Chapter 34. Electromagnetic Induction

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• Homework set 3 is posted
• Due Tuesday by 5PM
• No late homework accepted
• Homework set 4 is posted
• Due Tuesday September 29th by 5PM
• Same day as Exam I
• No late homework accepted
• Exam I September 29th
• Chapter 33-36 omitting section 36.6

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Changing flux creates E-fields
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K2-42 LENZ'S LAW - MAGNET IN ALUMINUM TUBE
K2-44 EDDY CURRENT PENDULUM
K2-61 THOMSON'S COIL
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Back emf, Inductance examples Infinite
solenoid (inductor!)
Energy in B-fields
Inductor applications Transformers, LR and LC
circuits
E-fields and B-fields transform into one another
with relative motion!
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MIT simulation of EM waves
http//ocw.mit.edu/ans7870/8/8.02T/f04/visualizati
ons/light/07-EBlight/07-EB_Light_320.html
K8-05 ELECTROMAGNETIC PLANE WAVE MODEL
G3-01 SHIVE WAVE MACHINE - TRAVELING WAVES
M7-04 MALUS' LAW
K8-42 RADIOWAVES - ENERGY AND DIPOLE PATTERN
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E or B? Galilean transformation
Only consider constant velocity between reference
frames!
Sharon only observes an electric field from charge
Bill observes an electric field from charged
particle AND magnetic field produced by the
moving charge
Both observe no net force on particle
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E or B? Galilean transformation
Both observers agree on the net force on the
particle!
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E or B? Galilean transformation
Consider a TEST charge (to measure forces).
Bill (frame S) sets up B-field, observes charge
moving at velocity ? Force up
Sharon (frame S) is moving along with charge so
v0
There MUST be a force observed by Sharon since
Bill observes one.
There must be an E-field in Sharons frame that
pushs the charge!
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E or B? Galilean transformation
Bill (frame S) sets up B-field, observes charge
moving at velocity ? Force up
Sharon (frame S) is moving along with charge so
v0
Must have
Lorentz Force
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E or B? Two Aspects of same phenomenon
Bill (frame S) Force up
Sharon (frame S) is moving along with charge so
v0
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E or B? Two Aspects of same phenomenon
E field in frame S from E and B fields in frame
S How do the B-fields tranform from one frame to
another?
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B-field transformation Biot Savart Law
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E or B? Two Aspects of same phenomenon
The Galilean field transformation equations are
where V is the velocity of frame S' relative to
frame S and where the fields are measured at the
same point in space by experimenters at rest in
each reference frame. NOTE These equations are
only valid if V ltlt c.
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Something is wrong with Galilean transformation
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Something is wrong with Galilean transformation
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Magnetic Gausss Law
Since there are NO magnetic monopoles (only
dipoles and conglomerates of dipoles), Net
number of field lines piercing any closed surface
is zero
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Modification to Amperes Law
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Changing B-field induces E-field, Lenzs law
gives direction
Changing E-field induces B-field, Opposite of
Lenzs law gives B-field direction
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Quickly Review of Traveling Waves
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• Homework set 4
• Due Tuesday September 29th by 5PM
• Same day as Exam I
• No late homework accepted
• Exam I September 29th
• Chapter 33-36 omitting section 36.6
• Make-up exams are oral only valid excuses

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E-fields and B-fields transform into one another
with relative velocity between inertial
reference Frames.
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Review of traveling waves EM Plane waves
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http//ocw.mit.edu/ans7870/8/8.02T/f04/visualizati
ons/light/07-EBlight/EB_Light.mpg
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Last time
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MIT simulation of EM waves
http//ocw.mit.edu/ans7870/8/8.02T/f04/visualizati
ons/light/07-EBlight/07-EB_Light_320.html
K8-05 ELECTROMAGNETIC PLANE WAVE MODEL
G3-01 SHIVE WAVE MACHINE - TRAVELING WAVES
M7-04 MALUS' LAW
K8-42 RADIOWAVES - ENERGY AND DIPOLE PATTERN
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Energy and momentum of EM radiation
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Energy and momentum of EM radiation
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Radiation Pressure
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Polarization and Maluss law
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Polarization and Maluss law
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Producing and Receiving EM waves
Which way is the charge moving?
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Producing and Receiving EM waves
Which way is charge moving? To Left!
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Producing and Receiving EM waves
At large distances, E becomes flat ? Plane waves
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Producing and Receiving EM waves
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Producing and Receiving EM waves
(in the far field)
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Producing and Receiving EM waves
No radiation along axis of dipole Biot-Savart
law state there is no B-field along y if there is
current parallel to r-hat
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General derivation of EM wave equation
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General derivation of EM wave equation
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General derivation of EM wave equation
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General derivation of EM wave equation
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General derivation of EM wave equation