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Explain the nature of electromagnetic waves.

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It can be shown from Maxwell’s equations that electric and magnetic fields in an electromagnetic wave are perpendicular to each other, and to the direction of propagation as shown in figure.

In the above fig., a plane electromagnetic wave propagating along the z direction with time t. The electric field Ex is along the x-axis, and varies sinusoidally with z, at a given time. The magnetic field By is along the y-axis, and again varies sinusoidally with z. The electric and magnetic fields Ex and By are perpendicular to each other, and to the direction z of propagation. We can write Ex and By as follows: 

Ex = E0 sin (kz– ωt ) --------- (1) 

By = B0 sin (kz– ωt ) --------- (2) 

Here k is related to the wave length λ of the wave by the usual equation. k = 2π/λ and ω is the angular frequency. k is the magnitude of the wave vector (or propagation vector) k and its direction describes the direction of propagation of the wave. The speed of propagation of the wave is c = (ω /k ).

We can also prove that ω = ck, where, c = 1/ √µ0ɛ0 

This relation is often written in terms of frequency, ν (= ω/2π) and wavelength, λ (=2π/k) as 

It is also seen from Maxwell’s equations that the magnitude of the electric and the magnetic fields in an electromagnetic wave are related as B0 = (E0/c). 

In material medium, the description to electric and magnetic fields in Maxwell’s equations with the result that in a material medium of permittivity ε and magnetic permeability μ, the velocity of light becomes,

Thus, the velocity of light depends on electric and magnetic properties of the medium. 

As electromagnetic wave contains both electric and magnetic fields, there is a non-zero energy density associated with it. An electromagnetic wave (like other waves) carries energy and momentum. Since it carries momentum, an electromagnetic wave also exerts pressure, called radiation pressure. 

If the total energy transferred to a surface in time t is U, it can be shown that the magnitude of the total momentum delivered to this surface (for complete absorption) is, p = U/c. 

In 1903, the American scientists Nicols and Hull succeeded in measuring radiation pressure of visible light and verified eqn. p = U/c . It was found to be of the order of 7 × 10–6 N/m2. Thus, on a surface of area 10 cm2 , the force due to radiation is only about 7 × 10–9 N.

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