# Generation of electromagnetic waves

With the help of Maxwell's equation, explain how he predicted the existence of electromagnetic waves.

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1.What is a mechanical wave? What are its characteristics?

A mechanical wave involves transfer of mechanical energy (potential and/or kinetic) in a direction (direction of propagation of the wave) without actual transfer of the molecules of the medium. The molecules of the medium oscillate about a mean position but do not move in the direction of propagation of the wave. Examples of mechanical wave are: waves generated in a placid pond when a stone is dropped at any point, sound waves. Essential characteristics of a mechanical wave are:

â€¢Molecules of the medium oscillate about a mean position. In case of water waves, the water molecules oscillate up-down about their equilibrium position.

â€¢Energy transfer takes place continuously either perpendicular to the direction of oscillation of the molecules (transverse waves) or parallel to the direction of oscillations (longitudinal waves).

â€¢Molecules of the medium do not move in the direction of propagation of the wave

2.What is an electromagnetic wave?

Main difference between a mechanical wave and an electromagnetic wave (EM wave) is that a mechanical wave needs a medium for propagation (water, air, wood etc.) whereas an EM wave does not need any medium. In an EM wave there are no molecules to oscillate; it is the electric field vector (E) and magnetic field vector (B) which oscillate in space, perpendicular to each other. The direction of propagation of the wave (electromagnetic energy) is perpendicular to the plane in which the E and B vectors lie. Hence, an EM wave is transverse in nature.

3. Who first predicted the possibility of electromagnetic waves?

In 1865 James Clerk Maxwell predicted the existence of EM waves based upon the earlier works of Coulomb, Gauss and Faraday and his own modifications to the same. He did this in the form of four equations which are discussed hereunder.

4. Recapitulate the equations which form the basis for Maxwell's equations?

The set of equations known as Maxwell's equations were not really developed by Maxwell. These well known equations were in fact written by other scientists before Maxwell viz. Gauss, Ampere and Faraday. What Maxwell did really was: first he pointed out certain discrepancies in the Ampere's law and proposed modifications to overcome the same. Secondly he integrated these in a set of symmetrical, consistent and coherent set of equations. The inevitable consequence of the same was the prediction of possibility of electromagnetic waves traveling at the speed of light. Thus while each one of these equations individually is named after its author, collectively (with the modifications), these are known as Maxwell's equations.

Equations which eventually formed the basis of Maxwell equations are discussed here under:

Gauss' equation of electrostatics: As per Gauss theorem, net electric flux passing through a closed surface is equal to the net charge enclosed in the closed surface divided by Îµ0. This is written as :

âˆ«E.dS = Q/Îµ0 ...(1) where E is the electric field intensity vector at the surface which is integrated over the closed surface S, only the component of E vertical to the surface at any point contributing to the integration (dot product). Q is the net charge enclosed within the surface.

Gauss' equation of magnetism: Gauss' equation of electrostatics as applied to magnets can be written as:

âˆ«B.dS = 0 ...(2) where B is the magnetic flux density vector at the surface which is integrated over the closed surface. Zero at the right hand side being the outcome of non-existence of magnetic monopoles (in any closed surface there has to be as much north pole as the south pole, the net effect being zero).

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