Physics 1051 – Workshop 6
Faraday's Law
Physics 1051 - General Physics II
Oscillations, Waves and Magnetism
Workshop 6 - Contents
I. What is Faraday's Law all about?
II. Faraday's Law
I. General Case
II.Lenz's Law
III. Motional Emf (also includes 'non-Faraday' case)
III. Advice on Problem Sovling
IV. Example
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Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
Oscillations, Waves and Magnetism
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I – What is Faraday's Law all
about?
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Physics 1051 - General Physics II
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Faraday
●
Experiments show that changing magnetic flux
through a loop gives rise to a current and an
associated emf.
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Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
Oscillations, Waves and Magnetism
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Summary of Induced emf
●
Motional
emf
●
●
Situations creating an induced emf
−
Changing magnetic field or angle
−
Moving closed loop conductor (circuit)
−
Moving non-closed conductor (not a circuit)
Faraday's Law
i.e. Changing
magnet flux.
At the moment we are looking at the two
motional emf cases
The moving non-closed conductor can be
considered a special case of emf in that it is not
explained by Faraday's law. [I will refer to this
as 1st case of motional emf in the notes.]
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Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
Oscillations, Waves and Magnetism
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II – Faraday's Law
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Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
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I. General Case
d B
=−
dt
−
−
−
d B
=−N
dt
Quantity Type
Scalar
SI Unit
V
 is induced emf
 B is magnetic flux
N is number concentric loops through which mag.
Field passes through
“The rate of change of magnetic flux with time is
equal to emf induced by the changing flux.”
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Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
Oscillations, Waves and Magnetism
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Magnetic Flux
 B=
∫

B⋅d A
Quantity Type
Scalar
SI Unit
Weber (Tm2)
surface
−
−
−
 B is magnetic flux

B is magnetic field
d A is infinitesimal Area along closed surface
Note On Area Vector for Flux In Case you were Wondering: Direction is always normal (of
which there are always 2 options). For a closed surface, the area vector always points
outwards. When it comes to an open surface, it is actually ambiguous as to which one of
the two directions it is, in which case we pick the one that gives is positive flux.
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Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
Oscillations, Waves and Magnetism
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II. Lenz's Law
●
●
●
Faraday's Law does not tell the direction of
induced current.
Lenz's Law determines that...
The polarity (sign) of the induced emf in a loop
is such that it produces a current whose
associated magnetic field opposes the change
in magnetic flux of the loop. In other words, the
induced current is in a direction such that the
induced magnetic field attempts to maintain the
original flux through the loop.
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Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
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III. Motional emf
●
Flux can be created by a moving loop.
−
●
●
known as motional emf
As mentioned, there is also a case of motional
emf without flux
Types of motional Emf
−
Moving closed loop conductor (circuit)
−
Moving non-closed conductor (not a circuit)
27/07/10
Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
Oscillations, Waves and Magnetism
Solve using
Faraday's Law
Solve using
Newton's Law
10
st
1 Case of Motion of Conductor Causing
Electric Field –Applying Newton's Law
●
Newton's Second Law
∑ F =m a
 B F
 E =0
F
+y
Interested in
situation where
particles stop
accelerating.
+x
F E j −F B j =0
F E j=F B j
F E =F B
qE=qvB sin 
E=vB
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Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
Oscillations, Waves and Magnetism
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st
1 Case of Motion of Conductor Causing
Electric Field –Applying Newton's Law
●
●
●
Know in Electric Field, we can find potential
difference.
E=vB
Because Electric Field is Uniform, it follows that the
+y
the potential difference is give by

⋅d ds
 V =E l
 V =−∫ E
 V =B l v
A potential difference is maintained as long as
wire is moving (v ) through a uniform field ( B )
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Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
Oscillations, Waves and Magnetism
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+x
nd
2 Case of Motion of Conductor
Causing Electric Field – Finding emf
●
We can describe the area of loop
dA=−dA k
+y
Thus the magnetic flux is
 ∫ −B k ⋅−dA k =BA= Blx
 B =∫ 
B⋅dA=
●
●
Applying Faraday's Law gives
d B
=−N
dt
d  Blx
dx
=−N
=−Bl
dt
dt
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Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
Oscillations, Waves and Magnetism
+x
=−Blv
13
III – Problem Solving
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Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
Oscillations, Waves and Magnetism
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III. Motinal emf
●
If your asked for emf it is almost certainly a
Faraday's Law and/or motional emf question
1)No motion of conductor
◦
Use general case of Faraday's Law
2)Types of Emf
A)Moving closed loop conductor (circuit)
◦
Use Faraday's Law (velocity will like come from derivative)
B)Moving non-closed conductor (not a circuit)
◦
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Use Newton's law
Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
Oscillations, Waves and Magnetism
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IV - Example
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Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
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Example
Faraday's Law OR Motional emf
A coil of 15 turns and radius 10.0cm surrounds a
long solenoid of radius 2.00cm and 1.00x10^3
turns/m. The current in the solenoid changes as
I =5.00A sin 120t
Find the induced emf in the 15 turn coil as a
function of time.
27/07/10
Physics 1051 – Bill Kavanagh
Physics 1051 - General Physics II
Oscillations, Waves and Magnetism
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