similar to electric flux E
Think of B as the number of field lines passing through the surface
B
A
Electricity & Magnetism Lecture 17, Slide 7
Example 17.1 (Magnetic Flux)
A copper disk with radius 5cm is placed in a magnetic field of uniform strength 0.2T.
What is the magnetic flux through the disk?
5cm
Notice Units:
AdBB
Electricity & Magnetism Lecture 17, Slide 8
Units
= T * m2
= N / C /(m/sec) * m2
= (V/m)/(m/sec) * m2
= V*sec
dt
demf B
In Words: • When the flux B through a loop changes, an emf is
induced in the loop.• The emf will make a current flow if it can (like a battery).
• Magnetic fields alone don’t cause currents
• Changing magnetic fields cause currents
Faraday’s Law:
dt
ddEemf B
I
Electricity & Magnetism Lecture 17, Slide 9
Question
Unit 17, Slide 10
A circular wire loop is placed in a uniform magnetic field pointing to the right. The loop is rotated with constant angular velocity around a vertical axis (dashed line).
At which of the three times shown is the induced emfgreatest?
Unit 17, Slide 11
A circular wire loop is placed in a uniform magnetic field pointing to the right. The loop is rotated with constant angular velocity around a vertical axis (dashed line).
At which of the three times shown is the induced emf greatest?
||||sinsin||||
cos||||
AdBdt
dAdB
dt
d
dABAdBB
Notice Units:
AdBB
Electricity & Magnetism Lecture 17, Slide 12
Units
= T * m2
= N / C /(m/sec) * m2
= (V/m)/(m/sec) * m2
= V*sec
dt
demf B
Electricity & Magnetism Lecture 17, Slide 13
Faraday’s Law
dt
AdBdemf
)(
Three ways to change flux
Change |B|Change |A|
Change the angle between the two
A 10cm X 20m loop is formed by a motionless conducting bar (green) rests on two frictionless wires connected by a resistor R = 50W.
The entire apparatus is placed in a magnetic field that varies from 0 to 1.2 T in 30 seconds.
Example 17.2 (Change |B|)
What is the current through the resistor?
B varies
Unit 17, Slide 14
A 10cm conducting bar (green) rests on two frictionless wires connected by a resistor R = 50W.
The entire apparatus is placed in a uniform magnetic field of 0.5 T pointing into the screen.
Example 17.3 (Change Area)
What is the current through the resistor?
The bar is pulled to the right by a force, F, at a velocity of 8m/sec.
Unit 17, Slide 15
17.4 (Change the angle)
A 10cm X 20 cm loop is rotated at 10rev/sec in a magnetic field of 0.1T.
If the loop is connected to a R = 50W resistor, what is the current?
Unit 17, Slide 16
In words:Whenever the magnetic flux through a
surface changes a current is formed which creates a magnetic field which opposes that change.
dt
ddEemf B
Lenz’s Law
Question
Electricity & Magnetism Lecture 17, Slide 18
If I attempt to drop a magnet down an iron pipe, it will just stick to the side of the pipe.
What will happened if I attempt to drop a magnet down a copper pipe?
A) It will fall straight through B) It will stick to the side of the pipeC) It will fall very slowly through the pipeD) It will be pulled very fast down the pipe
CheckPoint 1
Electricity & Magnetism Lecture 17, Slide 19
Suppose a current flows in a horizontal conducting loop in such a way
that the magnetic flux produced by this current points upward.
As viewed from above, in which direction is this current flowing?
CheckPoint 2
Electricity & Magnetism Lecture 17, Slide 20
A magnet makes the vertical magnetic field shown by the red arrows. A
horizontal conducting loop is entering the field as shown.
At the instant shown below left, what is the direction of the additional flux
produced by the current induced in the loop?
CheckPoint 3
Electricity & Magnetism Lecture 17, Slide 21
A magnet makes the vertical magnetic field shown by the red arrows. A
horizontal conducting loop is entering the field as shown.
The upward flux through the loop as a function of time is shown by the
blue trace. Which of the red traces below it best represents the current
induced in the loop as a function of time as it passes over the magnet?
(Positive means counter-clockwise as viewed from above):
A point of confusion….
Unit 17, Slide 22
dt
ddEemf B
Induced
Faraday’s Law:
0
dEInduced
Note:
Induced electric field is not conservative!
VldEInduced
Question
Unit 17, Slide 23
A bar magnet is being pushed to the right into a
coil of wire North end first .
According to Lenz’s law, which way will this new
magnetic field point?
A. clockwise
B. up
C. down
D. to the left
E. to the right
Question
Unit 17, Slide 24
A bar magnet is being pushed to the right into a
coil of wire South end first.
According to Lenz’s law, which way will this new
magnetic field point?
A. clockwise
B. up
C. down
D. to the left
E. to the right
Question
Unit 17, Slide 25
A bar magnet is being pulled to the left away
from a coil of wire South end first.
According to Lenz’s law, which way will this new
magnetic field point?
A. clockwise
B. up
C. down
D. to the left
E. to the right
Question
Unit 17, Slide 26
If magnet moves towards a loop in the screen with
the North pole pointed away from the screen. In
what direction is the induced current?
1) clockwise
2) counter-clockwise
3) no induced currentN
Question
Unit 17, Slide 27
If magnet moves towards a loop in the screen with the North pole pointed away from the screen. In what direction is the
induced current?
1) clockwise
2) counter-clockwise
3) no induced current
NIncreasing magnetic field
pointing away so you want
a increasing pointing
towards. Clockwise
Question
Unit 17, Slide 28
A wire loop is being pulled through a uniform
magnetic field. What is the direction of the
induced current?
1) clockwise
2) counter-clockwise
3) no induced current
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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 x x x x x x
Question
Unit 17, Slide 29
A wire loop is being pulled through a uniform
magnetic field that suddenly ends. What is the
direction of the induced current?
1) clockwise
2) counter-clockwise
3) no induced current
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
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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
B
A circular loop of radius R is moving to the right a velocity v in a magnetic field that points to the left. The current in this loop caused by this motion is:
a) clockwiseb) counter-clockwisec) zero
Question
Electricity & Magnetism Lecture 17, Slide 30
V
(Define “clockwise current” to be current that goes up on the front (left) edge of the loop.)
Question
Unit 17, Slide 31
If a coil is shrinking in a magnetic field
pointing into the page, in what direction
is the induced current?
1) clockwise
2) counter-clockwise
3) no induced current
Example 17.5 (Bar on Ramp)
Unit 17, Slide 32
A square metal bar has a
length of 1m and a mass
1.2kg and slides down
between two legs of a
conducting U shaped rail that
is at an angle of 45o to the
ground.
45o
The entire rails/rod system has a resistance of 2.5W
and is contained in a vertical 0.7T magnetic field.
What is the maximum velocity of the rod?
. . . .
. . . .
. . . .
Side
view
Top
view
Question
Unit 17, Slide 33
As the bar slides down the
ramp, which way will the
current flow in the bar?45o
A. Into the screen
B. Out of the screen
C. No current will flow in the
bar
. . . .
. . . .
. . . .
Side
view
Top
view
Question
Unit 17, Slide 34
As the bar slides down the
ramp, which way will the
magnetic force on it point?45o
A. Left
B. Right
C. Up
D. Down
E. Into the screen
Side
view
Example 17.6 (solenoid)
Unit 17, Slide 35
A long solenoid has 220
turns/cm and carries a current
I=1.5A. It’s diameter is 3.2cm.
At the center, we place a
closely packed coil, C, with 32
turns that is 2.1cm in diameter.
The current in the solenoid is reduced to zero in 25ms.
What is the magnitude of the EMF induced in the coil while
the current in the solenoid is changing?
Example 17.6 (solenoid)
Unit 17, Slide 36
A long solenoid has 220 turns/cm
and carries a current I=1.5A. It’s
diameter is 3.2cm. At the center, we
place a closely packed coil, C, with
32 turns that is 2.1cm in diameter.
The current in the solenoid is reduced to zero in 25ms.
I’m going to use Faraday’s law to find the EMF caused by
the changing flux. To find the flux, I’m going to find the
magnetic field over what area?
A) (0.032m)2p B) (0.021m)2p
C) (0.032m/2)2p D) (0.021m/2)2p
Example 17.6 (solenoid)
Unit 17, Slide 37
Bo = moIn = 0.00414T
o = B*[p*(0.021/2)2]= 1.44X10-5 T m2
d/dt =1.44X10-5/25X10-3 = -5.76X10-4V
= -N d/dt = 32*(5.76X10-4) = 18.4mV
Executive Summary:
emf → current → field a) induced only when flux is changingb) opposes the change
Faraday’s Law:
dt
ddEemf B
where AdBB
Electricity & Magnetism Lecture 17, Slide 38
Remember?
Unit 15, Slide 39
surface
AdB 0
ENCLo
loop
IldB m
0loop
ldE
o
enc
surface
QAdE
A Change…..
Unit 15, Slide 40
surface
AdB 0
ENCLo
loop
IldB m
dt
dldE B
loop
o
enc
surface
QAdE
Electricity and magnetism are now connected!