W13D3 More PatternsFields, Patterns, Maxwell’s Equations and Begin Induction/Faraday’s Law2049SCALE-UP

EASY!

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14

Chapter 22Gauss

16 (Read rest of chapter)2 WebAssignsChapter 22Gauss

18QUIZ

Chapter 22Lentz & More

21

Chapter 23Faraday

23QUIZ

Chapter 23Faraday

HOLIDAY

28

Chapter 23Faraday

30

Chapter 24EM

2Chapter 24 EMOptional Exam

(22-24)

3

FINAL EXAM

THE EVAN SHOW

Field Patterns From Last Time

“Curly Field”No diverging source

Diverging FieldPoint Sources

Electrostatic Fields Magnetic Fields

Maxwell’s Equations

0

0 .

0

? =Faraday's Law of Induction - Next Topic

(One additional term)

inside

inside path

qdA

dA

d

d I

E n

B •n

E l

B l

A puzzlement ..

enclosedid 0 sB

Let’s apply this to the gap of a capacitor.

Consider the poor little capacitor…

i i

CHARGING OR DISCHARGING …. HOW CAN CURRENTFLOW THROUGH THE GAP

In a FIELD description??

Through Which Surface Do we measure the current for Ampere’s Law?

I=0

In the gap… DISPLACEMENT CURRENT

dtd

dtdqI

ntDisplaceme

Idtdq

Letdtdq

dtd

qEA

Ed

d

E

E

0

0

0

2

Current

gap)(in

1

S through FLUX ELECTRIC The

0

0 . 0

0

? =Faraday's Law of Induction - Next Topic

( + )

inside

Einside path

qdA

dA

d

dd I

dt

E n

B •n

E l

B l

NEXT

Fix the Last Maxwell Equation

? =Faraday's Law of Induction - d E l

The Coil and the Magnet

Coil

Galvanometer

Magnetic Flux M

Integral over a SURFACE

What’s Happening Here??

A

Observation

Meter Deflects

There must be an emf around the loops!

VariablesDirectionPolarityPitchVelocity

Down the Hatch

Aluminum Pipe

Down the Hatch

B

Aluminum Pipe

N

S

Induced Current

NREPEL!!

There must bean Electric Fieldin the metal thatis pushing the current!!

You said that there is a conducting loop.You said that there is therefore a current induced around the loop if the flux through the loop changes.But the beginning and end point of the loop are the same so how can there be a voltage difference around the loop?Or a current???‘tis a puzzlement!

HEY BINDELL – WAIT A SECOND …….

REMEMBER when I said E Fields start and end on CHARGES???

DID I LIE??

Electric fields that are created by static charges must start on a (+) charge and end on a (–) charge as I said previously.Electric Fields created by changing magnetic fields (NON-Coulombic) can actually be shaped in loops.

The truth

BUT WAIT, YOU STILL LIE!

Why do you STILL think I am a liar?

Because you said that an emf is a voltage so if I put a voltmeter from one point on the loop around to the same point, I will get ZERO

volts, won’t I? How can there be a current??

Yes … butthis doesn’t make

me a liar!Let Me Explain.

Is the WORK that an external agent has to do to move a unit charge from one point to another.But we also have (neglecting the sign):

The POTENTIAL between two points

sEV

s

So, consider the following:

E

Conductor

x x x x x x xx x x x x x xx x x x x x xx x x x x x xx x x x x x xx x x x x x x

zeroREemf

sEsEemf

2

THEREFORE WHAT WILL A VOLTMETER READ FROM A to A?

E

Conductor

x x x x x x xx x x x x x xx x x x x x xx x x x x x xx x x x x x xx x x x x x x

A

A The emfB ZeroC Can’t tell

How Big is the emf?

temf loopthe

Through

Faraday’s Law

Michael Faraday (1791-1867)

MINUS????

Q: Which way does E point?A: The way that you don’t want it to point! (Lenz’s Law).

Lenz’s Law Explains the (-) sign!

Push a magnet into a coil of two wires and a current is produced via an emf.

In this case, 2 coils, each have the SAME emf so we add..Ohm’s Law still works, so

coilRemfi

tNemf

Faraday’s Experiments

??

Insert Magnet into Coil

Remove Coil from Field Region

That’s Strange …..

These two coils are perpendicular to each other

All Involve Changing The Magnetic

Flux through the Loops

Remember the Definition of TOTAL ELECTRIC FLUX through a CLOSED surface:

dA

is surface aLEAVING FieldElectric theofFlux Total

outE

surface EE d

nE

Magnetic FluxApplies to an OPEN SURFACE only.“Quantity” of magnetism that goes through a

surface.

AB dBsurface

In the figure below a 120-turn coil of radius 1.8 cm and resistance 6.8 W is coaxial with a solenoid with 209 turns/cm and diameter 3.2 cm. The solenoid current drops from 1.5 A to zero in time interval Δt = 25 ms. What current is induced in the coil during Δt?

0.0224 A

DONE