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Physics 2112
Unit 17
Today’s Concept:
Faraday’s Law
Lenz’s Law
 
d B
emf   E  d   
dt
Electricity & Magnetism Lecture 17, Slide 1
The Plan
•
•
Define Magnetic Flux, B
Introduce Faraday’s Law in terms of magnetic
flux
 
d B
emf  E  d   

•
dt
Do some examples to show how Faraday’s Law
explains motional emf results we had last time.
Electricity & Magnetism Lecture 17, Slide 2
Define B
Magnetic Flux:
 
 B   B  dA
B
A
Similar to electric flux E
Think of B as the number of field lines
passing through the surface
Electricity & Magnetism Lecture 17, Slide 3
Example 17.1 (Magnetic Flux)
B
5cm
A
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?
Electricity & Magnetism Lecture 17, Slide 4
Units
Notice Units:
 
 B   B  dA
= T * m2
= N / C /(m/sec) * m2
= (V/m)/(m/sec) * m2
= V*sec
d B
emf  
dt
Electricity & Magnetism Lecture 17, Slide 5
Faraday’s Law:
 
d B
emf   E  d   
dt
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).
I
•
•
Magnetic fields alone don’t cause
currents
Changing magnetic fields cause currents
Electricity & Magnetism Lecture 17, Slide 6
Faraday’s Law
Three ways to change flux
Change |A|
Change |B|
emf  
 
d (  B  dA)
dt
Change the angle
between the two
Electricity & Magnetism Lecture 17, Slide 7
Example 17.2 (Change |B|)
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.
B varies
What is the current through the resistor?
Unit 17, Slide 8
Example 17.3 (Change Area)
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.
The bar is pulled to the right by a force, F, at a velocity of 8m/sec.
What is the current through the resistor?
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 = 50W resistor, what
is the current?
Unit 17, Slide 10
Lenz’s Law
 
d B
emf   E  d   
dt
In words:
Whenever the magnetic flux through a
surface changes a current is formed which
creates a magnetic field which opposes that
change.
CheckPoint 1
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?
Electricity & Magnetism Lecture 17, Slide 12
CheckPoint 2
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?
Electricity & Magnetism Lecture 17, Slide 13
CheckPoint 3
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):
Electricity & Magnetism Lecture 17, Slide 14
A point of confusion….
Faraday’s Law:


d B
emf   EInduced  d   
dt
Note:


 EInduced  d   0
Induced electric field is
not conservative!


  E Induced  dl   V
Unit 17, Slide 15
Example 17.5 (Bar on Ramp)
A square metal bar has a
Side
view
1.2kg and slides down
45o
.
.
.
.
length of 1m and a mass
.
.
.
between two legs of a
.
.
.
conducting U shaped rail that
.
.
Top
view
is at an angle of 45o to the
ground.
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?
Unit 17, Slide 16
Example 17.6 (solenoid)
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?
Unit 17, Slide 17
 
d B
Faraday’s Law: emf   E  d   
dt
where
 
 B   B  dA
Executive Summary:
emf → current → field a) induced only when flux is changing
b) opposes the change
Electricity & Magnetism Lecture 17, Slide 18
Remember?
 
B

d
A

0

surface
 
B

d
l


I
o
ENCL

loop
  Qenc
E

d
A



o
surface
 
E

d
l

0

loop
Unit 15, Slide 19
A Change…..
 
B

d
A

0

surface
 
B

d
l


I
o
ENCL

loop
  Qenc
E

d
A



o
surface
 
d B
E

d
l


loop
dt
Electricity and magnetism are now connected!
Unit 15, Slide 20