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E & M Induction
Flux, Induction,
Faraday, & Lenz
1
Magnetic fields
* constant current creates a magnetic field
B= uo I / (2pr)
•
Current + magnet=motor
(1st Invention was a
Homopolar motor)
•
F= BIL= qvB
(current pushes on magnet too)
2
EM Induction - Discovery
• Symmetry  if I  B,then B  I?
• 1831 Faraday discovers the switch
( DB  I …. Key is change)
I= V/R
V= emf = flux change / time
•
= D (NBA/time)
N=#loops
Source: Hecht’s Physics w/ Algebra & Trig.
3
EM Induction & B Flux
• Magnetic Flux = magnetic field
passing  to area x that area
• M=B A =BA =BAcos
Back to Flux Questions
4
Flux
• The figure below shows 5 loops in a B
field. Rank the magnetic flux (Φ)from
largest to smallest.
1. 2=4, 1, 3, 5
2. 1=4, 2=3=5
3. 4, 2, 1, 3, 5
4. 4=2, 1, 5, 3
From Knight’s Physics for Scientists & Engineers
Flux Instruction Slide is # 5
5
How can you
D =
BAcos
•Change B
•Change A
•Change 
6
How is induction done?
•Move magnet or wire
•Change current in wire
•Rotate wire or magnet
7
Changing Flux Voltage
Call it: voltage,“emf”, or potential
 = - N(DM)/Dt = V
• How Is energy conserved?
• Lenz’s Law: Induced EMF
must produce current that
opposes the change that
caused it
8
Lenz law check
A bar magnet is positioned below a horizontal loop of wire with
its North pole pointing toward the loop. Then the magnet is
pulled down, away from the loop. As viewed from above, is the
induced current in the loop clockwise or counterclockwise?
Answer: The B-field from a bar magnet
points out of the North pole. As seen from
above, the field through the loop is out
(toward the observer). As the magnet is
pulled away, the flux is decreasing. To
fight the decrease, the induced B-field
should add to the original B-field, and also
be out (toward the observer). The
induced current will be (B),
counterclockwise, in order to make an
induced B-field out.
Answer
Induction check
A loop of wire lies in the plane of
the page. A decreasing magnetic
field is directed into the page. The
induced current in the loop is:
1.counterclockwise
2.clockwise
3.zero
4.depends upon whether or not B is
decreasing at a steady rate
Question modified from unknown source
Induction Instruction
11
Faraday’s Law
•
Does the loop of wire
have a 1-clockwise, 2counter-clockwise, or 3no current when:
1. The B field strength is
increasing.
2. The B field strength is
constant.
3. The B field strength is
decreasing.
1. 1
2. 3
3. 2
12
From Knight’s Physics for Scientists & Engineers
Induction tips
• There is always voltage
(only current if closed wire or conductive)
• Earth’s field can induce in moving things
• There is also induced an electric force
F= qE where E =V/d (d is length of wire)
this is the resistive force you must overcome
to start induction, ie. takes work to get energy!
13
Tranformers: 2 ac solenoids
• Ac current: already changing B field
(B= uIN/L where L= solenoid length
• transfers voltage w/o connecting them
• New voltage depends on N turns
(2x turns, 2x voltage, but ½ current)
14
Transformer
You have a transformer with Np=6 primary
windings, and Ns=3 secondary windings, as shown.
If Vp=120 V AC, what is the current measured by
the ammeter "A" in the secondary circuit?
A) 120 A
B) 60 A
C) 240 A
D) Nothing is measured
because the fuse in the ammeter blows!
Answer
The fuse in the ammeter blows! The
secondary voltage is 60 VAC (it's a
step-down transformer). The internal
resistance of the ammeter is zero. So
the ammeter current is I = V/R = 60
V/(0 ohms) = infinite current. The
fuse will blow.
(that’s what she said- mitch)