Physics ELECTROMAGNETIC WAVES AND THEIR CHARACTERISTICS

Displacement Current and Maxwell's Equations

It is a current which produces in the region in which the electric field and hence the electric flux changes with time.

Displacement current, `I_D = epsilon_0*(dphi_E)/(dt)`

where, `phi_E` is the electric flux.

`text(Ampere-Maxwell Law :)`

`oint(B.dI)=mu_0(I+I_D)`

`text(Maxwell's Equations :)`

a. `oint(E*dA) =Q//ε_0` (Gauss's Law for electricity)

b. `ointB*dA =0` (Gauss's Law for magnetism)

c. `ointE*dI=(-dphi_B)/(dt)` (Faraday's Law)

d. `ointB*dI= mu_0i_c + mu_0epsilon_0 (dphi_E)/(dt)` (Ampere - Maxwell Law)


Electromagnetic Waves

Consider a charge oscillating with some frequency. (An oscillating charge is an example of accelerating charge.) This produces an oscillating electric field in space, which produces an oscillating magnetic field, which in turn, is a source of oscillating electric field, and so on.

The oscillating electric and magnetic fields thus regenerate each other, so to speak, as the wave propagates through the space. The frequency of the electromagnetic wave naturally equals the frequency of oscillation of the charge.

The energy associated with the propagating wave comes at the expense of the energy of the source - the accelerated charge.

Electromagnetic waves are those waves in which electric and magnetic field vectors changes sinusoidally and are perpendicular to each other as well as at right angles to the direction of propagation of wave.

`text(Properties of EM Waves :)`

(i) These waves are transverse in nature.

(ii) These waves propagate through space with speed of light.

(iii) The speed of electromagnetic waves, `c=1/sqrt(mu_0epsilon_0)`

`c=(E_0)/(B_0)` where `E_0` and `B_0` are maximum values of electric and magnetic field vectors.

According to Maxwell, when a charged particle is accelerated, it produces electromagnetic wave. The total radiant flux at any instant is given by,

`phi=(q^2a^2)/(6piepsilon_0c^2)`

(iv) The rate of flow of energy in an electromagnetic wave is described by the vector S called the poynting vector, which is ; defined by the expression,
`vecS=1/mu_o vecExxvecB`

(v) Its magnitude S is related to the rate at which energy is transported by a wave across a unit area at any instant.

(vi) The energy in electromagnetic waves is divided equally between electric field and magnetic field vectors.

(vii) The average electric energy density is -

`U_E=1/2 epsilon_0 E^2 = 1/4 epsilon_0 E_(max)^2`

(viii) The average magnetic energy density is -

`U_B=1/2\(B^2)/mu_0 = 1/4\ (B_(max)^2)/mu_0`

(ix) The electric vector is responsible for the optical effects of an electromagnetic wave.

(x) Intensity of electromagnetic wave is defined as energy crossing per unit area per unit time perpendicular to the directions of propagation of electromagnetic wave.

`I= 1/2 cepsilon_0E_(max)^2`

(xii) The existence of electromagnetic waves was confirmed by Hertz experimentally in 1888.



Radiation Pressure


 
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