Localized sources for electromagnetic waves

LOCALIZED SOURCES FOR ELECTROMAGNETIC WAVES

Any stationary charge produces only electric field. When the charge moves with uniform velocity, it produces steady current which gives rise to magnetic field (not time dependent, only space dependent) around the conductor in which charge flows.

If the charged particle accelerates, it produces magnetic field in addition to electric field.

Both electric and magnetic fields are time varying fields. Since the electromagnetic waves are transverse waves, the direction of propagation of electromagnetic waves is perpendicular to the planes containing electric and magnetic field vectors.

Any oscillatory motion is also an accelerated motion. So, when the charge oscillates (oscillating molecular dipole) about their mean position (Fig. 2.7), it produces electromagnetic waves

It the electromagnetic field in free space propagates along x-direction and if the electric field vector points along y-axis, then the magnetic field vector is mutually perpendicular to both electric field and the direction of wave propagation. Thus

where E0 and B0 are amplitudes of oscillating electric and magnetic field, k is a wave number denotes the direction of propagation of electromagnetic wave, w is the angular frequency of the wave.

Note both electric field and magnetic field oscillate with a frequency (frequency of electromagnetic wave) which is equal to the frequency of the source (here, oscillating charge is the source for the production of electromagnetic waves).

In free space or in vacuum, the ratio between E0 and B0 is equal to the speed of electromagnetic wave and is equal to speed of light c.

In any medium, the ratio of E0 and B0 is equal to the speed of electromagnetic wave in that medium. Thus

Further, the energy of electromagnetic waves comes from the energy of the oscillating charge.