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
ÎInductance
ÎRL
circuits
ÎMagnetic
energy
ÎGenerators,
transformers
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Magnetic Flux
Electric flux
Magnetic flux
r r
ΦB = ∫ B ⋅ dA
(T m2)
r r
Φ = ∫ E ⋅ dA
(N m2/C)
Surface defined by a
conductive loop
Closed surface
(Gaussian surface)
Units: 1 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
emf
dΦ B
= −N
dt
Flux through the loop
# of turns of the loop
Î To
avoid errors
‹ Use Faraday’s law to calculate only the
magnitude of emf
‹ Use Lenz’s law to find the direction
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Lenz’s Law
Î Same
as the negative sign in Faraday’s law
‹ Lenz’s
law: Direction of induced emf is such that
resulting current opposes change in ФB.
Î Let’s
coil
examine three ways to change ФB through a
‹ Change
B
‹ Change
area of the coil (motional emf)
‹ Change angle θ of the coil with respect to B (motional
emf) – principle of the generator
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Changing B
Q1 Is the induced emf and
current clockwise or
counterclockwise?
S
N
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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Changing Area
v
B field points into screen. Is induced emf
clockwise or couterclockwise?
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Another Example
ÎWhat
is the direction of induced emf?
‹(a) Clockwise
RHR #3 and Lenz
‹(b) Counterclockwise
‹(c) No emf
RHR #2
pull
I
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Motional emf and Energy
|
Î
ε |= LvB
Current i due to emf receives force from B
i=
Î
i
|
ε|
R
F = iLB
F
i
Force required to pull the loop
Freq = iLB
Î
Power (work per time) required to pull the loop
Preq =
Î
Freq (distance )
(time)
= Freq
2
(
LvB )
v=
Power dissipated in the wire as heat
(LvB )
 LvB 
= i2R = 
R
=

R
 R 
2
Pdiss
2
PHY2049: Chapter 30
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Agrees!
10
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 (Longmans Green, London, 1899)
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