Electromagnetic waves

1) Equations of Maxwell :

2) Equations of the electromagnetic waves:

It is necessary porsi in the case of absence of charges and of currents localized, have the following relations :

is obtained calculating the rotor of and taking advantage of to the first member relation rot rot = - `² grad div while in 2° the member it becomes part .

3) Dalambertiano Operator:

4) Forehead of wave :

The wave forehead is the place of the points where the wave assumes the same value in a data moment.

5) Equation of a sinusoidale wave :

f(x, t) = Asen(kx - wt j ) inoltre (kx - wt j ) comes said phase of the wave.

6) Relation between temporal period and period spaces them :

The temporal period is T, the period spaces them is l, ha being itself v the speed with which the phase of the wave moves.

7) Carrier of wave k:

The direction of propagation of the wave is directed second, its module is called wave number and is worth .

8) Speed of propagation of a electromagnetic wave :

The speed of propagation of a electromagnetic wave in means is , in empty it is worth 3*10⁸ m/s.

9) Refractive index :

It is the relationship between the speed of the light in the empty c and the speed of the light in material means .

It is also legacy to the wavelength of the cancellation which assumes a various value in function of means, the relation is had.

10) Relations between B, E and the direction of propagation :

B and and is between orthogonal they and both are also orthogonal to the propagation direction, that is to the carrier k. In formulas is had that is obtained placing itself in the case of a linearly polarized flat wave.

11) characteristic Stiffness and value in the empty one :

The characteristic stiffness of means is given from the that in the case of empty vale the 377 Ohm.

12) relative Phase of B and and :

B and and always turns out to be in phase therefore laddove has a maximum for and, a maximum also for B is had.

13) Relationship between the density of energy of B and and :

The density of energy associated to the electric field u_and is equal to the density of energy associated to the magnetic field u_B as it is gained replacing nella finding

14) Standing wave :

A standing wave is produced when they come to interfere with 2 equal waves but with wave carriers antiparallels therefore as it happens when it records on a conductor. They are come therefore to create ventri and nodes that have a precise breakup space them, the fact wave is not a true one and own wave in how much at the same time does not turn out to be function of the time and the space. It can be obtained easily being and having to be and_{( )} = and_(-) in how much must be conserved the tangent member of the electric field and this in the conductor is worth 0 well-known. For H it is replaced in the la .

15) Breakup of the ventri and the nodes in a standing wave :

From the enough to find those values of z that they cancel sen(kz) or they place it par to 1, one finds that 1° the node is on the discontinuity surface and the others are distance you of l / 2.

16) Phase between and and H in a standing wave :

And and H is in quadrature that is sfasa you between of they of 90°.

17) spherical Wave :

A spherical wave is emitted from a point source and has equazione

18) Effect skin :

A electromagnetic wave that travels in a conductor, will be carried alone on the surface of the same one, will not travel to its inside, the effect is strengthened to growing of the frequency and this evidently determines an increase of the resistance of the same conductor.

19) Infrared, ultraviolet, beams x and beams g :

The infrared has frequencies little more lowlands of visible, the draft of cancellations emitted from the warm bodies. The ultraviolet ones have frequencies little higher of the visible one and are emitted from the sun or in gases subordinates to scariche electrical workers. I beams x come generate to you from accelerated particles that they go to hit against an obstacle and finally are the beams g generate to you from nuclear decays radioatti to you.

20) Carrier of Poynting and its physical interpretation:

The carrier of Poynting is and indicates the direction in which propaga the wave, its module is equal to the instantaneous intensity of the wave. It is useful to describe the fact that the variation of energy of a present electromagnetic wave to the inside of a surface S sluice is equal to the energy transferred to the free charges of the matter more the energy that crosses the surface.

21) instantaneous Intensity :

It is the module of the wave carrier and indicates how much cancellation invests the unitary surface arranged orthogonally to the speed of propagation in the time unit, it is worth therefore .

22) medium Intensity of the wave :

23) medium Intensity of a spherical wave :

It clearly diminishes to growing of the beam therefore will have itself

24) Pressure of cancellation :

Surface to normal and perfectly absorbent it is the pressure exercised from the wave incident on one.

25) Pressure of recoil:

It is the pressure to which the source of the wave is subject.

26) It upgrades them carrier:

27) It upgrades to climb them :

It upgrades them to scale V is such that as she is obtained replacing in the .

28) electrodynamic Equations :

The B carriers are obtained replacing in the e and and therefore as they are obtained from the definition of upgrades them to climb and carrier e . Draft of equations not disaccoppiate that they can it are rendered by means of an opportune transformation of Gauge which that tax from the condition of Lorentz such.

29) Transformations of Gauge :

Where j it is a derivabile function at least 2 times in x, y, z, t said function of Gauge.

30) Condition of Lorentz :

If the function of Gauge j satisfies this condition, the electrodynamic equations can be disaccoppiate.

31) disaccoppiate electrodynamic Equations and they dalambertiana shape:

32) Relation between the equations of upgrades them dynamic and the equations of upgrade them stationary :

They are equal only that for it upgrades them dynamic uses the dalambertiano operator while for upgrades them stationary uses the laplaciano.

33) It upgrades delays them to you :

They are the solutions of the electrodynamic equations in the source case localized in an ended region, they are said delays to you because To and V in one point in a data moment they are function of sources to the previous moment in which it has been emitted the cancellation and therefore.

34) near Field :

Is field localized around to sources and that it varies in the time because varies in the time the source, to it that is is not only associated no transport of energy.

35) Doppler Effect :

The Doppler effect is the phenomenon for which it marks them to one given frequency emitted from a source in motion, comes received from one firm station to one various frequency from that one of emission.