el mag induction and maxwell theory

7/28/2019 El Mag Induction and Maxwell Theory

1/19

02.04.2013 asoc.prof.Blms 1

Electromagnetic induction

dt

d mi

dt

d mi

sVWb 11 cosBSm

The induced emf in a circuit is equal (except for a minus

sign) to the rate at which the flux through the circuit is

changing.


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2

Lenzs Law:

The induced current will appear in such a direction thatit opposes the change that produced it.

- defines the direction of the induced current.

The direction of the

induced current if

dB > 0

The direction of the

induced current if

dB < 0

S

B

S

B


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Self-induction

ILM

Linductivity of the coil

[1 H = 1 Wb/A]

dt

dLI

dt

dIL

S= - self-induction emf

IfL = const, than S= dt

dIL

I

An induced emf appears in a coil if the current in that same

coil is changed.


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Switch-in current L

RP

1

2 0

+

I0

I

t

12 > 1

L2 > L1

e

RI tL

R

1

R

L

- time constant.


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Switch-off current

eIIt

LR 0

I0

I

t

2>1

L2 > L1

1


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Mutual induction- induction of emf in a coil, if the

change of current in other coil

proceeds

I

N1

N2

1. 2.

12 2121 IMM

1212 IMM

MMM 2112 - coefficient ofmutual induction

21= dt

dIM 1 12= dt

dIM 2

Transformers:1

2

1

2

N

N

U

U

1

2

U

U The coefficient oftransformation


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7

Energy of the magnetic field

.2

2ILWm

A part of energy of current always is used for creation of

magnetic field, therefore,

The energy of magnetic field is equal to the work done by the

current during creation of magnetic field or to the flux of

magnetic field related to the current.

Work done for creation of magnetic flux is

.20

2

I

LILIdIA

The magnetic field energy, related to

the curcuit with the current:


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8

Maxwells equations forelectromagnetic field


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9

Maxwells theory is:

phenomenologic - the processes taking place in the media arenot examined, properties of the media are described by three

constants: dielectric constant , magnetic constant and

electric conductivity ;

macroscopicfield generated by atoms (and inside it) arenot examined, field are characterised bymean values for

relatively small volumes (but, nevertheless, many times

bigger than atoms);

fundamentalnot only known physical phenomena were

discribed, but also the existence of additional were forecasted:

electromagnetic waves, the nature of the light etc.


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The generalization of the Faraday EM

induction lawAccording to the Maxwells theory alternating electric field

creates alternating magnetic field and vice versa: alternating

magnetic field creates alternating electric field.

These secondary field have eddy flow

(vortex) characterlines of secondary

field are closed concentric lines withprimary lines in center.


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11

The generalization of the Faraday EM induction law

As a result, electric and magnetic field, initially related to the

electric charges and currents, becomes free and can propagate

in the space:


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12

Displacement current

According to te Maxwells hypothesis that conduction

currents, flowing in the conductors are continued between theplates of capacitor by other, special kind of the current

displacement current; it is directly proportional to the rate of

change of intensity of electric field and is equal to the

conduction current in outer circuit.

~

In the capacitor existing

magnetic field J.Maxwell

has explained by theexistence of such current.

B

E


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13


dt

Pd

dt

Edjnb

0

the density of the displacement current invacuum;

the density of polarisation current in

dielectrics.

Having filled the volume between electrodes of the capacitor

with dielectrical substance we can conclude that the change ofthe intensity of electric field is related with the orientation of

the dipoles (molecules or atoms). The shift of the charges,

taking place during this orientation creates additional

displacement currentpolarization current.The density of the total current will be:

dt

dP

dtdE0


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14


nbv jjj

- the density of the total currentin the circuit.

It means, every change of the electric field in time (also invacuum) is related with the arising of the magnetic field in

surrounding space.

The conduction and displacement current can exist simultaneously:


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1. Maxwells equation

S

N

k

k

K

dSndt

BdldE

1

Other definition of the equationspoint: in the space, where

magnetic field is changed, vortex (lines ofEare closed)

electric field appears.

is equal to

Induced in K emf

and the sum of other (nature) emfs.

The circulation of the intensity vector along the closed pathK


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dSntDjldH

SK

The circulation of the magnetic field

intensity along the closed path K

Other definition of the equationspoint: in the space,

where electric field is changed, vortex (lines ofHare

closed) magnetic field appears.

is equal to

The total current inside this path.


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17


The 3rd Maxwells equation is the Gauss law for magnetic

field:

.0 s

dSnB

Other definition of the equationspoint: in the nature doesnt

exist magnetic charges.


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18


. s

VQdSnD

4th Maxwells equation is the Gauss law for electric field:

Other definition of the equationspoint: in the nature exist

electrical charges (acting as sources of electric field).


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19

,0 ED

,0HB

.Ej

It makes sense to add equations showing the influence of the

ambient on electric and magnetic characterizing values:

el mag induction and maxwell theory

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