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Travelling Waves and Maxwell’s Equations


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Physics    Electromagnetism  Maxwell’s Equation and Waves

Travelling Waves and Maxwell’s Equations

 

                The Maxwell equations can be used to describe the travelling electromagnetic waves. The electric component of the traveling wave is given as:

  

Similarly, the magnetic component of the travelling wave is given as:

Here the velocity of electromagnetic wave is given as:

The above components are for plane polarized monochromatic waves. These are obtained as solutions from the wave equations for electromagnetic waves. The wave equations for electromagnetic waves can be obtained by using the Maxwell’s equations.

Energy Transport and Poynting vector:

 
                              

 

An electric plane wave as obtained previously can be written as:


where c = E0/B0. The electric energy density is given by and the magnetic energy density is same as that of the electric energy density. Thus, for light electric and magnetic energy densities are equal. Then the total energy density is given as:

The pointing vector is defined as:

The direction of the pointing vector is the direction of energy flow. The magnitude of the pointing vector is given as:

The magnitude of the pointing vector is also equals to the energy per unit time per unit area.

 

                 

Radiation Pressure:

Electromagnetic radiation pressure is proportional to the energy density. The radiation pressure exerted by an electromagnetic wave on the surface of a target is defined as the averaged intensity divided by the speed of light. The averaged intensity of radiation is given as:

Then the radiation pressure is given as:

                                                          
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