Chapter 30: Electromagnetic Induction
PHY2049: Chapter 30
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Subjects
ÎInduced
emf
‹ Faraday’s
law (law #3 of electricity and magnetism)
‹ Lenz’s law
‹ Motional emf
ÎMagnetic
energy
ÎInductance
ÎRL
circuits
ÎGenerators,
transformers
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Faraday and Henry’s Discovery
Changing magnetic field produces current in a wire
loop.
{
• Induced current i depends on:
rate of change of B
wire resistance
• Induced emf that drives i depends only on the rate of
change of B
• Direction of emf depends on:
direction of B
whether B increases or decreases
{
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Magnetic Flux
Magnetic flux
r r
ΦB = ∫ B ⋅ dA
Electric flux
(T m2)
r r
Φ = ∫ E ⋅ dA
Surface defined by a
conductive loop
Î1
(N m2/C)
Closed surface
(Gaussian surface)
T m2 = 1 weber = 1 Wb
ΦB = BAcosθ
if B is uniform and surface is flat.
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Faraday’s Law (Law #3 of E&M)
ε
dΦ B
= −N
dt
Flux through the loop
emf
# of turns of the loop
Î
Use Faraday’s law to calculate only the magnitude
Î
Use Lenz’s law to find the direction
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Lenz’s Law
Î
About the negative sign in Faraday’s law
‹
Î
Lenz’s law: Direction of induced emf is such that resulting current
opposes change in ФB.
Let’s examine three ways to change ФB through a coil
Change B
‹ Change area of the coil (motional emf)
‹ Change angle θ of the coil with respect to B (motional emf)
‹
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Check Point: Changing B
Q1 Is the induced emf
and current clockwise or
counterclockwise?
Clockwise
Q2 What does the ammeter
read, when the magnet is held in place? Zero
Q3 What happens while the magnet is being
pulled back? Counterclockwise emf and current
Q4 What happens if the S pole of the magnet
is pushed toward the loop?
Counterclockwise emf and current
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Check Point : Changing Area
v
Is induced emf clockwise or couterclockwise?
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Motional emf and Energy
|
Î
ε |= LvB
Current i due to emf receives force from B
i=
Î
|
ε|
R
F = iLB
Force required to pull the loop
Freq = iLB
Î
Power (work per time) required to pull the loop
Preq = Freq
Î
2
(
LvB )
v=
R
Power dissipated in the wire as heat
(LvB )
 LvB 
= i2R = 
 R=
R
 R 
2
Pdiss
2
PHY2049: Chapter 30
Checks!
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Electric Power Generation
… when Faraday was endeavouring to explain to Gladstone
(Chancellor of the Exchequer) and several others an important
new discovery in science, Gladstone's only commentary was
“but, after all, what use is it?” “Why, sir,” replied Faraday,
“there is every probability that you will soon be able to tax it!”
W. E. H. Lecky, Democracy and Liberty (London, 1899).
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