Physics 220 Class 32

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Physics 220 Class 32

• Today you will learn
• how to work a variety of Faradays Law Problems
• about Eddy Currents

2
Reminders

• Chapter Test 10 due Friday
• Labs 9 and 10 are up
• No labs will be set up next week
• HW 10 due Monday 11/27
• Chapter Test 10 due Tuesday 11/28

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Maxwells Equations in Integral Form

• Gausss Law of Electricity
• Gausss Law of Magnetism
• Amperes Law
• Faradays Law

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Maxwells Equations in Integral Form

• Gausss Law of Electricity
• Gausss Law of Magnetism
• Amperes Law
• Faradays Law

Flux through a Gaussian surface
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Maxwells Equations in Integral Form

• Gausss Law of Electricity
• Gausss Law of Magnetism
• Amperes Law
• Faradays Law

Flux through a Gaussian surface
Line integral around an Amperian loop
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Maxwells Equations in Integral Form

• Gausss Law of Electricity
• Gausss Law of Magnetism
• Amperes Law
• Faradays Law

Flux through a Gaussian surface
Line integral around an Amperian loop
Flux through the Amperian loop
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Maxwells Equations in Differential Form

• Gausss Law of Electricity
• Gausss Law of Magnetism
• Amperes Law
• Faradays Law

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Faradays Law of Induction

Faradays Law of Induction
works for both motional EMF and the EMF of
accelerating charges!
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Calculating Flux through a Loop

We will assume that the magnetic field is
constant over a loop. Then, the flux is
Remember that points in the direction of the
normal to the loop.
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Three Ways to Generate an EMF

1) The magnetic field changes in time. 2) The
area changes in time. 3) the angle changes in
time.
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Eddy Currents

A wire loop is moved into a region where there
is a magnetic field. In what direction does
current flow?
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Eddy Currents

A wire loop is moved into a region where there
is a magnetic field. In what direction does
current flow?
i
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Eddy Currents

Viewing the same thing from the side, the loop
becomes a magnet that is repelled by the external
field. (Remember field lines come out of the N
pole.)
S
S
N
S
N
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Eddy Currents

It takes force to push the loop into the field.
Where does this energy go?
S
S
N
S
N
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Eddy Currents

If the wire loop is moved out of the magnetic
field, in what direction does current flow?
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Eddy Currents

If the wire loop is moved out of the magnetic
field, in what direction does current flow?
i
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Eddy Currents

Viewing the same thing from the side, the loop
becomes a magnet that is attracted by the
external field.
S
S
N
N
N
S
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Eddy Currents

A disk is even more effective at producing
induced currents. Such currents are called eddy
currents.
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Changing Area

But a moveable length of wire on a fixed
u-shaped wire in a uniform magnetic field.
R
a
x
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Lenzs law

Which way does the induced current flow?
R
a
x
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Lenzs law

Which way does the induced current flow?
R
a
i
x
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Find the Flux

R
a
x
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Find the Flux

R
a
x
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Find the EMF

R
a
x
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Find the EMF

Not worrying about the minus sign
R
a
x
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Find the Current

R
a
x
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Find the Current

R
a
x
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Find the Power Dissipated in the Resistor

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Find the Power Dissipated in the Resistor

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Find the Force on the Moveable Wire

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Find the Force on the Moveable Wire

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Find the Work Done in Moving ?x

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Find the Work Done in Moving ?x

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Find the Mechanical Power

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Find the Mechanical Power

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Changing the Magnetic Field

a
b
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Lenzs law
Which way does the induced current flow?
a
b
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Lenzs law
Which way does the induced current flow?
a
i
b
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Find the Flux
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Find the Flux
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Find the EMF
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Find the EMF
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Where does the energy come from this time?
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Where does the energy come from this time?
If the external field comes from a permanent
magnet, the magnetic field of the loop attracts
the permanent magnet, making it more difficult to
move away.
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Where does the energy come from this time?
If the external field comes from an
electromagnet, the interaction of the loop with
the electromagnet takes some energy from the
electromagnets circuit.
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We can use Faradays Law to calculate the
electric field as well as the EMF in one problem
only!
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A Circular Loop in the Field of an Electromagnet
with Circular Pole Faces

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A Circular Loop in the Field of an Electromagnet
with Circular Pole Faces

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A Circular Loop in the Field of an Electromagnet
with Circular Pole Faces

Flux through the Amperian loop of radius r.
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A Circular Loop in the Field of an Electromagnet
with Circular Pole Faces

Flux through the Amperian loop of radius r.
Line integral around the Amperian loop of radius
r.
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A Circular Loop in the Field of an Electromagnet
with Circular Pole Faces

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A Circular Loop in the Field of an Electromagnet
with Circular Pole Faces

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A Circular Loop in the Field of an Electromagnet
with Circular Pole Faces

Flux through the Amperian loop of radius r.
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A Circular Loop in the Field of an Electromagnet
with Circular Pole Faces

Flux through the Amperian loop of radius r.
But the field stops at R!
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A Circular Loop in the Field of an Electromagnet
with Circular Pole Faces

Flux through the Amperian loop of radius r.
But the field stops at R!
Line integral around the Amperian loop of radius
r.
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Changing the Angle

Attach a handle to a circular loop of wire.
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Changing the Angle

Place the loop in a magnetic field with the shaft
perpendicular to .
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Changing the Angle

We rotate the handle with angular speed . The
flux is The EMF is