# Chapter 34. Electromagnetic Induction

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 Last time

Changing flux creates E-fields: Last time

K2-42: LENZ'S LAW - MAGNET IN ALUMINUM TUBE K2-44: EDDY CURRENT PENDULUM

K2-61: THOMSON'S COIL Last time

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! MIT simulation of EM waves http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/light/

07-EBlight/07-EB_Light_320.html G3-01: SHIVE WAVE MACHINE - TRAVELING WAVES

M7-04: MALUS' LAW K8-05:

ELECTROMAGNETIC PLANE WAVE MODEL K8-42: RADIOWAVES ENERGY AND DIPOLE

PATTERN 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 E or B? Galilean transformation

Both observers agree on the net force on the particle! 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 v=0

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!

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 v=0 Must have: Lorentz Force:

E or B? Two Aspects of same phenomenon Bill (frame S) Force up: Sharon (frame S) is moving along with charge so v=0:

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? B-field transformation: Biot Savart Law

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 << c.

Something is wrong with Galilean transformation: Something is wrong with Galilean transformation:

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

Modification to Amperes Law Changing B-field induces E-field,

Lenzs law gives direction Changing E-field induces Bfield, Opposite of Lenzs law gives B-field direction

Quickly Review of Traveling Waves

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

Last time E-fields and B-fields transform into one another with relative velocity between inertial reference

Frames. Last time Review of traveling waves

E&M Plane waves: Last time

http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/light/ 07-EBlight/EB_Light.mpg

Last time MIT simulation of EM waves http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/light/

07-EBlight/07-EB_Light_320.html G3-01: SHIVE WAVE MACHINE - TRAVELING WAVES

M7-04: MALUS' LAW K8-05:

ELECTROMAGNETIC PLANE WAVE MODEL K8-42: RADIOWAVES ENERGY AND DIPOLE

PATTERN Energy and momentum of EM radiation

Polarization and Maluss law Polarization and Maluss law

Producing and Receiving EM waves Which way is the charge moving?

Producing and Receiving EM waves Which way is charge moving? To Left!

Producing and Receiving EM waves At large distances, E becomes flat Plane waves

Producing and Receiving EM waves Producing and Receiving EM waves

(in the far field) 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

General derivation of EM wave equation General derivation of EM wave equation

General derivation of EM wave equation General derivation of EM wave equation

General derivation of EM wave equation

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