In the free space , we have (or the atomsphericair) we have perm activity of the free - PowerPoint Presentation

Slide1

In the free space , we have (or the atomsphericair) we have perm activity of the free species suitability of the free is , volume charge density and density of the conduction current is there for , the differential forms of Max well's equations, areWhich are the different tail forms of Max well's equations in the free space By taking for both sides of eq. 3 , we obtainBy substituting from eqns 1 and 4 in eqn (5, 4 ) which is the wave equation for the electric field in the free space.

The electro magnetic waves in the free space

Slide2

By taking for both sides of eqn 4 we getBy substituting g from eqns 2 and 3 in eqn 6 we obtain : xwhich is the wave equation for the magnetic field in the free space . For simplicity , the electromagnetic yField sin one dimension in the carte Sian coordinal atiesare : B ( x , y , z , t ) = E ( z , t ) z ( x , y , z , t ) = B ( z , t ) There fore, the wave equation stake the forms : and

Which are the wave equations for the electric and the magnetic fields in one dimension

Slide3

The general form for the wave equation isBy comparing the general equation with the wave equations of the electric and the magnetic fields , we find that :

ɛ

̥

µ̥

C

The result indicates that there are electromagnetic waves move in the free space by the

speed light this in addition to the light consists of electromagnetic waves that is could explained these facts experiment enthalpy the solution of the wave equations is the

wave functions: and ByWhere and are the maximum values for the electric and the magnetic fields , K is

the wave number and W is angular frequency for the electric field we find that 2 ,

,

)

Slide4

By substituting in the wave equation where these equation in dictate that the wave function of satisfies the wave equation of

,

the previous method applied also to the magnetic filed

Equations the wave functions show propagation of the

electrom

a

gneti

cwaves

in the free space as in the figure.

Slide5

The relation between the electric , and the magnetic fields in the free spaceFaradays lawis -In cartesian coordinaties , we have :

Then

Slide6

In general , we get : therelation between B , h space

Slide7

The electromagnetic waves in isotro pic in sulating medium : Suppose that we have an isotropic insulating mediums has , , and there fore , the differential forms of Max well’s equation are: By taking for both sides of eq. 3 , weget.

By substituting from eqns

1

and

4

in eqn (5, 4 )

Slide8

It is know that whereWhich is the wave equation for the electric field in is tropic insulating medium.Similarly , be taking for both , sides of eqn . 4 , we get : By substituting from eqns 2 and 3 in eqn 6 We get :

It is known that

Which is the wave equation for the magnetic

field in an isotropic insulating medium

Slide9

It is known that , the general wave equation is By comparing the general wave equation with the wave equation of the electric and the magnetic fields , we get : , where , and is called C= The refractive in dex of the is otropic in sulfating medium.Which is the law of refraction of light

Slide10

Suppose that : and There for : and which are the wave equations in one dimension only .The solution of these equations are :

Slide11

The relation between the electric , and the magnetic fields in isotropic in sulating mediumfaraday’s law isIn one dimension , we have : andThen ampere’s law takes the form :Where

But

In general ,

Slide12

Energy of the electrom gnetic waves in the free spaceThe energy density perunit volume of the electric fieldsThe energy density per unit volume of the magnetic , fieldisThe total energy density inside the boxes shown in the figure is Where v is the volume of the box we know that and there fore

The average energy density per unit time with in the box

Where T is the periodic time.

Slide13

but There fore the average energy passing the unit area per the unit time in the direction of propagation of the wave is called pointing vector , as follows. pointing vectorIsotropic insulating medium .

Slide14

Isotropic insulating medium.In isotropic insulfating we have .There fore , the pouting vector for an electromagnetic wave propagates in an istropic in sulating medium

Slide15

Absorption of the electromagnetic waves in the conductors :The conductors (the metals)μ Have , andSubsequently , the max well’s equations for the conductors are By taking for both sides of eq. 3 , we get:From Eqn 1 and 4 in Eq. 5 , we obtain :

Slide16

Which is the wave equation for the electric field in the conductor materials similarly , by taking for both sides of eq. 4 we getFrom Eq. ns 2 and 3 in Eq. 6 , we obtain:(Which the wave equation for the magnatic field in the conductor materials (metalsFor simplicity , suppose that .

Slide17

AndThere for , the wave equations are :Which are the wave functions in one dimension. Supposethat the solution of the wave function of the wave furiction of the electric field is : where There for :

By substituting in the wave equation , we get

,

Suppose that

Slide18

Real :Imaginary :There for , the wave equation of the electric field takes the form :For most of the conductor materials, we have : then : the equation tends to : andSubsequently , the equation ginesus : , and the wave function in equation becomes : Similarly , the wave function of the magnetic field is :

Slide19

The wave function for the electric and the magnetic field in dicate that the field decreases exponentiallyWith the increase of z , as show in the figure The attend auction depth sis the distant trance at whichThe electric (or the magnetic) Field component approaches zero , where

Slide20

Speed of the electromagnetic waves in the conductor whenBut And Imaginary…. reel

Slide21

There forAnd the speed

Slide22

Spherical capacitor has capacitance and is connected to an ac source of correct of is passing through the . Capacitor .The electric field vector (component) of an electric tromagnatic wave propagates in the positive direction of is , where the physical quantities , are expressed in (cm , gm , s ) system. Find :a)The wave length of the wave b) Frequency of the wave c) Component of the magnetic field Sols a)

Slide23

A TV station Tran smelted its programs with frequency ofFind the wave lung the of the trans milted electromagnetic waves.