Key concept in Magnetic Flux

7/30/2019 Key concept in Magnetic Flux

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Electromagnetic Induction

Key Concept is Magnetic Flux


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Faradays Law

Key Concept is CHANGE in Magnetic Flux

A CHANGING

B through any closed loopinduces an EMF around the loop.

The induced EMF equals the negative of

the time rate of change of the total magnetic

flux through the loop

dt

d B =


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Faradays Law

It doesnt matter why the flux changes

dt

d B =

1) Constant B, Changing Area:

2) Constant Area, Changing B:

3) Constant Area, Constant B, Changing Cos :

==surface surface

B cosBdAAdB rr

where


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Direction of the Induced EMFs and Currents

In the previous problem, we found the directionof the induced current by noting that the forceresulting from the induced current had tooppose the applied force. This obbservation canbe generalized into:

Lenzs Law

The direction of any magnetic induction effect

is such as to oppose the cause of the effect


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The Alternator(see Y&F example 30-4)

The magnetic field ,and the angular frequency , are constant

tcosBAcosBAB ==

By Faradays Law:

r

tcosABdt

d B

==


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The Generator(see Y&F example 30-5)

The magnetic field ,and the angular frequency , are constant

tcosBAcosBAB ==

The split-ring commutator rectifies the EMF:

r

tcosABtcosAB ==


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Direction of the Induced EMFs and Currents

In the previous problem, we found the directionof the induced current by noting that the forceresulting from the induced current had tooppose the applied force. This obbservation canbe generalized into:

Lenzs Law

The direction of any magnetic induction effect

is such as to oppose the cause of the effect


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Induced Electric Fields

nIABA 0B ==

dt

dInA

dt

d0

B

==

This seems very mysterious because there isNO magnetic field outside the solenoid and

therefore there can be NO force on the chargesinside the conducting loop!

The EMF will induce a current that will be

indicated by the Galvanometer.


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Induced Electric Fields

Faradays Law hold even if there is

no Motion and no Magnetic Field

nIABA 0B ==

dt

dInA

dt

d0

B

==

Faradays Law implies that there is an

Induced Electric Field

= ldErr

=dt

dldE B

rr

This Induced Electric Field is a

non-electrostatic field that arises,

not from static charges, but from a

changing B field alone.


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Maxwells Equations

The equations below summarize all of the

underlying physics of Electricity and Magnetism

=0

enclosedQAdE

rr

= 0AdBrr

+= dt

dildB E0C0

rr

= dtd

ldE Brr

Gausss Law

Gausss Law for

magnetism

Amperes Law

Faradays Law

( )BvEqFr

v

vv

+= Lorentz Force Law

AND


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Maxwells Equations in Free Space

If there are no charges and no currents,

Maxwells Equations have a very simple andvery symmetric form:

= 0AdErr

= 0AdBrr

dt

dldB E00

=

rr

= dtd

ldE Brr

Note that a changing B will induce an E and

a changing E will induce a B. This B can in turn induce

an E, which will induce a B, and so on

It can be shown that these equations predict the

existence of a self-sustaining wave that propagates

with a velocity of:

00

1v=

Experimentally this velocity is found to be exactlyequal to the speed of light.

All visible light, as well as radio wave,

microwaves, x-rays, gamma rays, ultraviolet andinfrared radiation are all electromagnetic in origin!


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Inductance

Mutual

Inductance


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Inductance


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Inductance


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How Big is a Henry


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SELF-INDUCTANCE


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Circuit Elements

Key concept in Magnetic Flux

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