Chapter 28 Magnetic Induction

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Chapter 28Magnetic Induction
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Topics

• Magnetic Flux
• Faradays Lenzs Laws
• Inductance
• Magnetic Energy

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Magnetic Flux
The magnetic flux through a surface is defined by
In the 1830s, Michael Faraday and Joseph Henry
discovered that a changing magnetic flux can
induce currents
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Magnetic Flux
The unit of magnetic flux is T m2, that is, a
weber (Wb)
Usually, an engineer is interested in the flux
through a surface bounded by a wire
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Magnetic Flux
For a constant magnetic field, the flux through
a wire loop of area A is
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Magnetic Flux
For N loops of wire, and a constant magnetic
field, the flux is N times greater that is, it is
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Magnets _at_ CERN
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Magnetic Flux CMS
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Magnetic Flux CMS
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Magnetic Flux CMS
The magnetic field of a solenoid is
Flux
For CMS B 4 T I 20,000 A l 12.5 m r 3
m
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Magnetic Flux CMS
Putting in the numbers for CMS, we get
Flux
For CMS B 4 T I 20,000 A l 12.5 m r 3
m
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Faradays Law
Faraday and Henry discovered that a changing flux
through a wire loop creates an electric
field, which, in turn, induces an emf (a
potential) in the wire
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Faradays Law
The experimental observations can be summarized
in the following law
Faradays Law
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Lenzs Law
The induced emf is such as to oppose the change
that produces it
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Lenzs Law
B2 is the magnetic field caused by current
induced in the wire. By Lenzs law, this field
acts in a direction opposite the
changing magnetic field B1
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Lenzs Law
We use the right-hand rule to determine the
direction of the current I
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Example Induced emf
A conductor moving through a magnetic field will
have an electric field induced in it, given by qE
q v B, that is, E v B
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Example Induced emf
The induced potential difference is then DV E
l v B l, once the current stops.
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Inductance
The magnetic flux through a coil is proportional
to the current flowing through it, so we can
write The proportionality constant L is
called the self-inductance of the coil, whose
unit is the henry (H 1 Wb/A )
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Inductance
Example Self-inductance of a long solenoid
that is,
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Inductance
Consider a changing magnetic flux through a coil
But, since
we find a self-induced emf of
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Magnetic Energy
Consider a circuit containing a resistor R and a
coil of self-inductance L. From Kirchoffs
loop rule, we can write
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Magnetic Energy
Multiply throughout by I and re-arrange
battery power joule heating power in coil
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Magnetic Energy
Therefore, the energy stored in the inductor (the
coil in this case) is found by integrating the
power in the coil with respect to time
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Magnetic Energy CMS
The energy stored in the CMS solenoid is
For CMS B 4 T I 20,000 A l 12.5 m r 3
m
This is enough to melt 18 tons of gold!