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**Electromagnetic Waves Facts**

We know that an electric charge at rest has electric field in the region around it, but no magnetic field. A moving charge produces both the electric and magnetic fields. If a charge is moving with a constant velocity if current is not changing with time), the electric and magnetic fields will not change with time hence no electromagnetic wave can be produce but if the charge is moving with a non- zero acceleration (charge is accelerated) both the magnetic field and electric field will change with space and item it then produces electromagnetic wave. The shows that an accelerated charge emits electromagnetic waves.

L-C circuit is an oscillatory circuit where the charge is oscillating across the capacitor plates. An oscillating charge in L – C circuit has a non- zero acceleration hence it emits electromagnetic waves which have the same frequency as that of the oscillating change.

In an atom an electron while orbiting around the nucleus in a stable orbit thought accelerating does not emit electromagnetic waves electromagnetic waves are emitted only when it falls from higher energy orbit to lower energy orbit.

Electromagnetic waves are also produced when fast moving electors are suddenly stopped by the metal target of high stoic number.

Important facts about the electromagnetic waves

The electromagnetic waves are produces by accelerated or oscillating charge.

These waves do not require any material medium for propagation.

These waves travel in free space with a speed 3 x 10 (seed of light) give by the relation **c = 1 √(μ _{0} ϵ_{0})**.

The sinusoidal variation in both electric and magnetic field vectors ( E and B) occurs simultaneously as a result they attain the maxima and minima at the same place and at the same time. The amplitudes of the electric and magnetic fields in free space are electric by **E _{0} / B_{0} = C**.

The directions of variation of electric and magnetic field vectors are perpendicular to each other as well as perpendicular to the direction of propagation of waves. Therefore electromagnetic waves are transverse in nature like light waves.

The velocity of electromagnetic waves depends entirely on the electric and magnetic properties of the medium in which these waves travel and is independent of the amplitude to the field vectors.

The velocity of electromagnetic wave in dielectric is less than **c = (3 X 10 ms ^{-1})**

The electromagnetic waves carry energy which is divided equally between electric field and magnetic field vectors.

In vacuum the average electric energy density (Ug) and average magnetic energy density **(uB)** due to static electric field E and magnetic field B which do not vary with time are given by

**uE = ½ ϵ _{0} E^{2} and uB = 1 / 2 B^{2} / μ**

_{0}

Due to both the fields, total average energy density is

**u = uE + uB = 1 / 2 ϵ _{0} E^{2} + 1 / 2 B^{2} / μ**

_{0}

in electromagnetic waves the electric and magnetic fields vary sinusoidal with space (x) and time (t). the above expressions will be valid for electromagnetic waves if E and B are replaced by their rms values therefore,

**uE = 1 / 2 ϵ _{0} E^{2} and uB = 1 / 2 B^{2} /μ**

here** uB = B ^{2} / 2 μ_{0} = o 1 / 2 μX E^{2} / c^{2} = μ_{0} ϵ_{0} / 2μ_{0} E^{2} = 1 / 2 ϵ_{0} E^{2}= uE**

**[ ∴ B = E /c and c = 1 / √(μ _{0} ϵ_{0}) ]**

**∴ **Total average energy density is** u = uE + uB = 2 uE = 2UB = 2 X ½ ϵ _{0} E^{2} = ϵ_{0} E^{2} = B^{2} / μ_{0} = ϵ_{0} E^{2}_{0} /2 = 1 / μ_{0}B /2**.

The electric vector is responsible for the optical effects of an wave and is called the light vector

The electromagnetic waves being uncharged are not deflected by electric and magnetic fields.

**Intensity of electromagnetic wave **

Intensity of electromagnetic wave is defined as the energy crossing per second per unit area perpendicular to the direction of propagating of electromagnetic wave.

Consider the propagation of electromagnetic wave with speed c along the X axis take and imaginary cylinder of area of cross section A and length C so that the wave crosses the area A normally let be the average energy density of electromagnetic wave

The energy of electromagnetic wave (U) crossing the area of cross section at P normally in time is the energy of wave contained in a cylinder of length c and area of cross- section A. it is given by** U = U (c ∆t) **

The intensity of electromagnetic wave at P is

**I = U / A ∆t = u c ∆t A / A ∆t = u c.**

In terms of maximum electric fields

**U = 1 / 2 ϵ _{0} E^{2}.**

So** I = 1 . 2 ϵ _{0 }E^{2} c = E_{0} E^{2} c**

In terms of maximum magnetic field

**U = 1 /2 B ^{2} / μ_{0} so I = 1 / 2 B^{2 }/ μ_{0} c = 1 / μ_{0} B^{2} c**

Momentum and radiation pressure of electromagnetic wave. The electromagnetic waves carry energy and momentum. If a portion of electromagnetic wave of energy U is propagating with speed then linear momentum of electromagnetic wave is given by

**P = U / C**

If the incident electromagnetic wave is completely absorbed by a surface it delivers energy U and momentum U/c to the surface if the electromagnetic waves is totally reflected then the momentum delivered to the surface is 2 U /c as te momentum of electromagnetic wave changes form p to p. this shown that the electromagnetic wave exerts a force on the surface an which it is incident.

This force exerted by electromagnetic wave on unit area of the surface is called radiation pressure. Pressure on the surface it fails. This electromagnetic wave exerts radiation pressures on the surface it falls.

**Radiation pressure = force / area = change in momentum/ time/ area = change in momentum are X time**

In 1903, the American scientist’s nicol and hull measured radiation pressure of visible light **7 X 10 ^{ -6} N/ m**

^{2}. It means the force due to radiation pressure of visible light on the surface of area

**10 cm**

^{2}is = (7 X**10**.

^{-6}) X (10 X 10^{ -4}) = 7 X 10^{ -9}N