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Physics 2112Unit 17
Today’s Concept:Faraday’s LawLenz’s Law
dt
ddEemf B
Electricity & Magnetism Lecture 17, Slide 1
The Plan
• Define Magnetic Flux, FB
• 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 2
dt
ddEemf B
B
A
Magnetic Flux: AdBB
Electricity & Magnetism Lecture 17, Slide 3
Define FB
Similar to electric flux FE
Think of FB as the number of field lines passing through the surface
B
A
Electricity & Magnetism Lecture 17, Slide 4
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 5
Units
= T * m2
= N / C /(m/sec) * m2
= (V/m)/(m/sec) * m2
= V*sec
dt
demf B
In Words: • When the flux FB 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 6
Electricity & Magnetism Lecture 17, Slide 7
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 = 50 . W
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?
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 varies
Unit 17, Slide 8
A 10cm conducting bar (green) rests on two frictionless wires connected by a resistor R = 50 . WThe 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.
x x x x x x x x
x x x x x x x x
x x x x x x x x
Unit 17, Slide 9
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 = 50 W resistor, what is the current?
Unit 17, Slide 10
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
CheckPoint 1
Electricity & Magnetism Lecture 17, Slide 12
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 13
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 14
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 15
dt
ddEemf B
Induced
Faraday’s Law:
0dEInduced
Note:
Induced electric field is not conservative!
VldEInduced
Example 17.5 (Bar on Ramp)
Unit 17, Slide 16
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
Example 17.6 (solenoid)
Unit 17, Slide 17
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?
Executive Summary:
emf → current → field a) induced only when flux is changing b) opposes the change
Faraday’s Law:
dt
ddEemf B
where AdBB
Electricity & Magnetism Lecture 17, Slide 18
Remember?
Unit 15, Slide 19
surface
AdB 0
ENCLo
loop
IldB
0loop
ldE
o
enc
surface
QAdE
A Change…..
Unit 15, Slide 20
surface
AdB 0
ENCLo
loop
IldB
dt
dldE B
loop
o
enc
surface
QAdE
Electricity and magnetism are now connected!
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