Electromagnetic Wave Vector

Electromagnetic waves are the waves which are self propagating in vacuum. The electromagnetic wave comprises of the electric and the magnetic field components which are perpendicular to each other and they are also perpendicular to the direction of the propagation of the waves through which the energy is propagated.

Classification of Electromagnetic Waves

Electromagnetic waves are classified according to their frequency and  wavelength like the radio waves , microwaves , infrared waves , visible waves, ultraviolet waves, x-rays and the gamma rays. These waves were first postulated by Maxwell and then subsequently confirmed by Hertz. According to Maxwell's equations the spatially varying electric fields can generate the time varying magnetic fields and vice versa. Thus we can say that an oscillating electric field generates an oscillating magnetic field which in turn generates the oscillating electric field and these oscillating fields are bound together to form an electromagnetic wave.

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Electromagnetic Wave Vector :

The Maxwell's equations in the free space is given as

The solution of the above waves is wave like and they are given as

In the above solutions the vector k is named as the electromagnetic wave vector and the property of the wave like the direction of propagation and the velocity of the waves is depends on the wave vector. The wave vector can be use for determine the phase velocity of the waves as

v = ω / k

The wave vector is also used to find the wavelength of the wave as

λ = 2π / k

Conclusion for Electromagnetic Wave vector

The wave vector also determines the values of the electric and magnetic field of the electromagnetic wave thus it is necessary to have an appropriate value of the wave vector. For a given value of the wave vector the electric field can take any direction and it is normal to the plane of the wave or wave vector as the wave vector is parallel to the direction of the wave.