Lecture 10 Faradays Law

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Induction
 An induced current is produced by a changing
magnetic field
 There is an induced emf associated with the induced
current
 A current can be produced without a battery present in
the circuit
 Faraday’s law of induction describes the induced emf
Faraday’s Experiment –
Conclusions
 An electric current can be induced in a loop by a
changing magnetic field
 This would be the current in the secondary circuit of this
experimental set-up
 The induced current exists only while the magnetic
field through the loop is changing
 Faraday’s law of induction states that “the emf induced
in a circuit is directly proportional to the time rate of
change of the magnetic flux through the circuit”
dB
ε
dt
Motional emf
 A motional emf is the
emf induced in a
conductor moving
through a constant
magnetic field
 The electrons in the
conductor experience a
force, F  qv  B that is
directed along ℓ
Sliding Conducting Bar
 A bar moving through a uniform field and the
equivalent circuit diagram
dB
dx
ε
 B
 B v
 The induced emf is
dt
dt
 Since the resistance in the circuit is R, the current is
I  ε R B v R
Lenz’s Law
 Lenz’s law: the induced current in a loop is in the
direction that creates a magnetic field that opposes the
change in magnetic flux through the area enclosed by
the loop
 The induced current tends to keep the original
magnetic flux through the circuit from changing
Lenz’ Law, Example
 The conducting bar slides on the
two fixed conducting rails
 The magnetic flux due to the
external magnetic field through
the enclosed area increases with
time
 The induced current must
produce a magnetic field out of
the page
 If the bar moves in the opposite
direction, the direction of the
induced current will also be
reversed
Induced emf and Electric Fields
 The emf for any closed path can be expressed as the
line integral of
over the path
 Faraday’s law can be written in a general form:
d B
 E ds   dt
 This induced electric field is nonconservative
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